find the parametric equation for the part of sphere x^2 + y^2 + z^2 = 4 that lies above the cone z = √(x^2 + y^2)

Answers

Answer 1

The parametric equation for the part of the sphere x^2 + y^2 + z^2 = 4 that lies above the cone z = √(x^2 + y^2) can be expressed as follows:

x = 2cos(u)sin(v)

y = 2sin(u)sin(v)

z = 2cos(v)

Here, u represents the azimuthal angle and v represents the polar angle. The azimuthal angle u ranges from 0 to 2π, covering a complete circle around the z-axis. The polar angle v ranges from 0 to π/4, limiting the portion of the sphere above the cone.

To obtain the parametric equations, we use the spherical coordinate system, which provides a convenient way to represent points on a sphere. By substituting the expressions for x, y, and z into the equations of the sphere and cone, we can verify that they satisfy both equations and represent the desired portion of the sphere.

To know more about sphere click here: brainly.com/question/22849345

#SPJ11


Related Questions

how many integer solutions are there to 2x1 2x2 2x3 x4 x5 = 9 with xi ≥ 0?

Answers

To find the number of integer solutions to the equation 2x1 + 2x2 + 2x3 + x4 + x5 = 9 with xi ≥ 0, we can use a technique called "stars and bars" or "balls and urns."

In this technique, we imagine distributing 9 identical balls (representing the total value of 9) into 5 distinct urns (representing the variables x1, x2, x3, x4, and x5). We can visualize this by placing dividers (represented by bars) between the balls to separate them into groups.

For this problem, we have 9 balls and 4 dividers (bars) since there are 5 variables (x1, x2, x3, x4, x5). So, we need to arrange these 9 balls and 4 dividers.

The total number of arrangements is given by (9 + 4) choose 4, or (9 + 4)! / (4! * 9!).

Calculating this, we get:

(9 + 4)! / (4! * 9!) = 13! / (4! * 9!)

= (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)

= 13 * 11 * 5

= 715

Therefore, there are 715 integer solutions to the equation 2x1 + 2x2 + 2x3 + x4 + x5 = 9 with xi ≥ 0.

To know more about Equation visit-

brainly.com/question/14686792

#SPJ11

determine the slope of the tangent line to the curve x(t)=2t3−1t2 6t 4y(t)=9e6t−6 at the point where t=1.

Answers

The slope of the tangent line to the curve at the point where t = 1 is 9.

To determine the slope of the tangent line to the curve defined by the parametric equations x(t) = 2t^3 - t^2 + 6t and y(t) = 9e^(6t - 6) at the point where t = 1, we can use the concept of differentiation.

First, let's find the derivative of x(t) and y(t) with respect to t:

dx(t)/dt = d/dt (2t^3 - t^2 + 6t)

= 6t^2 - 2t + 6

dy(t)/dt = d/dt (9e^(6t - 6))

= 54e^(6t - 6)

Next, we need to evaluate these derivatives at t = 1:

dx(1)/dt = 6(1)^2 - 2(1) + 6

= 6

dy(1)/dt = 54e^(6(1) - 6)

= 54e^0

= 54

Now, we have the slope of the tangent line at t = 1, which is given by dy(1)/dx(1). So, let's calculate that:

dy(1)/dx(1) = dy(1)/dt / dx(1)/dt

= 54 / 6

= 9

Therefore, the slope of the tangent line to the curve at the point where t = 1 is 9.

It's important to note that the slope represents the rate of change of y with respect to x at that specific point on the curve.

For more questions on curve

https://brainly.com/question/30452445

find the values of x for which the series converges. (enter your answer using interval notation.) [infinity] (−2)nxn n = 1 find the sum of the series for those values of x.

Answers

The series converges for -1/2 < x < 1/2. The sum of the series for those values of x is S = (-2x) / (1 + 2x).

To determine the values of x for which the series converges, we need to consider the convergence of the geometric series. A geometric series converges when the absolute value of the common ratio is less than 1.

In this case, the series is given by:

[tex]∑ (-2)^n * x^n[/tex], where n = 1 to infinity.

To find the convergence values, we need to consider the common ratio, which is (-2x). We want the absolute value of (-2x) to be less than 1:

|-2x| < 1

Simplifying this inequality, we have:

2|x| < 1

Dividing by 2, we get:

|x| < 1/2

So, the values of x for which the series converges are -1/2 < x < 1/2.

To find the sum of the series for those values of x, we can use the formula for the sum of a convergent geometric series:

S = a / (1 - r),

where a is the first term and r is the common ratio.

In this case, the first term a is given by [tex]a = (-2x)^1[/tex]

= -2x.

The common ratio r is (-2x).

Therefore, the sum of the series for the values of x in the interval (-1/2, 1/2) can be found as:

S = (-2x) / (1 - (-2x)) = (-2x) / (1 + 2x).

To know more about series,

https://brainly.com/question/31472371

#SPJ11

The sum of the series for the values of x in the interval (-1/2, 1/2) is (-2x) / (1 + 2x).

To determine the values of x for which the series converges and find the sum of the series for those values, we need to analyze the given series:

∑ [infinity] (-2)^n * x^n, n = 1

This is a geometric series with the common ratio being -2x. For a geometric series to converge, the absolute value of the common ratio must be less than 1. In this case, we have:

| -2x | < 1

Let's solve the inequality to find the values of x:

|-2x| < 1

Since the absolute value of a number is always non-negative, we can remove the absolute value signs and split the inequality into two cases:

-2x < 1 and -2x > -1

Case 1: -2x < 1

Divide both sides by -2 (and reverse the inequality since we are dividing by a negative number):

x > -1/2

Case 2: -2x > -1

Divide both sides by -2 (and reverse the inequality):

x < 1/2

Therefore, the values of x for which the series converges are -1/2 < x < 1/2, or in interval notation:

(-1/2, 1/2)

To find the sum of the series for those values of x, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Where "a" is the first term of the series and "r" is the common ratio. In this case, the first term "a" is (-2) * x and the common ratio "r" is -2x. Thus, the sum of the series is:

S = (-2x) / (1 - (-2x))

Simplifying further:

S = (-2x) / (1 + 2x)

Therefore, the sum of the series for the values of x in the interval (-1/2, 1/2) is (-2x) / (1 + 2x).

To know more about series visit,

brainly.com/question/31472371

#SPJ11

A stone is thrown upward from ground level. The initial speed is 176 feet per second. How high will it go?
a. 484 feet
b) 510 feet
c. 500 feet
d., 492 feet
e/. 476 feet

Answers

The correct option is D. The stone will go 492 feet high.

The maximum height (h) that a stone thrown upward from ground level would go with an initial velocity (u) of 176 feet per second can be determined using the formula for projectile motion.

The formula for projectile motion

h = u²/2g

Where u is the initial velocity and g is the acceleration due to gravity, which is 32 feet per second squared.

Substituting the values

h = (176)²/(2 × 32) = 492 feet

Therefore, the stone will go 492 feet high. Hence, option D is correct.

To know more about high visit:

https://brainly.com/question/32218693

#SPJ11

If the 5th term of a geometric progression (GP) is 6.25 and the 7th term is 1.5625, determine the 1st term, and the common ratio. Select one: O a. a₁ = 10, r=0.5 O b. a₁ = -100, r = 0.5 Oca₁ = 100, r = ±0.5 O d. a₁ = 100, r = ±0.25

Answers

Answer:

[tex]\mathrm{a=10,\ r=0.5}[/tex]

Step-by-step explanation:

[tex]\mathrm{The\ nth\ term\ of\ any\ geometric\ sequence\ is\ given\ by:}\\\mathrm{t_n=ar^{n-1}}\\\mathrm{Given,}\\\mathrm{5th\ term(t_5)=6.25}\\\mathrm{or,\ ar^{5-1}=6.25}\\\mathrm{or,\ ar^4=6.25......(1)}\\\\\mathrm{And,\ 7th\ term(t_7)=1.5625}\\\mathrm{or,\ ar^{7-1}=1.5625}\\\mathrm{or,\ ar^6=1.5625.........(2)}[/tex]

[tex]\mathrm{Dividing\ equation(2)\ by\ (1),}\\\mathrm{\frac{ar^6}{ar^4}=\frac{1.5625}{6.25}}\\\\\mathrm{or,\ r^2=\frac{1}{4}}\\\\\mathrm{or,\ r=\frac{1}{2}}[/tex]

[tex]\mathrm{From\ equation(1)\ we\ have}\\\mathrm{ar^4=6.25}\\\mathrm{or,\ a(0.5)^4=6.25}\\\mathrm{or,\ a=100}[/tex]

Alternative method:

[tex]\mathrm{Here,\ the\ sixth\ term\ of\ the\ sequence\ is\ geometric\ mean\ of\ the\ 5th\ and\ 7th}\\\mathrm{term.}\\\mathrm{So,\ we\ may\ say:}\\\mathrm{t_6=\sqrt{t_5\times t_7}}=\sqrt{6.25\times 1.5625}=3.125\\\mathrm{Now,\ common\ ratio(r)=\frac{t_6}{t_5}=\frac{3.125}{6.25}=\frac{1}{2}=0.5}\\\mathrm{We\ know,\ t_6=3.125}\\\mathrm{or,\ ar^5=3.125}\\\mathrm{or,\ a(0.5)^5=3.125}\\\mathrm{or,\ a=100}[/tex]

The first term and common ratio of the geometric progression (GP) can be determined based on given information. First term (a₁) is 100, and the common ratio (r) is ±0.5, leading to correct answer c. a₁ = 100, r = ±0.5.

By analyzing the values of the 5th and 7th terms, we can find the relationship between them and solve for the unknowns. The correct answer is c. a₁ = 100, r = ±0.5. In a geometric progression, each term is obtained by multiplying the previous term by a constant ratio. Let's denote the first term as a₁ and the common ratio as r. Based on the given information, the 5th term is 6.25 and the 7th term is 1.5625.

Using the formula for the nth term of a geometric progression, we can express these terms in terms of a₁ and r:

a₅ = a₁ * r⁴ = 6.25

a₇ = a₁ * r⁶ = 1.5625

To solve for a₁ and r, we can divide the equations:

(a₇ / a₅) = (a₁ * r⁶) / (a₁ * r⁴)

1.5625 / 6.25 = r²

0.25 = r²

Taking the square root of both sides, we have:

r = ±0.5 Substituting the value of r back into one of the equations, we can solve for a₁:

6.25 = a₁ * (0.5)⁴

6.25 = a₁ * 0.0625

a₁ = 6.25 / 0.0625

a₁ = 100

Therefore, the first term (a₁) is 100, and the common ratio (r) is ±0.5, leading to the correct answer c. a₁ = 100, r = ±0.5.

To learn more about geometric progression click here : brainly.com/question/30447051

#SPJ11

find two power series solutions of the given differential equation about the ordinary point x=0: y′′ x2y′ xy=0.

Answers

The two power series solutions of the given differential equation about the ordinary point x=0 are [tex]y1(x) = ∑_(n=0)^∞▒〖(-1)^n x^(2n) 〗 and y2(x) = ∑_(n=0)^∞▒〖(-1)^n x^(2n+1) 〗.[/tex]

The given differential equation is [tex]y′′ x²y′ xy = 0[/tex].

We must find two power series solutions of the given differential equation about the ordinary point x=0.

The power series solution of the differential equation is given by

[tex]y (x) = ∑_(n=0)^∞▒〖a_n x^n 〗[/tex]

Differentiating the equation w.r.t. x, we get

[tex]y′(x) = ∑_(n=1)^∞▒〖a_n n x^(n-1) 〗[/tex]

Differentiating again w.r.t. x, we get

[tex]y′′(x) = ∑_(n=2)^∞▒〖a_n n (n-1) x^(n-2) 〗[/tex]

Substitute the above expressions of y(x), y′(x), and y′′(x) in the differential equation:

[tex]y′′ x²y′ xy = ∑_(n=2)^∞▒〖a_n n (n-1) x^(n-2) 〗x^2[∑_(n=1)^∞▒〖a_n n x^(n-1) 〗]x[∑_(n=0)^∞▒〖a_n x^n 〗] = 0[/tex]

We can simplify the above expression to get:

[tex]∑_(n=2)^∞▒〖a_n n (n-1) a_(n-1) x^(n-1) 〗+ ∑_(n=1)^∞▒〖a_n x^n+1[/tex]

[tex]∑_(n=0)^∞▒〖a_n x^n 〗〗 = 0n = 0: a_0 x^2 a_0 = 0a_0 = 0n = 1: a_1[/tex]

[tex]x^2 a_0 + a_1 x^2 a_1 x = 0a_1 = 0 or a_1 = -1n ≥ 2: a_n x^2 a_(n-1) n(n-1) + a_(n-2) x^2 a_n = 0a_n = (-1)^n x^2 (a_(n-2))/n(n-1)[/tex]

Therefore, the two power series solutions of the given differential equation about the ordinary point x=0 are:

y1(x) = a_0 + a_1 x + (-1)^2 x^2(a_0)/2! + (-1)^3 x^3(a_1)/3! + ……= ∑_(n=0)^∞▒〖(-1)^n x^(2n) 〗y2(x) = a_0 + a_1 x + (-1)^3 x^3(a_0)/2! + (-1)^4 x^4(a_1)/4! + ……= ∑_(n=0)^∞▒〖(-1)^n x^(2n+1) 〗

The two power series solutions of the given differential equation about the ordinary point x=0 are

[tex]y1(x) = ∑_(n=0)^∞▒〖(-1)^n x^(2n) 〗 and y2(x) = ∑_(n=0)^∞▒〖(-1)^n x^(2n+1) 〗.[/tex]

Know more about power series here:

https://brainly.com/question/28158010

#SPJ11

find the unique solution to the differential equation that satisfies the stated = y2x3 with y(1) = 13

Answers

Thus, the unique solution to the given differential equation with the initial condition y(1) = 13 is [tex]y = 1 / (- (1/4) * x^4 + 17/52).[/tex]

To solve the given differential equation, we'll use the method of separation of variables.

First, we rewrite the equation in the form[tex]dy/dx = y^2 * x^3[/tex]

Separating the variables, we get:

[tex]dy/y^2 = x^3 * dx[/tex]

Next, we integrate both sides of the equation:

[tex]∫(dy/y^2) = ∫(x^3 * dx)[/tex]

To integrate [tex]dy/y^2[/tex], we can use the power rule for integration, resulting in -1/y.

Similarly, integrating [tex]x^3[/tex] dx gives us [tex](1/4) * x^4.[/tex]

Thus, our equation becomes:

[tex]-1/y = (1/4) * x^4 + C[/tex]

where C is the constant of integration.

Given the initial condition y(1) = 13, we can substitute x = 1 and y = 13 into the equation to solve for C:

[tex]-1/13 = (1/4) * 1^4 + C[/tex]

Simplifying further:

-1/13 = 1/4 + C

To find C, we rearrange the equation:

C = -1/13 - 1/4

Combining the fractions:

C = (-4 - 13) / (13 * 4)

C = -17 / 52

Now, we can rewrite our equation with the unique solution:

[tex]-1/y = (1/4) * x^4 - 17/52[/tex]

Multiplying both sides by -1, we get:

[tex]1/y = - (1/4) * x^4 + 17/52[/tex]

Finally, we can invert both sides to solve for y:

[tex]y = 1 / (- (1/4) * x^4 + 17/52)[/tex]

To know more about differential equation,

https://brainly.com/question/29112593

#SPJ11

1-- Voters in a particular city who identify themselves with one or
the other of two political parties were randomly selected and asked
if they favor a proposal to allow citizens with proper license

Answers

The aim of the study is to determine whether the majority of voters in the city supports a proposal to allow licensed citizens to carry weapons in public areas.

In order to do so, voters who identified themselves with one or the other of two political parties were randomly selected, and they were asked if they favor the proposal.It is essential to ensure that the sample size is adequate, and the sample is representative of the entire population. The sample size should be large enough to reduce the chances of errors and to increase the accuracy of the results. The sample must be representative of the entire population so that the results can be generalized. This ensures that the sample accurately reflects the opinions of the entire population.

There are several potential biases to consider when conducting this study.

For example, people who do not identify with either of the two political parties may have different views on the proposal, and the study would not capture their opinions.

To know more about licensed citizens visit:

https://brainly.com/question/28318562

#SPJ11

2 Which statistical tool defines the prediction for the dependent variable? (1 Point) Correlation O Regression O t-test Confidence Interval

Answers

The statistical tool that defines the prediction for the dependent variable is regression. Regression analysis is a statistical tool that defines the prediction for the dependent variable.

Regression analysis is used to examine the relationship between one dependent variable (usually denoted as Y) and one or more independent variables (usually denoted as X). It involves the calculation of the equation that best describes the relationship between these variables.

The equation is then used to make predictions about the dependent variable. Regression analysis is widely used in business, economics, and social science research to identify the factors that affect the outcome of a particular phenomenon.

For instance, a business can use regression analysis to determine how various factors such as advertising, price, and location affect the sales of a product. The results of the analysis can then be used to develop a marketing strategy that will increase the sales of the product. In conclusion, regression analysis is an important statistical tool that defines the prediction for the dependent variable.

To know more about statistical tool, refer

https://brainly.com/question/31380359

#SPJ11

which event most contributed to the changing troop levels shown in this graph? The Twenty-Sixth Amendment lowered the draft age to 18 from 21.
U.S. and North Vietnamese ships exchanged fire in the Gulf of Tonkin.
Congress expanded presidential powers to wage war under the War Powers Act.
Communist troops launched a series of attacks during the Tet Offensive.

Answers

The event that most contributed to the changing troop levels shown in the graph is when Communist troops launched a series of attacks during the Tet Offensive.

The Communist troops launched a series of attacks during the Tet Offensive to try to undermine American and South Vietnamese morale, cause a general uprising and seize control of the cities in South Vietnam.

However, this didn't go as planned, since the Communist troops suffered devastating losses on the battlefield.

The Tet Offensive, which was one of the most important turning points in the Vietnam War, led to changes in troop levels that are shown on the graph.

The Tet Offensive significantly increased troop levels because American forces had to respond with more soldiers and resources to defend against the attacks.

To know more about Tet Offensive visit:

https://brainly.in/question/16972839

#SPJ11

The event which most contributed to the changing troop levels shown in the graph was the Communist troops launching a series of attacks during the Tet Offensive.

The Tet Offensive was a series of attacks on the cities and towns of South Vietnam by the People's Army of Vietnam (PAVN) (also known as the North Vietnamese Army or NVA) and the National Liberation Front of South Vietnam (NLF), commonly known as the Viet Cong.

The Tet Offensive began in the early hours of 30th January 1968, during the Vietnam War. This event had a significant impact on public opinion and led to the escalation of the war.The graph in question, which depicts the troop levels, demonstrates that there was a considerable rise in US troop numbers during the years leading up to the Tet Offensive.

Following this event, troop numbers rose even higher before declining in the years that followed.

Therefore, the Communist troops launching a series of attacks during the Tet Offensive contributed most to the changing troop levels shown in the graph.

To know more about Tet Offensive, visit:

https://brainly.com/question/1114419

#SPJ11

Find the exact value of each expression, if it is defined. Express your answer in radians. (If an answer is undefined, enter UNDEFINED.)
(a) sin (3)
(b) cos-4 - )
(C) tan (- 15).

Answers

a) The exact value of sin 3 in radians is 0.05233.

b) The exact value of cos-4 cannot be found.

c) The exact value of tan (-15) in radians is -sqrt(6) + sqrt(2).

(a) sin (3) :

Exact value of sin 3 in radians: We know that sin 3 is a value of a trigonometric function. We can find the exact value of sin 3 with the help of a trigonometric circle.

To calculate sin 3, we will divide the length of the opposite side of the triangle by the length of the hypotenuse. sin (3) = Opposite side / Hypotenuse = 0.05233

(b) cos-4

The value of cos-4 cannot be calculated without context. If -4 is the power of cosine function, then it can be calculated, and if -4 is the inverse of cosine function, then we need to be given an angle.

Hence, the exact value of cos-4 cannot be found with the given information.

(C) tan (- 15):

We know that: tan (- 15) = -tan 15

We can calculate tan 15 as we know that sin 15 = (sqrt(6) - sqrt(2))/4 and cos 15 = (sqrt(6) + sqrt(2))/4.

Then, tan 15 = sin 15/cos 15

Therefore, tan (- 15) = -tan 15 = -(sin 15/cos 15)

= -(sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))

= -sqrt(6) + sqrt(2)

Know more about the trigonometric circle.

https://brainly.com/question/29268357

#SPJ11

Shadow A person casts the shadow shown. What is the approximate height of the person?

Answers

Answer:

height of person ≈ 6 ft

Step-by-step explanation:

using the tangent ratio in the right triangle.

let the height of the person be h , then

tan16° = [tex]\frac{h}{21}[/tex] ( multiply both sides by 21 )

21 × tan16° = h , then

h ≈ 6 ft ( to the nearest whole number )

While performing a certain task under simulated weightlessness, the pulse rate of 12 astronauts increase on the average by 27.33 per minute with a standard deviation of 4.28 beats per minute. Construct a 99% confidence interval for o2, the true variance the increase in the pulse rate of astronauts performing a given task (under stated conditions). a. [7.53, 77.41] b. [8.53, 78.41] c. [9.53, 79.41] d. [10.53, 80.41] e. [11.53.81.411

Answers

The correct option is (a) [7.53, 77.41].

To construct a 99% confidence interval for the true variance (σ²) of the increase in pulse rate of astronauts performing a given task, we can use the Chi-Square distribution.

The formula for the confidence interval for the variance is:

[ (n-1) * s² / χ²_upper , (n-1) * s² / χ²_lower ]

Where:

n is the sample size

s² is the sample variance

χ²_upper and χ²_lower are the upper and lower critical values from the Chi-Square distribution, respectively, based on the desired confidence level and degrees of freedom (n-1).

In this case, we have:

n = 12 (number of astronauts)

s² = (standard deviation)² = 4.28² = 18.2984

degrees of freedom = n - 1 = 12 - 1 = 11

critical values from the Chi-Square distribution for a 99% confidence level are χ²_upper = 26.759 and χ²_lower = 2.179

Now we can substitute these values into the formula to calculate the confidence interval:

[ (11 * 18.2984) / 26.759 , (11 * 18.2984) / 2.179 ]

Simplifying:

[ 7.531 , 77.414 ]

Therefore, the 99% confidence interval for the true variance (σ²) of the increase in the pulse rate of astronauts performing the given task is approximately [7.53, 77.41].

The correct option is (a) [7.53, 77.41].

For more questions on option

https://brainly.com/question/30643700

#SPJ8

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x/ x + 6 , [1, 12]]

Answers

The function f(x) = x/(x + 6) does satisfy the hypothesis of the Mean Value Theorem on the given interval [1, 12].

To determine if the function satisfies the hypothesis of the Mean Value Theorem, we need to check two conditions: continuity and differentiability on the interval [1, 12].

Continuity: The function f(x) = x/(x + 6) is continuous on the interval [1, 12] because it is a rational function and the denominator (x + 6) is nonzero for all x in the interval.

Differentiability: The function f(x) = x/(x + 6) is differentiable on the interval (1, 12) since it is a quotient of two differentiable functions.

The derivative of f(x) can be calculated using the quotient rule, which yields f'(x) = 6/(x + 6)². The derivative is defined and nonzero for all x in the interval (1, 12).

Since the function is continuous on [1, 12] and differentiable on (1, 12), it satisfies the hypothesis of the Mean Value Theorem on the given interval.

To learn more about Mean Value Theorem visit:

brainly.com/question/32214297

#SPJ11

The joint density function of X and Y is given by f(x, y) = xe¯²(y+¹) for x > 0, y > 0. (a) Find the conditional density of X, given Y = y, and that of Y, given X = x. (b) Find the density function

Answers

a. the conditional density of X given Y = y is 0, which means that X and Y are independent.

b.  the density function of Z = X + Y is:

f(Z) = d/dZ [f(V)]

= d/dZ [(1/2)e^(-2)V^2]

= (1/2)e^(-2)(Z^2)

(a)

To find the conditional density of X given Y = y, we use the formula:

f(X | Y = y) = f(X, Y)/f(Y)

where f(Y) is the marginal density function of Y.

First, we find the marginal density function of Y:

f(Y) = ∫ f(X, Y) dx (from x=0 to infinity)

= ∫ xe^(-2)(y+1) dx (from x=0 to infinity)

= e^(-2)(y+1) ∫ x dx (from x=0 to infinity)

= e^(-2)(y+1) [x^2/2] (from x=0 to infinity)

= infinity (since the integral diverges)

Since the integral diverges, we know that f(Y) cannot be a valid probability density function. However, we can still proceed to find the conditional density of X given Y = y:

f(X | Y = y) = f(X, Y)/f(Y)

= xe^(-2)(y+1) / infinity

= 0

So the conditional density of X given Y = y is 0, which means that X and Y are independent.

Similarly, to find the conditional density of Y given X = x, we use the formula:

f(Y | X = x) = f(X, Y)/f(X)

where f(X) is the marginal density function of X.

First, we find the marginal density function of X:

f(X) = ∫ f(X, Y) dy (from y=0 to infinity)

= ∫ xe^(-2)(y+1) dy (from y=0 to infinity)

= x/e^2 ∫ e^(-2)y dy (from y=0 to infinity)

= x/e^2 [e^(-2)y/-2] (from y=0 to infinity)

= xe^(-2)/2

Now we can find the conditional density of Y given X = x:

f(Y | X = x) = f(X, Y)/f(X)

= xe^(-2)(y+1)/[x e^(-2)/2]

= 2(y+1)/x

= 2/x * (y+1)

So the conditional density of Y given X = x is a function of y that depends on x.

(b)

To find the density function of Z = X + Y, we use the transformation method. We need to find the joint density function of U = X and V = X + Y, and then integrate over all possible values of U to get the marginal density function of V.

First, we need to find the inverse transformation functions:

X = U

Y = V - U

The Jacobian determinant of the transformation is:

J = |d(x,y)/d(u,v)| = |[∂x/∂u ∂x/∂v; ∂y/∂u ∂y/∂v]|

= |[1 0; -1 1]|

= 1

So the joint density function of U and V is:

f(U,V) = f(X,Y) * |J| = xe^(-2)(V-U+1)

We want to find the marginal density function of V:

f(V) = ∫ f(U,V) dU (from U=0 to V)

= ∫ xe^(-2)(V-U+1) dU (from U=0 to V)

= e^(-2)V ∫ x dx (from x=0 to V) + e^(-2) ∫ x dx (from x=V to infinity) + e^(-2) ∫ dx (from x=0 to V)

= e^(-2)V [V^2/2 - V^3/6] + e^(-2) [(x^2/2)] (from x=V to infinity) + e^(-2)V

= (1/2)e^(-2)V^3 - (1/6)e^(-2)V^3 + (1/2)e^(-2)V

+ (e^(-2)/2)(V^2 - 2V(V+1) + (V+1)^2) + e^(-2)V

= (1/2)e^(-2)V^2

So the density function of Z = X + Y is:

f(Z) = d/dZ [f(V)]

= d/dZ [(1/2)e^(-2)V^2]

= (1/2)e^(-2)(Z^2)

Learn more about independent here

https://brainly.com/question/29863918

#SPJ11

HW 3: Problem 8 Previous Problem List Next (1 point) Find the value of the standard normal random variable z, called Zo such that: (a) P(zzo) 0.7196 Zo = (b) P(-20 ≤z≤ 20) = = 0.4024 Zo = (c) P(-2

Answers

The standard normal random variable, denoted as z, represents a normally distributed variable with a mean of 0 and a standard deviation of 1. To calculate the probabilities given in your question, we use the standard normal table (also known as the z-table).

(a) P(Z > 0.70) = 0.7196

This probability represents the area to the right of z = 0.70 under the standard normal curve. By looking up the value 0.70 in the z-table, we find that the corresponding area is approximately 0.7580. Therefore, the probability P(Z > 0.70) is approximately 0.7580.

(b) P(-2 ≤ Z ≤ 2) = 0.4024

This probability represents the area between z = -2 and z = 2 under the standard normal curve. By looking up the values -2 and 2 in the z-table, we find that the corresponding areas are approximately 0.0228 and 0.9772, respectively. Therefore, the probability P(-2 ≤ Z ≤ 2) is approximately 0.9772 - 0.0228 = 0.9544.

(c) P(-2 < Z < 2) = 0.9544

This probability represents the area between z = -2 and z = 2 under the standard normal curve, excluding the endpoints. By subtracting the areas of the tails (0.0228 and 0.0228) from the probability calculated in part (b), we get 0.9544.

Note: It seems there might be a typographical error in part (b) of your question where you mentioned P(-20 ≤ z ≤ 20) = 0.4024. The probability for such a wide range would be extremely close to 1, not 0.4024.

To know more about standard normal, visit:

https://brainly.com/question/31379967

#SPJ11

use the definition of taylor series to find the taylor series (centered at c) for the function. f(x) = 7 sin x, c = 4

Answers

The Taylor series is a way to represent a function as a power series of its derivatives at a specific point in the domain. It is a crucial tool in calculus and its applications. The Taylor series for a function f(x) is given by:$$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(c)}{n!}(x-c)^n$$Where f^(n) (c) is the nth derivative of f evaluated at c.

In this case, we are asked to find the Taylor series centered at c=4 for the function f(x)=7sin(x).We first find the derivatives of f(x). The first four derivatives are:$f(x)=7sin(x)$;$f'(x)=7cos(x)$;$f''(x)=-7sin(x)$;$f'''(x)=-7cos(x)$;$f''''(x)=7sin(x)$;Notice that the pattern repeats after the fourth derivative. Thus, the nth derivative is:$f^{(n)}(x)=7sin(x+\frac{n\pi}{2})$Now, we can use the formula for the Taylor series and substitute in the derivatives evaluated at c=4:$f(x)=\sum_{n=0}^\infty \frac{7sin(4+\frac{n\pi}{2})}{n!}(x-4)^n$.

Thus, the Taylor series for f(x)=7sin(x) centered at c=4 is:$$7sin(x)=\sum_{n=0}^\infty \frac{7sin(4+\frac{n\pi}{2})}{n!}(x-4)^n$$.

To know more about power series visit:-

https://brainly.com/question/29896893

#SPJ11

find the solution of the differential equation that satisfies the given initial condition. xy' y = y2, y(1) = −7

Answers

The solution to the given differential equation [tex]\(xy' - y = y^2\)[/tex] that satisfies the initial condition (y(1) = -7) is (y = -7x).

What is the particular solution of the differential equation with the initial condition, where [tex]\(xy' - y = y^2\)[/tex] and (y(1) = -7)?

To solve the given differential equation [tex](xy' - y = y^2)[/tex] with the initial condition (y(1) = -7), we can use the method of separable variables.

First, we rearrange the equation by dividing both sides by [tex]\(y^2\):[/tex]

[tex]\[\frac{xy'}{y^2} - \frac{1}{y} = 1\][/tex]

Now, we separate the variables and integrate both sides:

[tex]\[\int \frac{1}{y}\,dy = \int \frac{1}{x}\,dx + C\][/tex]

where (C) is the constant of integration.

Integrating the left side gives:

[tex]\[\ln|y| = \ln|x| + C\][/tex]

Next, we can simplify the equation by exponentiating both sides:

[tex]\[|y| = |x| \cdot e^C\][/tex]

Since (C) is an arbitrary constant, we can combine it with another constant,[tex]\(k = e^C\):[/tex]

[tex]\[|y| = k \cdot |x|\][/tex]

Now, we consider the initial condition (y(1) = -7). Substituting (x = 1) and (y = -7) into the equation, we get:

[tex]\[-7 = k \cdot 1\][/tex]

Therefore, (k = -7).

Finally, we can write the solution to the differential equation with the initial condition as:

[y = -7x]

where (x) can take any value except (x = 0) due to the absolute value in the solution.

The solution to the given differential equation that satisfies the initial condition (y(1) = -7) is (y = -7x).

Learn more about differential equation

brainly.com/question/32538700

#SPJ11

y=3x-7 Work out the value of y when x=5

Answers

Step-by-step explanation:

you know how functions work ?

the variable (or variables) in the findings expression is a placeholder for actual values.

when we have an actual value, we put that into the place of the variable and then simply calculate.

x = 5

therefore, the functional calculation is

y = 3×5 - 7 = 15 - 7 = 8

keep in mind the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

therefore, we need to calculate "3×5" before we deal with the "- 7" part.

Answer:

Step-by-step explanation:

y=8


Find the measurement of the following angles if arc ED is 72 degrees, and CD is the diameter,

A. CED=?
B. ECD=?
C. CDE ?
D. CAB ?
E. DAB=?

Answers

Arc ED is 72 Degrees-A)CED = 72 degrees ,B)ECD = 36 degrees ,C)CDE = 144 degrees, D)CAB = 90 degrees .E)DAB = 90 degrees

The measurements of the angles in the given scenario, we need to apply the properties of angles in a circle.

Given:

- Arc ED is 72 degrees.

- CD is the diameter of the circle.

Using the properties of angles formed by a chord and an arc, we can determine the measurements of the angles as follows:

A. CED:

The angle CED is formed by the arc ED. Since arc ED is given as 72 degrees, the measurement of angle CED is also 72 degrees.

B. ECD:

Angle ECD is an inscribed angle that intercepts arc ED. By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore, angle ECD is half of 72 degrees, which is 36 degrees.

C. CDE:

Angle CDE is formed by the chord CD. It is an opposite angle to angle ECD. Since the sum of opposite angles formed by a chord is always 180 degrees, angle CDE is also 180 - 36 = 144 degrees.

D. CAB:

Angle CAB is formed by the diameter CD. When a diameter of a circle creates an angle with any other point on the circle, the angle is always a right angle (90 degrees). Therefore, angle CAB is 90 degrees.

E. DAB:

Angle DAB is an inscribed angle that intercepts arc CD. Since CD is the diameter of the circle, the intercepted arc CD is a semicircle, which has a measure of 180 degrees. By the inscribed angle theorem, angle DAB is half of 180 degrees, which is 90 degrees.

To summarize:

A. CED = 72 degrees

B. ECD = 36 degrees

C. CDE = 144 degrees

D. CAB = 90 degrees

E. DAB = 90 degrees

For more questions on Degrees.

https://brainly.com/question/29165823

#SPJ8

I am getting solution wrong and
the third attempt is the last attempt.
Problem #1: Solve the following initial value problem. x= -13y₁ + 4y2 1/₂ = -24y₁ + 7y₂ y₁ (0) = 5, y₂(0) = 2. Enter the functions y₁(x) and y₂(x) (in that order) into the answer box b

Answers

(2/3)e^(5x) + (4/3)e^(-4x) is correct for given initial value problem. x= -13y₁ + 4y2 1/₂ = -24y₁ + 7y₂ y₁ (0) = 5, y₂(0) = 2.

To solve the initial value problem

`x = -13y₁ + 4y₂ 1/2 = -24y₁ + 7y₂; y₁ (0) = 5, y₂(0) = 2`,

we first need to find the solution of the system of differential equations.

The solution is given by:

y₁(x) = (19/3)e^(5x) + (5/3)e^(-4x)y₂(x)

= (2/3)e^(5x) + (4/3)e^(-4x)

Therefore, the functions y₁(x) and y₂(x) are:

y₁(x) = (19/3)e^(5x) + (5/3)e^(-4x)y₂(x)

= (2/3)e^(5x) + (4/3)e^(-4x)

Note: As per the given information, the third attempt is the last attempt. If you have already used two attempts and the solution is incorrect, please make sure to check your calculations and try again before using the last attempt.

To know more about initial value visit

https://brainly.com/question/32051956

#SPJ11

ind the average value of f over the region d.f(x, y) = 6xy, d is the triangle with vertices (0, 0), (1, 0), and (1, 9)

Answers

The function is f(x,y)= 6xy. The region D is a triangle with vertices (0,0), (1,0), and (1,9).The region D can be represented by the limits 0 ≤ x ≤ 1 and 0 ≤ y ≤ 9x.

Therefore, the average value of f over D is given by:[tex]$$\bar f=\frac{\int_D f(x,y) dA}{\int_D dA}$$$$\int_D[/tex] [tex]f(x,y)dA= \int_{0}^{1}\int_{0}^{9x}6xydydx$$$$=\int_{0}^{1}3x(9x)^2dx$$$$=[/tex][tex]243/4$$[/tex]and the area of the region D is: $$\int_D dA = [tex]\int_{0}^{1}\int_{0}^{9x}dydx$$$$=\int_{0}^{1}9xdx$$$$=9/2$$[/tex]Therefore, the average value of f over D is[tex]:$$\bar f=\frac{\int_D f(x,y) dA}{\int_D dA}$$$$= \frac{243/4}{9/2}$$$$=27/2$$[/tex]Therefore, the average value of f over D is 27/2.

To know more about vertices visit :-

https://brainly.com/question/29154919

#SPJ11

4. Use a calculator to solve the equation on the on the interval [0, 277). Round to the nearest hundredth of a radian. sin 3x = -sinx O A. 0, 1.57, 3.14, 4.71 OB. 0, 3.14 O C. 1.57, 4.71 O D. 0, 0.79,

Answers

In order to determine the values of x that meet the equation sin(3x) = -sin(x) on the interval [0, 277), we must first solve the sin(3x) equation.

We can proceed as follows using a calculator:

1. Enter sin(3x) = -sin(x) as the equation.

2. To isolate x, use the sine(-1) inverse function.

3. Find the value of x.

It's crucial to switch a calculator to radian mode before using it. After making the necessary computations, we discover that the equation's approximate solutions for the specified interval are:x ≈ 0, 1.57, 3.14, 4.71Consequently, the appropriate response isA. 0, 1.57, 3.14, 4.71

learn more about equation here :

https://brainly.com/question/29538993

#SPJ11

5 people are sitting around a table. Let x be the number of people sitting next to at least one woman and y be the number of people sitting next to at least one man. How many possible values of the ordered pair (x,y) are there? (For example, (5,0) is the pair if all 5 people are women, since all 5 people are sitting next to a woman, and 0 people are sitting next to a man.)

Answers

Let's consider the possible scenarios for the arrangement of the 5 people around the table in terms of their gender. Since there are only two genders, namely men and women, we can have the following cases:

All 5 people are women: In this case, each woman is sitting next to 4 other women, so x = 5 and y = 0. Therefore, the ordered pair is (5, 0).

4 people are women, and 1 person is a man: In this scenario, each woman is sitting next to 3 other women and the man. Thus, x = 4 and y = 1. The ordered pair is (4, 1).

3 people are women, and 2 people are men: In this case, each woman is sitting next to 2 other women and both men. Therefore, x = 3 and y = 2. The ordered pair is (3, 2).

2 people are women, and 3 people are men: Here, each woman is sitting next to 1 other woman and both men. Hence, x = 2 and y = 3. The ordered pair is (2, 3).

1 person is a woman, and 4 people are men: In this scenario, the woman is sitting next to all 4 men. So, x = 1 and y = 4. The ordered pair is (1, 4).

All 5 people are men: In this case, each man is sitting next to 4 other men, so x = 0 and y = 5. The ordered pair is (0, 5).

To summarize, we have the following possible ordered pairs: (5, 0), (4, 1), (3, 2), (2, 3), (1, 4), and (0, 5). Therefore, there are six possible values for the ordered pair (x, y).

To know more about Case visit-

brainly.com/question/31374625

#SPJ11

Please answer everything! thank you!
Probability S# 19xbo sluboM alomoss 7. A recent study of USF students found that 30 percent walk to class, 20 percent bike, and 12 percent do both. What is the percent of USF students who walk or bike

Answers

The percent of USF students who walk or bike is 38%.

Given that  Percent of students who walk to class is 30%

Percent of students who bike to class = 20%

Percent of students who do both (walk and bike) = 12%

To calculate the percent of students who walk or bike, we can use the principle of inclusion-exclusion.

We add the percentages of those who walk and bike and then subtract the percentage of those who do both.

Percent of students who walk or bike = Percent who walk + Percent who bike - Percent who do both

Percent of students who walk or bike = 30% + 20% - 12%

Percent of students who walk or bike = 50% - 12%

Percent of students who walk or bike = 38%

Therefore, the percent of USF students who walk or bike is 38%.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ4

what is the most nearly volume created when the area bounded by y=0, x=0, and y=sq. rt.(4-x^2) is rotated about y-axis?
a) 3.1
b)8.4
c)17
d)34

Answers

Answer of the above question is in the correct option is (b) 8.4.

Given the area bounded by y = 0, x = 0, and y = √(4 - x²) and we need to find the most nearly volume created when it is rotated about the y-axis.What we need is the calculation of the volume created by a rotation around the y-axis using the formula given below:V = π∫ [f(y)]² dy, where f(y) is the radius, and the limits of the integral are the values of y.Volume of the generated solid (V) by rotating the area bounded by y = 0, x = 0, and y = √(4 - x²) about the y-axis can be calculated as follows:

To know more about, integral visit

https://brainly.com/question/31059545

#SPJ11

Give examples of (a) A sequence (2n) of irrational numbers having a limit lim.In that is a rational number. (b) A sequence (rn) of rational numbers having a limit lim in that is an irrational number.

Answers

(a) A sequence (2n) of irrational numbers having a limit lim in that is a rational number:Consider the sequence (2n), where n is a positive integer. Here's the proof that this sequence converges to a limit, which is a rational number.

Observe that for every positive integer n, 2n can be written in terms of 2 as a power of 2, that is, 2n = 2^n. Since 2 is rational, so is 2^n. Therefore, (2n) is a sequence of irrational numbers having a limit that is a rational number, which is 0 when n approaches to negative infinity.(b) A sequence (rn) of rational numbers having a limit lim in that is an irrational number:Consider the sequence {rn} where rn = 1/n, n∈N.For every n∈N, rn is a rational number and lim (rn) = 0 which is an irrational number.

To know more about integer , visit ;

https://brainly.com/question/929808

#SPJ11

The sequence 2, 2.8, 2.98, 2.998, 2.9998… is a sequence of irrational numbers which converges to a rational number 3.

The sequence (rn) is a sequence of rational numbers having a limit lim in that is an irrational number.

(a) A sequence (2n) of irrational numbers having a limit lim. In that is a rational number is:

There exist infinitely many sequences of irrational numbers, which converge to rational numbers.

Let us consider a sequence (2n) of irrational numbers, which converges to a rational number. 2, 2.8, 2.98, 2.998, 2.9998…

The sequence 2, 2.8, 2.98, 2.998, 2.9998… is a sequence of irrational numbers which converges to a rational number 3.

The limit of the sequence is 3, which is a rational number.

(b) A sequence (rn) of rational numbers having a limit lim in that is an irrational number:

One such example of a sequence (rn) of rational numbers having a limit lim in that is an irrational number is given below:

Consider the sequence (1 + 1/n)n, which is a sequence of rational numbers and converges to an irrational number e. The first few terms of the sequence are 2, 1.5, 1.33, 1.25, 1.2… and so on.

The limit of the sequence is e, which is an irrational number.

Thus, this sequence (rn) is a sequence of rational numbers having a limit lim in that is an irrational number.

To know more about sequence, visit:

https://brainly.com/question/30262438

#SPJ11

Find The Radius Of Convergence, R, Of The Series
Sigma n=1 to infinity (n!x^n)/(1.3.5....(2n-1))
Find the interval, I, of convergence of the series. (Enter your answer using interval notation)

Answers

The radius of convergence, R, of the series is 1. The interval of convergence, I, is (-1, 1) in interval notation.

The ratio test can be used to find the radius of convergence, R, of the given series. Applying the ratio test, we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term. In this case, the (n+1)th term is [tex]((n+1)!x^{(n+1)})/(1.3.5....(2n+1))[/tex], and the nth term is [tex](n!x^n)/(1.3.5....(2n-1))[/tex].

Simplifying the ratio and taking the limit, we find that the limit is equal to the absolute value of x. Therefore, for the series to converge, the absolute value of x must be less than 1. This means that the radius of convergence, R, is 1.

To determine the interval of convergence, we need to find the values of x for which the series converges. Since the radius of convergence is 1, the series converges for values of x within a distance of 1 from the center of convergence, which is x = 0. Therefore, the interval of convergence, I, is (-1, 1) in interval notation.

Learn more about radius of convergence here:

https://brainly.com/question/31440916

#SPJ11

What is the equation of the parabola opening upward with a focus at and a directrix of ?
A. f(x) = 1/32(x - 9)^2 + 19 =
B. f(x) = 1/32(x + 9)^2 + 19 =
C. f(x) = 1/16(x - 9)^2 + 19 =
D. f(x) = 1/16(x + 9)^2 - 19 =

Answers

The equation of the parabola opening upward with a focus at and a directrix  is  f(x) = 1/32(x - 9)² + 19

Therefore option A  is correct.

How do we calculate?

Our objective is to find the equation of the parabola opening upward with a focus at (9, 19) and a directrix of y = -19

The standard form of the equation of a parabola with a vertical axis is:

4p(y - k) = (x - h)²

(h, k) = (9, 0)  we know this because the focus lies on the x-axis and the directrix is a horizontal line.

The distance between the vertex and the focus = 19.

4 * 19(y - 0) = (x - 9)²

76y = (x - 9)²

y = 1/76(x - 9)²

Comparing this equation to the options provided, we see that the likely answer is: A. f(x) = 1/32(x - 9)² + 19

Learn more about vertex  at:

https://brainly.com/question/21191648

#SPJ1

A plane is headed due south at a speed of 298mph. A wind from direction 51 degress is blowing at 18 mph. Find the bearing pf the plane

Answers

To find the bearing of the plane, we will use the concept of vector addition. The process of adding two or more vectors together to form a larger vector is known as vector addition. If two vectors, A and B, are added, the resulting vector is the sum of the two vectors, and it is denoted by A + B.The plane is heading towards the south at a bearing of 24.68°.

The plane is flying towards south direction. So, we can assume that it has an initial vector, V, in the south direction with a magnitude of 298 mph. Also, the wind is blowing in the direction of 51° with a speed of 18 mph. So, the wind has a vector, W, in the direction of 51° with a magnitude of 18 mph.To find the bearing of the plane, we need to calculate the resultant vector of the plane and the wind.

Let's assume that the bearing of the plane is θ.Then, the angle between the resultant vector and the south direction will be (θ - 180°).Now, we can use the sine law to calculate the magnitude of the resultant vector.According to the sine law,`V / sin(180° - θ) = W / sin(51°)`

Simplifying this equation, we get:`V / sinθ = W / sin(51°)`Multiplying both sides by sinθ, we get:`V = W sinθ / sin(51°)`Now, we can calculate the magnitude of the resultant vector.`R = sqrt(V² + W² - 2VW cos(180° - 51°))`

Substituting the given values, we get:`R = sqrt((18sinθ / sin(51°))² + 18² - 2(18sinθ / sin(51°))18cos(129°))`Simplifying this equation, we get:`R = sqrt(324sin²θ / sin²51° + 324 + 648sinθ / sin51°)`

Now, we can differentiate this equation with respect to θ and equate it to zero to find the value of θ that minimizes R.`dR / dθ = (648sinθ / sin51°) / 2sqrt(324sin²θ / sin²51° + 324 + 648sinθ / sin51°) - (648sin²θ / sin²51°) / (2sin²51°sqrt(324sin²θ / sin²51° + 324 + 648sinθ / sin51°)) = 0`

Simplifying this equation, we get:`324sin²θ / sin⁴51° - 3sinθ / sin²51° + 1 = 0`Solving this equation, we get:`sinθ = 0.4078`Therefore, the bearing of the plane is:`θ = sin⁻¹(0.4078) = 24.68°`

So, the plane is heading towards the south at a bearing of 24.68°.

For more such questions on vector addition.

https://brainly.com/question/2927458

#SPJ8

Other Questions
Bike n Work Co. is a shop that sells bike groupsets. In selling the product, the shop is applying only all-cash policy. However, due to increasingly fierce competition in the industry, the shop is considering of implementing a 30-day credit policy. At the moment, the shop sells 10 units of groupset every month. The current price and the variable cost per unit are IDR 12 million and IDR 8 million, respectively. If Bike n Work does switch to net 30 days on sales, it predicts that the quantity sold may rise by 40% and costs will increase by 25% per unit. Meanwhile, the groupset's price under the new policy will be (10+Y)% higher.Question:a. If the required return is 0.90 percent per month, should Bike n Work determine if the company should proceed or not.b. Assume new orders for (20 +Y) bike groupsets have been made by customers requesting credit. Credit is extended for one period. Based on historical experience, payment for about 1 out of every 50 such orders is never collected. Assuming that this is a one-time order, should credit be extended? (Hint: use the predicted price and variable cost if the new policy is applied).c. What is the break-even probability of default in part (b)? by what age does one internalize and identify with ones gender? A coil 3.75 cm radius, containing 470 turns, is placed in a uniform magnetic field that varies with time according to B =( 1.2010-2 T/s)t+(2.5010-5 T/s4 )t4. The coil is connected to a 520- resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. Part A Find the magnitude of the induced emf in the coil as a function of time. E = 7.9310- V +(6.61105 V/s )t =2.4910-2 V +(5.1910-5 V/s )t =2.4910- V +(2.0810-4 V/s )t E = 7.9310-3 V +(2.0810-4 V/s )t Previous Answers Part B What is the current in the resistor at time to = 4.70 s? VE ? I = Submit Correct APrevious question Nirenberg and Leder used the triplet binding assay to determine specific codon assignments. A complex of which of the following components was trapped in the nitrocellulose filter? uncharged tRNAs and ribosomes sense and antiserse strands FONA free tRNAS ribosomes and DNA charged RNA, RNA triplet and ribosome when he reaches the bottom, 4.2 mm below his starting point, his speed is 2.2 m/sm/s . by how much has thermal energy increased during his slide? Select all of the following that are TRUE.Question 6 options:If the fixed expenses increase in a company, and all other factors remain unchanged, then we can expect the margin of safety to decrease.At a given level of sales, a low contribution margin ratio will result in less net income than a high contribution margin ratio.If fixed expenses increase by $15,000 per year, then the level of sales needed to break even will also increase by $15,000Once the break-even point has been reached, increases in contribution margin will be reflected dollar for dollar in increased net income.In determining contribution margin, all manufacturing costs are deducted.The margin of safety percentage is equal to the margin of safety in dollars divided by the number of units sold. let x2 13x=3 . what values make an equivalent number sentence after completing the square? enter your answers in the boxes. x2 13x = the presence of these two factors coupled with abdominal obesity indicates metabolic syndrome. Two objects with masses of m1 and m2 have the same kinetic energy and are both moving to the right. The same constant force F-> is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is: A. 1:4 B. 4:1 C. 1:2 D. 2:1 E. 1:1 Our goal for this discussion is to revlew the purpose behind and the reasons for establishing the Securities and Exchange Commission (SEC). What is the SEC and the principal legislation the agency enforces? Within your response, make sure to discuss the SEC's organization and structure, Including the agency's responsibility from an accounting standpoint, namely regarding U.S. Generally Accepted Accounting Principles (U.S. GAP). What role does the SEC have in the development of accounting theory and practices? Seitz Glassware is trying to determine its growth rate for an annual cash dividend. The most recent dividend, Divo, was $0.30 per share. The stock's target return rate is 10%. What is the stock's price if a. the annual growth rate is 2%? b. the annual growth rate is 4%? c. the annual growth rate is 6%? d. the annual growth rate is 8%? e. the annual growth rate is 9%? A very long line of charge with charge per unit length +8.00 C/m is on the z-axis and its midpoint is at a 0. A second very long line of charge with charge per unit length -4.00 C/m is parallel to the x-axis at y 15.0 cm and its midpoint is also at z = 0. Part A At what point on the y-axis is the resultant electric field of the two lines of charge equal to zero? Enter the y-coordinate of the point and include the appropriate units. 3 d ? is the concentration gradeint is higher, is osmis rate faster Question 51 Grapevine Bank receives a deposit of $200,000. Its required reserve ratio is 12 percent. How much of this deposit is available to be loaned to borrowers? O $12.000 O $200,000 O $176.000 O $24,000 Question 52 Pinnacle Finance Bank has a 12 percent reserve requirement ratio. What is Pinnacle Finance's money multiplier? O 1.2 O 12 O 8.33 O 6 Question 53 If Pinnacle Finance Bank receives a new cash deposit of $150,000, and it has a required reserve ratio of 12 percent, how much total money could potentially be created from that deposit? O $18,000 O $1,800,000 O $1,250,000 O $150,000 An object lies outside the focal point of a diverging lens. Which of the following statements about the image formed by this lens must be true? A. The image is always virtual and inverted. B. The image could be real or virtual, depending on how far the object is past the focal point. C. The image could be erect or inverted, depending on how far the object is past the focal point. D. The image is always virtual and on the same side of the lens as the object. or both B and C i need help with engineering economy question;Steven plans to withdraw his money RM 10,000 each year from his savings account at theend of year 10 and Year 11. To make sure these withdrawals are possible, FOUR (4)annuity amounts (A) will be deposited in a bank at the end of year 2, 3, 4, and 5. The banksinterest rate is 12% per year.(a) Draw a cash-flow diagram for this situation(b) Determine the value of the annual amount (A) at the end of year 2, 3, 4 and 5 thatshould be deposited to withdraw the money at the end of year 10 and year 11 asstated. the total cost of ownership of an information system refers to in xyz, y=90 and x=26. zwy=79 and xw=810. find the length of zy to the nearest integer. choice of true or false:Many firms choose to achieve target cost through adding additional profit centers.Many firms are finding it is difficult to compete successfully on cost leadership or differentiation alone, and they must, in fact, compete on both design and cost.Target cost can be defined as competitive price minus throughput margin per unit.Capacity must be considered when analyzing the merits of a special order. The Harris Company is the lessee on a four-year lease with the following payments at the end of each year: Year 1: Year 2: Year 3: Year 4: An appropriate discount rate is 7 percentage, yielding a present value of $86,637. $18.500 $23,500 $28,500 $33,500 a-1. If the lease is an operating lease, what will be the initial value of the right-of-use asset? Initial value of the right-of-use asset a-2. If the lease is an operating lease, what will be the initial value of the lease liability? Initial value of the lease liability a-3. If the lease is an operating lease, what will be the lease expense shown on the income statement at the end of year 1? Lease expense a-4. If the lease is an operating lease, what will be the interest expense shown on the income statement at the end of year 1? (Leave no cells blank - be certain to enter "0" wherever required.) Interest expense a-5. If the lease is an operating lease, what will be the amortization expense shown on the income statement at the end of year 1? (Leave no cells blank - be certain to enter "0" wherever required.) Amortization expense a-5. If the lease is an operating lease, what will be the amortization expense shown on the income statement at the end of year 1? (Leave no cells blank - be certain to enter "0" wherever required.) Amortization expense b-1. If the lease is a finance lease, what will be the initial value of the right-of-use asset? Initial value of the right-of-use asset b-2. If the lease is a finance lease, what will be the initial value of the lease liability? Initial value of the lease liability b-3. If the lease is a finance lease, what will be the lease expense shown on the income statement at the end of year 1? (Leave no cells blank - be certain to enter "0" wherever required.) Lease expense b-4. If the lease is a finance lease, what will be the interest expense shown on the income statement at the end of year 1? (Round your answer to the nearest dollar amount.) Interest expense b-5. If the lease is a finance lease, what will be the amortization expense shown on the income statement at the end of year 1? (Round your answer to the nearest dollar amount.) Amortization expense