Answer:
Since all three distances are equal to 2√3, we can conclude that the points 2, -1+i√3, -1-i√3 form an equilateral triangle on the Argand plane. This proves the statement.
Step-by-step explanation:
To prove that the points 2, -1+i√3, -1-i√3 form an equilateral triangle on the Argand plane, we need to show that each side of the triangle has the same length, which is equal to the distance between any two of the points.
Let's first find the distance between points 2 and -1+i√3. We can use the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) = (2, 0) and (x₂, y₂) = (-1, √3). Substituting in the values, we get:
d₁ = √[(-1 - 2)² + (√3 - 0)²] = √[9 + 3] = √12 = 2√3
Next, let's find the distance between points -1+i√3 and -1-i√3:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) = (-1, √3) and (x₂, y₂) = (-1, -√3). Substituting in the values, we get:
d₂ = √[(-1 - (-1))² + (-√3 - √3)²] = √[0 + 12] = 2√3
Finally, let's find the distance between points -1-i√3 and 2:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) = (-1, -√3) and (x₂, y₂) = (2, 0). Substituting in the values, we get:
d₃ = √[(2 - (-1))² + (0 - (-√3))²] = √[9 + 3] = √12 = 2√3
Since all three distances are equal to 2√3, we can conclude that the points 2, -1+i√3, -1-i√3 form an equilateral triangle on the Argand plane. This proves the statement.
Units were not specified in the question, so the distances are expressed in arbitrary units.
Using the standard normal table or a calculator, find the probability below assuming the distribution is a standard normal distribution. P(-0.6 < Z < 1.1)
Using the standard normal table the probability P(-0.6 < Z < 1.1) assuming a standard normal distribution is approximately 0.5900 or 59%.
To locate the possibility P(-zero.6 < Z < 1.1) the usage of the usual ordinary distribution, we need to find the place beneath the usual ordinary curve between the z-ratings -0.6 and 1.1.
Using a well known normale table or a calculator, we are able to discover the corresponding cumulative chances for these z-scores.
For z = -0.6, the cumulative probability is 0.2743.
For z = 1.1, the cumulative probability is 0.8643.
To discover the probability between those z-ratings, we subtract the cumulative probability of -0.6 from the cumulative chance of 1.1:
P(-0.6 < Z < 1.1) = 0.8643 - 0.2743 = 0.5900
Thus, the probability P(-0.6 < Z < 1.1) assuming a standard normal distribution is approximately 0.5900 or 59%.
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Help, please! Find the VOLUME of this complex shape.
Step-by-step explanation:
volume= length×breadth×height
8-3-3= 2 cm
2×2×4= 16 cm^2
4-2= 2 cm
3×2×4= 24 cm^2
3×4×4= 48 cm^2
total volume
= 16+24+48
= 88 cm^2
Every student of a school donated as much money as their number to make a fund for Corona- virus victims. If they collected Rs.13225 altogether, how many students donated money in the fund?
Answer:
The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.
In an arithmetic series, the sum S of n terms is given by:
S = n/2 * (a + l)
where:
- n is the number of terms (which represents the number of students in this case),
- a is the first term (in this case, the first student's number, which would be 1), and
- l is the last term (in this case, the last student's number, which we don't know yet).
Given that S = Rs. 13225, we have:
13225 = n/2 * (1 + l)
Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:
13225 = n/2 * (1 + n)
Multiplying through by 2 to clear the fraction gives:
26450 = n * (1 + n)
Rearranging to a quadratic equation gives:
n^2 + n - 26450 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.
Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.
So, there were 163 students who donated money to the fund.
Calculate the length of segment CD, given that AE is tangent to the circle, AE = 12, and EC = 8.
The length of segment CD is approximately 28.84.
To calculate the length of segment CD, we need to use the properties of a tangent line and the given information.
In a circle, when a line is tangent to the circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle AEC is a right triangle.
Given that AE = 12 and EC = 8, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of triangle AEC.
AC^2 = AE^2 + EC^2
AC^2 = 12^2 + 8^2
AC^2 = 144 + 64
AC^2 = 208
Taking the square root of both sides:
AC = √208
AC ≈ 14.42
Now, segment CD is a part of the diameter of the circle and passes through the center of the circle. Therefore, it is twice the length of the radius.
CD = 2 * AC
CD = 2 * 14.42
CD ≈ 28.84
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Before the search and collection of evidence, there must be _______.
A. Informed consent by the owner
B. A crime
C. A chain of custody
D. A search warrant
I’m stuck between D and B because law enforcement can conduct a search without a search warrant if there is consent by the owner. It is not C because that would be either during or after the collection of evidence.
Answer:
D) A search warrant
Step-by-step explanation:
A search warrant is required before the search and collection of evidence to ensure legal authorization and protection of individuals' rights against unreasonable searches and seizures.
Option B, "A crime", is incorrect because the presence of a crime is not a prerequisite for conducting a search and collection of evidence. There are various situations where searches and evidence collection may occur without a crime being involved, such as regulatory inspections, consented searches, or investigations into potential threats or risks.
By your logic when you say law enforcement can conduct a search without a search warrant if there is consent by the owner, that would mean option A would be right, but of course, it's not.
Complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and a compounded n times a year. Complete the table
The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.
To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.
The formula for calculating compound interest is as follows:
A = P(1 + r/n) ^nt,
where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.
The table is given below:
[tex]\begin{array}{|c|c|c|} \hline \text{n} &
\text{A = P(1 + r/n) }^{nt} &
\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &
\text{3100(1 + 0.04/1)}^{1*10} &
\text{\$4788.03} \\ \hline \text{2} &
\text{3100(1 + 0.04/2)}^{2*10} &
\text{\$4798.76} \\ \hline \text{4} &
\text{3100(1 + 0.04/4)}^{4*10} &
\text{\$4817.46} \\ \hline \text{12} &
\text{3100(1 + 0.04/12)}^{12*10} &
\text{\$4861.94} \\ \hline \end{array}[/tex]
The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.
In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.
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Your teacher will grade your response to this question to ensure you receive proper credit for your answer.
The equation (x + 6)2 + (y + 4)2 = 36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.
SOMEONE PLEAS HELP!
is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
Answer:
Step-by-step explanation:
Answer:
Chloe is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
a) Write an expression for the area of the table in terms of the width x.
One possible expression is:
A = (x + 2x) * h / 2
where A is the area of the table, x is the width of the table, and h is the height of the table.
To get this expression, we use the formula for the area of a trapezoid :
A = (a + b) * h / 2
where a and b are the lengths of the parallel sides of the trapezoid. Since Chloe is making the longest side of the table twice as long as the width, we can write:
a = x
b = 2x
Substituting these values into the formula, we get:
A = (x + 2x) * h / 2
b) Simplify the expression and find the area of the table if x = 3 feet and h = 4 feet.
To simplify the expression, we can combine like terms and apply the order of operations:
A = (x + 2x) * h / 2
A = (3x) * h / 2
A = 3 * x * h / 2
To find the area of the table if x = 3 feet and h = 4 feet, we can plug in these values into the simplified expression:
A = 3 * x * h / 2
A = 3 * 3 * 4 / 2
A = 9 * 4 / 2
A = 36 / 2
A = 18
Therefore, the area of the table is 18 square feet.
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..................................................................
Answer:
[tex]\mathrm{y=\frac{2}{5}x+2}[/tex]
Step-by-step explanation:
[tex]\mathrm{Here,\ we\ see\ that\ the\ line\ passes\ through\ (-5,0)\ and\ (0,2).}\\\mathrm{So\ the\ equation\ of\ line\ is:}\\\\\mathrm{y-0=\frac{2-0}{0-(-5)}(x-(-5))}\\\mathrm{or,\ y=\frac{2}{5}(x+5)}\\\mathrm{or,\ 5y=2x+10}\\\mathrm{or,\ y=\frac{2}{5}x+2}[/tex]
Alternative method:
[tex]\mathrm{Here,}\\\mathrm{x-intercept(a)=-5}\\\mathrm{y-intercept(b)=2}\\\mathrm{Now,}\\\mathrm{Equation\ of\ the\ line\ is:}\\\mathrm{\frac{x}{a}+\frac{y}{b}=1}\\\\\mathrm{or,\ \frac{x}{-5}+\frac{y}{2}=1}\\\\\mathrm{or,\ \frac{2x-5y}{-10}=1}\\\\\mathrm{or,\ 2x-5y=-10}\\\mathrm{or,\ 5y=2x+10 }\\\\\mathrm{or,\ y=\frac{2}{5}x+2\ is\ the\ required\ equation.}[/tex]
Answer:
[tex]y=\dfrac{2}{5}x+2[/tex]
Step-by-step explanation:
To determine the equation of the graphed line, first identify two points on the line:
(-5, 0)(0, 2)Substitute these points into the slope formula to find the slope (m) of the line:
[tex]\textsf{Slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-0}{0-(-5)}=\dfrac{2}{5}[/tex]
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
The line crosses the y-axis at y = 2. Therefore, the y-intercept is 2.
Substitute the found slope and the y-intercept into the slope-intercept formula to create an equation of the graphed line:
[tex]\boxed{y=\dfrac{2}{5}x+2}[/tex]
A cylindrical glass with a base radius of 1.4 inches and a height of 7.5 inches weighs 5.5 ounces when empty. The glass is filled with water 1.5 inches from the top. One cubic inch of water weighs 0.6 ounce. What statements about this situation are true? Select all that apply.
The weight of the empty glass is 5.5 ounces. [True]
The glass is filled with water 1.5 inches from the top. [True]
One cubic inch of water weighs 0.6 ounce. [True]
The weight of the water in the glass is approximately 11.88 ounces. [True]
Let's analyze the given information and determine which statements are true:
The weight of the empty glass is 5.5 ounces.
Water is poured into the glass until it is 1.5 inches from the top.
0.6 ounces equal one cubic inch of water in weight.
Now, let's consider some additional calculations to verify if other statements can be determined:
The glass is cylindrical, and we know its base radius is 1.4 inches and its height is 7.5 inches. To find the volume of the glass, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Substituting the given values:
Volume = π * (1.4 inches)^2 * 7.5 inches
Volume ≈ 29.484 cubic inches
Since the glass is filled with water up to 1.5 inches from the top, we can calculate the volume of water in the glass:
Water volume = Total volume - Volume of empty space
Water volume = 29.484 cubic inches - (1.5 inches * π * (1.4 inches)^2)
Water volume ≈ 29.484 cubic inches - 9.678 cubic inches
Water volume ≈ 19.806 cubic inches
Now, we can find the weight of the water in the glass by multiplying the volume by the weight of one cubic inch of water:
Water weight = Water volume * Weight per cubic inch
Water weight ≈ 19.806 cubic inches * 0.6 ounces/cubic inch
Water weight ≈ 11.8836 ounces
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Find the sum and difference of the greatest and smallest dig- its formed by the given numbers. i. 5,6
The sum of the greatest digit formed by the given numbers as required is; 11.
The difference of the greatest digit formed by the given numbers as required is; 1.
What is the sum and difference of the smallest and greatest number?It follows from the task content that the given digits are ; 5 and 6.
Hence, the greatest digit is 6 while the smallest digit is 5.
Hence, the sum of both digits is; 6 + 5 = 11.
The difference of both digits is; 6 - 5 = 1.
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loan amount $17,000 simple interest 6.8% total interest $867 loan in months
The monthly payment on the loan would be approximately $2,023.52.
To calculate the loan in detail, we need to determine the time period and the monthly payment. Let's break down the given information:
Loan amount: $17,000
Simple interest rate: 6.8%
Total interest: $867
First, we can calculate the interest amount using the formula for simple interest:
Interest = Principal × Rate × Time
We know the interest amount is $867, and the principal (loan amount) is $17,000. Let's solve for time (in years):
867 = 17,000 × 0.068 × Time
Dividing both sides of the equation by (17,000 × 0.068), we get:
Time = 867 / (17,000 × 0.068)
Time ≈ 0.7596 years
Since the loan term is usually expressed in months, we multiply the above result by 12 to convert it to months:
Time in months = 0.7596 × 12
Time in months ≈ 9.1152 months
Now that we have the time period in months, we can calculate the monthly payment (P) using the formula:
P = (Principal + Total Interest) / Time in months
P = (17,000 + 867) / 9.1152
P ≈ 2,023.52
Therefore, the monthly payment on the loan would be approximately $2,023.52.
To summarize, for a loan amount of $17,000 with a simple interest rate of 6.8% and a total interest of $867, the loan term would be approximately 9.1152 months, and the monthly payment would be around $2,023.52.
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What decimal number is represented by the light bulbs shown in the figure?
The decimal number which is represented by the light bulbs shown in the figure is 39.0
We have to find the decimal number which is represented by the the light bulbs.
Let us take the light bulbs as 1 and not lighted are 0.
The binary numeral of the light bulbs shown in the figure is 00100111.
Now let us find the decimal number.
(0×2⁷)+(0×2⁶)+(1×2⁵)+(0×2⁴)+(0×2³)+(1×2²)+(1×2¹)+(1×2⁰)
=32+4+2+1
=39
Hence, 39.0 is the decimal number which is represented by the light bulbs shown in the figure.
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Enter the fraction 4/5 as a mixed number.
Enter the correct answer in the box.
Answer:
1 1/4
Step-by-step explanation:
5/4 can be decomposed as 4/4 + 1/4
so, 1 + 1/4
or in mixed number notation,
1 1/4
Answer:
1 1/4
Step-by-step explanation:
assuming that the real question, see the picture you put, asks for 5/4 and not 4/5, (4/5 is not a whole number). Let's solve 5/4, with 4/4 you have 1 and you are left with 1/4, so the answer is 1 1/4
To calculate the variance for a population, SS is divided by N-1. True or False?
To calculate the variance for a population, the sum of squares (SS) is divided by the total number of observations in the population (N), not N-1. False.
The formula for population variance is:
Variance = SS/N
Where SS is the sum of squares, calculated by summing the squared differences between each observation and the population mean.
Dividing by N in the formula gives the population variance, which represents the average squared deviation from the population mean. This formula provides an unbiased estimate of the true variance of the entire population.
On the other hand, when calculating the variance for a sample (a subset of the population), we divide the sum of squares by N-1.
This correction factor of N-1 is used to account for the degrees of freedom lost when estimating the population variance from a sample.
By dividing by N-1, we obtain an unbiased estimate of the variance of the larger population from which the sample was drawn.
Therefore, for calculating the variance of a population, SS is divided by N, not N-1.
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Two investment portfolios are shown
In five years, Portfolio A is expected to be valued at around $7012. 75 while Portfolio B is anticipated to be worth roughly $7693. 10
How to solveThe formula to calculate the future value of an investment using simple annual interest is:
[tex]FV = PV * (1 + r)^n[/tex]
where:
FV = Future Value
PV = Present Value (the initial investment)
r = interest rate per period
n = number of periods
For Portfolio A (7%):
[tex]FV_A = $5000 * (1 + 0.07)^5[/tex]
= $5000 * 1.40255
= $7012.75
For Portfolio B (9%):
[tex]FV_B = $5000 * (1 + 0.09)^5[/tex]
= $5000 * 1.53862
= $7693.10
In five years, Portfolio A is expected to be valued at around $7012. 75 while Portfolio B is anticipated to be worth roughly $7693. 10
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The Complete Question
Two investment portfolios are shown, Portfolio A with a return of 7% annually and Portfolio B with a return of 9% annually. If you invest $5000 in each portfolio, what will be the total value of each portfolio after 5 years?
Desde que Renata se mudó a su casa en 2001 ha estado monitoreando la altura del árbol frente a su casa. Cuando llegó, el árbol medía 210 cm y ha estado creciendo 33 cm por año
a) ¿Cuál es la ecuación lineal que modela este suceso? b) ¿Cuánto medirá el árbol en 2067?
c) Área 3: Compruébalo como progresión aritmética.
Height = 210 + 33(t - 2001)
b) The tree will be 2388 cm tall in 2067
c) The heights form an arithmetic progression.
We have,
a)
To model the growth of the tree using a linear equation, we can express it as:
Height = Initial Height + Growth Rate x Number of Years
In this case:
Initial Height = 210 cm
Growth Rate = 33 cm/year
Number of Years = (Current Year) - (Year when Renata moved in)
Let's denote the Current Year as "t." Since Renata moved into her house in 2001, the number of years can be represented as (t - 2001).
Putting it all together, the linear equation that models the height of the tree is:
Height = 210 + 33(t - 2001)
b)
To find the height of the tree in 2067, we substitute t = 2067 into the equation:
Height = 210 + 33(2067 - 2001)
Height = 210 + 33(66)
Height = 210 + 2178
Height = 2388 cm
Therefore, the tree will be 2388 cm tall in 2067.
c)
To check if the heights form an arithmetic progression, we need to determine if the differences between consecutive terms are constant.
In this case, the growth rate of the tree is 33 cm per year, which means the height increases by 33 cm each year.
Since the growth rate is constant, the heights form an arithmetic progression.
Thus,
a)
Height = 210 + 33(t - 2001)
b) The tree will be 2388 cm tall in 2067
c) The heights form an arithmetic progression.
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The complete question:
Since Renata moved into her house in 2001, she has been monitoring the height of the tree in front of her house. When it arrived, the tree was 210 cm tall and has been growing 33 cm per yeara) What is the linear equation that models this event? b) How big will the tree be in 2067? c) Area 3: Check it as an arithmetic progression.
Angle a, b and c have a sum of 180 degrees. Prove that Sina +sinb - siny = y/2 * sinb/2 * cosc/2
4sin((a + b)/2)cos((a + b)/2)cos((a - b)/2) = 4sin(b/2)cos(c/2)
We can prove that sin(a) + sin(b) - sin(c) = (y/2) * sin(b/2) * cos(c/2).
How do we know?We apply the sum-to-product trigonometric identities.
We will express sin(c) as sin(180 - a - b):
sin(c) = sin(180 - a - b)
sin(180 - a - b) = sin(180)cos(a + b) + cos(180)sin(a + b)
= 0 * cos(a + b) + (-1) * sin(a + b)
= -sin(a + b)
substituting the expression for sin(c), we have:
sin(a) + sin(b) - sin(c) = sin(a) + sin(b) - (-sin(a + b))
= sin(a) + sin(b) + sin(a + b)
We know also that sin(A) + sin(B) = 2sin((A + B)/2)cos((A - B)/2),
sin(a) + sin(b) + sin(a + b) = 2sin((a + b)/2)cos((a - b)/2) + 2sin(a/2)cos(a/2) + 2sin(b/2)cos(b/2)
= 2sin((a + b)/2)(cos((a - b)/2) + cos(a/2) + cos(b/2))
= 2sin((a + b)/2)(cos((a - b)/2) + cos((a + b)/2))
Using the identity of cos(A) + cos(B) = 2cos((A + B)/2)cos((A - B)/2):
2sin((a + b)/2)(cos((a - b)/2) + cos((a + b)/2)) = 2sin((a + b)/2)(2cos((a + b)/2)cos((a - b)/2))
= 4sin((a + b)/2)cos((a + b)/2)cos((a - b)/2)
4sin((a + b)/2)cos((a + b)/2)cos((a - b)/2) = 4sin(b/2)cos(c/2)
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It should be noted that since the total volume of concrete figures is 5 cubic feet, the library should order 6 cubic feet of concrete to minimize leftover concrete.
How to calculate the valueWe can also solve this problem by using the following equation:
Total volume of concrete figures = Number of figures * Volume of each figure
Plugging in the known values, we get:
Total volume of concrete figures = 5 figures * 1 cubic foot/figure = 5 cubic feet
Since the total volume of concrete figures is 5 cubic feet, the library should order 6 cubic feet of concrete to minimize leftover concrete.
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..............................................
Answer:
A
Step-by-step explanation:
QUESTION 6
Solve for a. (round to tenths)
8
a
14
Answer:
11.5
Step-by-step explanation:
Given:
Left side = 8
Bottom = a
Right side = 14
Using the Pythagorean theorem:
[tex]ax^{2}[/tex] + [tex]8x^{2}[/tex] = [tex]14x^{2}[/tex]
Simplifying the equation:
[tex]ax^{2}[/tex] + 64 = 196
Subtracting 64 from both sides:
[tex]ax^{2}[/tex] = 132
Taking the square root of both sides:
a = [tex]\sqrt{132}[/tex]
Calculating the approximate value of "a":
a ≈ 11.5 (rounded to the nearest tenth)
Therefore, the value of "a" in the given right triangle is approximately 11.5.
(q8) Which of the following is the area of the surface obtained by rotating the curve
, about the y-axis?
The area of the surface generated when f(x) = x^2 is rotated about the y-axis is (π/6)(9^(3/2)-5^(3/2)).
To determine the surface area of a curve when it is rotated about an axis, we can use the formula S= 2π∫a^b xf(x)√(1+(f′(x))^2)dx, where a and b are the limits of integration.
This formula provides the area of the surface formed when a curve is rotated about an axis.Let's suppose we have a curve f(x) = x^2.
To find the area of the surface generated when the curve is rotated about the y-axis, we will have to use the formula S = 2π∫0^1 x√(1+(2x)^2)dx.
When we calculate this integral,
we get S= 2π∫0^1 x√(1+4x^2)dx.
Using a u-substitution,
let u=1+4x^2, du=8xdx.
This simplifies the integral to S = (π/2)∫5^9 u^(1/2)du.
This integral evaluates to (π/6)(9^(3/2)-5^(3/2)).
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Determine the size of angle B in triangle ABC below:
NO LINKS!
Answer:
x = 70 °
Step-by-step explanation:
Two sides (CB & CA) of an isosceles triangle are equal.
The two angles (CBA & CAB) surrounding the third side (BA) are also equal.
x = CBA = CABThe interior angles of a triangle add up to 180°.
180 = 40 + x + x
180 = 40 + 2x
Take 40 away from both sides.140 = 2x
Divide both sides by 2.x = 70
Answer: 70 °
Step-by-step explanation: I used a protractor and if there are 40 ° at the top and the side lengths are all the same then you get 70 ° for x.
a is a geometric sequence where the 1st term of the sequence is -1/4 and the 8th term of the sequence is -1/512. Find the 6th partial sum of the sequence.
The 6th partial sum of the geometric sequence is 63/4.
What is 6th partial sum of the sequence?To find the 6th partial sum of a geometric sequence, we first need to determine the common ratio (r) of the sequence.
Given that the 1st term (a₁) is -1/4 and the 8th term (a₈) is -1/512, we can use these values to find the common ratio.
We have the formula for the nth term of a geometric sequence:
aₙ = a₁ * r^(n-1)
Using this formula, we can write two equations based on the given information:
a₈ = a₁ * r⁸⁻¹
-1/512 = -1/4 * r⁷
Simplifying the equation:
r⁷ = (1/4) / (1/512)
r⁷ = (1/4) * (512/1)
r⁷ = 128
r = ∛(128)
r = 2
Now that we have the common ratio (r = 2), we can find the 6th partial sum (S₆) using the formula:
Sₙ = a₁ * (1 - rⁿ) / (1 - r)
Plugging in the values:
S₆ = (-1/4) * (1 - 2⁶) / (1 - 2)
S₆ = (-1/4) * (1 - 64) / (-1)
S₆ = (-1/4) * (-63) / (-1)
S₆ = 63/4
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What is the volume of a cone where the radius is 6cm and the height 25cm
Answer:
Step-by-step explanation:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
[tex]=\frac{1}{3} \times\pi \times6^2\times25[/tex]
[tex]=\frac{36\times25}{3\pi }[/tex]
[tex]=\frac{300}{\pi }[/tex]
[tex]=95.49\text{cm}^3[/tex]
The drive from city A to city D is 320 miles. On this route you pass cities B and C before reaching city D. It is 82 miles less form City A to city B than it is from city C to City D and 40 miles farther from city B to city C than from city A to city B. How far is it from city B to city D?
The distance from City B to City D is 194 miles.
How to find the distance from city B to city DNow, let's add up the distances to find the relationship between them:
Distance from City A to City D = Distance from City A to City B + Distance from City B to City C + Distance from City C to City D
320 miles = x miles + (x + 40) miles + (x + 82) miles
Now, let's solve this equation:
320 = 3x + 122
Subtracting 122 from both sides:
198 = 3x
Dividing both sides by 3:
x = 66
Therefore, the distance from City B to City D is:
Distance from City B to City D = Distance from City B to City C + Distance from City C to City D
Distance from City B to City D = (x + 40) + (x + 82)
Distance from City B to City D = 66 + 40 + 66 + 82
Distance from City B to City D = 194 miles
Hence, the distance from City B to City D is 194 miles.
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If the gravitational force produced between two masses kept 2 m apart is 100 N, what will be its value when the masses are kept 4m apart? Show your calculation.) Ans: 25 N
If the gravitational force produced between two masses kept 2 m apart is 100 N, the value when the masses are kept 4m apart is 25N
How can the gravitational force be calculated?The gravitational force, which is what pushes mass-containing objects toward one another. We frequently consider the pull of gravity from the Earth.
Since we were given the first force as 100 N and X represent he second force , then the distance between the mass at first was 2m , and the second is 4m, the we can calculate as
[tex]\frac{100}{x} =\frac{4^{2} }{2^{2} }[/tex]
[tex]\frac{100}{x} =\frac{16}{4}[/tex]
[tex]x=\frac{4*100}{16}[/tex]
[tex]X=25 N[/tex].
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Determine the company's accounting equation, and label each element as a debit amount or a credit amount. If you use $ for the owner's equity, why is the accounting equation out of balance?
Complete the accounting equation below, and then below each element, select whether it is a debit or credit account. Finally, enter the amount for each element into the accounting equation, using $ for owner's equity. Note that the equation will not balance.
Winchester Cottage Management Services
Unadjusted Trial Balance
March 31, 2022
Balance
Account Title
Debit
Credit
Cash
$19,205
Accounts receivable
4,900
Supplies
280
Land
13,000
Building
38,000
Accounts payable
$1,000
Note payable
44,900
Noah Calef, capital
29,000
Noah Calef, withdrawals
1,550
Service revenue
7,900
Interest expense
360
Rent expense
1,700
Salaries expense
3,600
Utilities expense
205
Total
$82,800
$82,800
The adjusted accounting equation would be:Assets = Liabilities + Owner’s Equity Assets = $0 + $83,800 + $360Assets = $84,160
The accounting equation is an essential part of any business or organization as it represents the fundamental relationship between assets, liabilities, and owner’s equity.
It is expressed as Assets = Liabilities + Owner’s Equity. To determine the company's accounting equation and label each element as a debit amount or a credit amount,
we need to analyze the given information. Here's the solution:Given data:$1,000360 Utilities expense$82,800
We can conclude that the accounting equation is as follows:Assets = Liabilities + Owner's Equity Assets = $0 + $83,800 (since there is no given liability)Assets = $83,800
We can now calculate the debit and credit amounts of each element:Utilities expense: debit $1,000Owner’s Equity: credit $83,800
The accounting equation is out of balance because the $360 of utilities expenses were recorded as a debit, reducing the balance of assets to $83,440.
Therefore, to balance the equation, we must increase the owner’s equity by the same amount, i.e., $360. This balances the equation and ensures that all transactions are accurately recorded in the books of accounts.
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1. Marissa is watching a honeybee return from her flower garden to a beehive in a branch of a nearby tree. She notices that the bee's path resembles part of a trigonometric function (see below).
Suppose that the flower is 2 ft above the ground, the beehive is 8 ft above the ground, and the horizontal distance from the flower to the beehive is 20 ft. Model this path with a sine or cosine function. Clearly indicate the following::
a. The maximum and minimum b. The midline c. The period and rate constant d. Write a formula for the function Clearly label all parts e. f. Sketch the graph
1) a. Maximum = 8
Minimum = 2
b. Mid-line => y = 5
c. Period = 40 ; Rate constant = 1/40
d. Formula => y = -3cos(πx/20) + 5
e. f. the graph is given below.
Here,
given that,
Marissa is watching a honeybee return from her flower garden to a beehive in a branch of a nearby tree. She notices that the bee's path resembles part of a trigonometric function (see below).
Suppose that the flower is 2 ft above the ground, the beehive is 8 ft above the ground, and the horizontal distance from the flower to the beehive is 20 ft. Model this path with a sine or cosine function.
we have,
from the given information, we get,
1) a. Maximum = 8
Minimum = 2
b. Mid-line => y = 5
c. Period = 40 ; Rate constant = 1/40
d. Formula => y = -3cos(πx/20) + 5
e. f. the graph is given below.
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Question Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.4 feet and a standard deviation of 0.4 feet. A sample of 38 men's step lengths is taken. Step 1 of 2: Find the probability that an individual man's step length is less than 1.9 feet. Round your answer to 4 decimal places, if necessary.
The probability that an individual man's step length is less than 1.9 feet is approximately 0.1056 or 10.56% (rounded to 4 decimal places).
Explain probabilityProbability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution,
According to the given informationThe standardized value, also known as the z-score, is given by:
[tex]Z = \dfrac{(\text{x} - \mu)}{\sigma}[/tex]
Substituting the given values, we get:
[tex]Z = \dfrac{(1.9 - 2.4)}{0.4}[/tex]
[tex]Z = -1.25[/tex]
Now we need to find the probability that an individual man's step length is less than 1.9 feet, which is equivalent to finding the area under the standard normal distribution curve to the left of the z-score -1.25.
Using a standard normal distribution table or calculator, we can find that the area to the left of -1.25 is 0.1056.
Therefore, the probability that an individual man's step length is less than 1.9 feet is approximately 0.1056 or 10.56% (rounded to 4 decimal places).
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