e) what is the probability that it will crash more than three times in a period of 6 months?

Answer:

126

Step-by-step explanation:

.45x=81

x=180

190*.7=126

The function F(s) can be rewritten as F(s) = (2e^(-2s)(s - 1)) / ((s - 1)^2 + 1). Now we can identify it as the Laplace transform of a function multiplied by an exponential, which corresponds to a shift in the time domain.

Let G(s) = 2(s - 1) / ((s - 1)^2 + 1), then F(s) = e^(-2s)G(s). To find the inverse Laplace transform of G(s), we can use the formula for the inverse Laplace transform of functions in the form of K(s - a) / ((s - a)^2 + b^2), which corresponds to K * e^(at) * sin(bt).

The inverse Laplace transform of G(s) = 2 * e^t * sin(t). Therefore, the inverse Laplace transform of F(s) is found by shifting the time domain of G(s) by 2 units, due to the e^(-2s) term.

To find the inverse Laplace transform of F(s) = [2(s − 1)e^−2s] / ( s^2 − 2s + 2 ), we first need to factor the denominator using the quadratic formula:

s = [2 ± sqrt(2^2 - 4(1)(2))] / 2
s = 1 ± j

So the denominator can be written as:

s^2 - 2s + 2 = (s - (1 + j))(s - (1 - j))

Now we can use partial fractions to simplify the expression:

[2(s − 1)e^−2s] / ( s^2 − 2s + 2 ) = A / (s - (1 + j)) + B / (s - (1 - j))

Multiplying both sides by (s - (1 + j))(s - (1 - j)), we get:

2(s - 1)e^(-2s) = A(s - (1 - j)) + B(s - (1 + j))

Setting s = 1 + j, we get:

2(1 + j - 1)e^(-2(1 + j)) = A(1 + j - (1 - j))

Simplifying and solving for A, we get:

A = -j e^(2 - 2j)

Setting s = 1 - j, we get:

2(1 - j - 1)e^(-2(1 - j)) = B(1 - j - (1 + j))

Simplifying and solving for B, we get:

B = j e^(2 + 2j)

Now we can rewrite F(s) as:

F(s) = -j e^(2 - 2j) / (s - (1 + j)) + j e^(2 + 2j) / (s - (1 - j))

Taking the inverse Laplace transform of each term, we get:

f(t) = -j e^(2 - 2j) e^(t - (1 + j)t) + j e^(2 + 2j) e^(t - (1 - j)t)

Simplifying, we get:

f(t) = e^(t - j*t) - e^(t + j*t)

Therefore, the inverse Laplace transform of F(s) is f(t) = e^(t - j*t) - e^(t + j*t).

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The directional derivative of f at point (2,1,1) in the direction of vector [tex]\hat{i} -2 \hat{j}+3\hat{k}[/tex] is [tex]-4/\sqrt{14}[/tex].

To find the directional derivative of f(x,y,z)=xy³+yz³ at point (2,1,1) in the direction of the vector [tex]\hat{i} -2 \hat{j}+3\hat{k}[/tex], we first need to find the unit vector in the direction of this vector.

The magnitude of the vector is [tex]\sqrt{(1^2+(-2)^2+3^2)} = \sqrt{14}[/tex], so the unit vector in the direction of [tex]\hat{i} -2 \hat{j}+3\hat{k}[/tex] is:
[tex](1/\sqrt{14})\hat{i} - (2/\sqrt{14})\hat{j} + (3/\sqrt{14})\hat{k}[/tex]

Next, we need to find the gradient of f at point (2,1,1):
grad(f) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y³, 3xy² + z³, 3yz²)

Evaluated at (2,1,1), this becomes:

grad(f)(2,1,1) = (1, 7, 3)

Finally, we can find the directional derivative by taking the dot product of the unit vector in the direction of [tex]\hat{i} -2 \hat{j}+3\hat{k}[/tex] with the gradient of f:

D_∆u f(2,1,1) = grad(f)(2,1,1) · u = (1, 7, 3) · [tex](1/\sqrt{14})\hat{i} - (2/\sqrt{14})\hat{j} + (3/\sqrt{14})\hat{k}[/tex]

Simplifying, we get:

D_∆u f(2,1,1) = [tex](1/\sqrt{14}) - (14/\sqrt{14}) + (9/\sqrt{14}) = -4/\sqrt{14}[/tex]

Therefore, the directional derivative of f at point (2,1,1) in the direction of vector [tex]\hat{i} -2 \hat{j}+3\hat{k}[/tex] is [tex]-4/\sqrt{14}[/tex].

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The height of the flagpole when marci who is 5 feet tall is standing in lines of sight to the top and bottom of the pole is 20 feet.

To estimate the height of the flagpole, we can use trigonometry.

Let's call the height of the flagpole "h" and the distance from Marci to the base of the pole "d".

We can set up a right triangle with the flagpole as the hypotenuse, Marci's height as one leg, and the distance from Marci to the base of the pole as the other leg.

Using the tangent function, we can say:

tan(θ) = perpendicular/base

In this case, the opposite is Marci's height (5 feet) and the adjacent is the distance from Marci to the base of the pole (d).

We don't know the angle yet, but we can use the fact that the angle formed by Marci's lines of sight to the top and bottom of the pole is the same as the angle formed by the top of the pole, Marci's eye, and the base of the pole (since these are alternate interior angles).

Let's call this angle "x".
So, we have:
tan(x) = 5/d
To find the height of the pole, we need to use another trig function. Since we know the adjacent and the hypotenuse, we can use the cosine function:
cos(x) = base/hypotenuse

In this case, the adjacent is still d and the hypotenuse is h + 5 (since Marci's height is included in the overall height of the flagpole).

So we have:

cos(x) = d/(h + 5)

We can rearrange this equation to solve for h:

h = (d/cos(x)) - 5

Now we just need to find the value of x.

We know that the tangent of x is 5/d, so we can use the inverse tangent function (tan^-1) to find x:

x = tan^-1(5/d)

Plugging this into the equation for h, we get:

h = (d/cos(tan^-1(5/d))) - 5

We can simplify this a bit by using the identity:

cos(tan^-1(x)) = 1/√(1 + x^2)

So we have:

h = (d * √(1 + (5/d)²)) - 5

Now we just need to plug in the values given in the problem. Let's say that Marci stands 20 feet away from the base of the pole. Then we have:

h = (20 * √(1 + (5/20)²)) - 5

h = 19 feet (rounded to the nearest foot)

So the answer is (b) 20 feet.

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The value of γ is greater than 1 for any v > 0, greater than 10 for v > 0.995c, and greater than 100 for v > 0.99995c.

To determine for what speed (in terms of c) the value of γ is greater than 1, 10, and 100, we'll use the formula for the Lorentz factor (γ):
γ = 1 / √(1 - v²/c²)
where v is the speed and
c is the speed of light.

(a) For γ > 1:
Since γ is always greater than 1 for any speed v greater than 0, we can say that γ is appreciably greater than 1 for any v > 0.

(b) For γ > 10:
We need to solve the equation 10 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 100 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/100 = 99/100.
So, v/c = √(99/100), which implies v > 0.995c for γ > 10.

(c) For γ > 100:
Similar to (b), solve the equation 100 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 10000 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/10000 = 9999/10000.
So, v/c = √(9999/10000), which implies v > 0.99995c for γ > 100.

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Answer:

y = 3/2x + 3

Step-by-step explanation:

Slope =

y = mx + b

y-intercept = 3

Slope = 3/2,

y = 3/2x + 3

(a) The implicit differentiation of 7x²-y² = 9 is 7x / y.
(b) The explicit differentiation of y' in terms of x is ±(7x / √(7x² - 9)).

(a) Given the equation 7x² - y² = 9, we want to find y' by implicit differentiation.
1: Differentiate both sides of the equation with respect to x.
d(7x² - y²)/dx = d(9)/dx

2: Apply the differentiation rules.
14x - 2yy' = 0 (Here, we used the chain rule for differentiating y^2, i.e., d(y²)/dx = 2y(dy/dx) = 2yy')

3: Solve for y'.
2yy' = 14x
y' = 14x / (2y)
y' = 7x / y

So, the implicit differentiation of y' is 7x / y.

(b) Now, we will solve the equation explicitly for y and differentiate to get y' in terms of x.

1: Solve the equation 7x² - y² = 9 for y.
y^2 = 7x² - 9
y = ±√(7x² - 9)

2: Differentiate both sides with respect to x.
For the positive square root:
y = √(7x²- 9)
y' = d(√(7x² - 9))/dx

Using the chain rule:
y' = (1/2) * (7x²- 9)-¹/² * 14x
y' = 7x / √(7x² - 9)

For the negative square root :
y = -√(7x²- 9)
y' = d(-√(7x² - 9))/dx

Using the chain rule:
y' = -(1/2) * (7x² - 9)^-¹/² * 14x
y' = -7x / √(7x² - 9)

So, the explicit differentiation of y' in terms of x is ±(7x / √(7x² - 9)).

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If the area of the base of the rectangular prism is 36.8 in2 and the height is 8.5 in, the volume is

The measurement of three-dimensional space is volume. It is frequently quantified numerically by various imperial or US customary units, SI-derived units, or both.

V=Bh, where B is the base area and h is the height, is the formula for a prism's volume. Volume (V) = base area height of the prism is the formula for calculating the volume of a rectangular prism.

Volume = l w h is another way to state this equation, where l is the prism's length, w is its width, and h is its height.

Volume = base x height

V = 36.8 x 8.5 = 312.8

Therefore, the volume of the rectangular prism is

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To design an arithmetic logic circuit to perform the addition of the binary numbers 11011 and 10111, follow these steps:

1. Identify the binary numbers to be added: 11011 and 10111.

2. Create a circuit with five full adders (FA) connected in series. Full adders are required because we need to add two binary numbers and account for any carry generated during the addition process.

3. Connect the least significant bits (LSB) of both binary numbers to the input of the first full adder (FA1). In this case, the LSBs are 1 (from 11011) and 1 (from 10111).

4. Connect the carry output (Cout) of FA1 to the carry input (Cin) of the second full adder (FA2).

5. Repeat the process of connecting the binary inputs and carry outputs for the remaining full adders (FA3, FA4, and FA5) in the series.

6. The sum outputs (S) of each full adder represent the resulting binary sum of the two input numbers.

By following these steps, your arithmetic logic circuit will successfully perform the addition of the binary numbers 11011 and 10111.

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To prove the identity (A+B) A + AB) = B using a truth table, we need to create a table that lists all possible combinations of truth values for the variables A and B, and then evaluate the expression on both sides of the equation for each of those combinations.

Here's how we can set up the truth table:

| A | B | A+B | (A+B)A | AB | (A+B)A + AB | B |
|---|---|-----|-------|----|------------|---|
| 0 | 0 |  0  |   0   |  0 |      0     | 0 |
| 0 | 1 |  1  |   0   |  0 |      0     | 1 |
| 1 | 0 |  1  |   1   |  0 |      1     | 0 |
| 1 | 1 |  1  |   1   |  1 |      2     | 1 |

In the table above, the column "A+B" represents the logical OR operation between A and B, which yields a result of 1 if either A or B is true (or both), and 0 otherwise. The column "(A+B)A" represents the logical AND operation between (A+B) and A, which yields a result of 1 only if both (A+B) and A are true. The column "AB" represents the logical AND operation between A and B, which yields a result of 1 only if both A and B are true. The column "(A+B)A + AB" represents the sum of the previous two columns. Finally, the column "B" represents the expected result of the expression on the right-hand side of the equation.

To evaluate the expression on the left-hand side of the equation, we substitute the values of A and B for each row of the table, and compute the result. For example, for the first row where A=0 and B=0, we have:

(A+B) A + AB = (0+0) * 0 + 0 * 0 = 0

We do the same for all the other rows, and fill in the corresponding values in the "(A+B)A + AB" column. The final step is to compare this column with the "B" column, and check whether they have the same values for all rows. If they do, then the identity is proven.

In our case, we see that the values in the "(A+B)A + AB" column and the "B" column are the same for all rows, which means that the identity holds true:

| A | B | A+B | (A+B)A | AB | (A+B)A + AB | B |
|---|---|-----|-------|----|------------|---|
| 0 | 0 |  0  |   0   |  0 |      0     | 0 |
| 0 | 1 |  1  |   0   |  0 |      0     | 1 |
| 1 | 0 |  1  |   1   |  0 |      1     | 0 |
| 1 | 1 |  1  |   1   |  1 |      2     | 1 |

Therefore, we can conclude that (A+B) A + AB) = B is indeed an identity.
To prove the identity (A+B)(A+AB) = B using a truth table, we will consider all possible combinations of A and B (true or false) and evaluate both sides of the equation. Here's the truth table:

A | B | A+B | AB | A+AB | (A+B)(A+AB) | B
--|---|-----|----|------|------------|--
T | T |  T  |  T |   T  |      T     | T
T | F |  T  |  F |   T  |      F     | F
F | T |  T  |  F |   F  |      T     | T
F | F |  F  |  F |   F  |      F     | F

In the table, T represents true, and F represents false. We can see that the values in the (A+B)(A+AB) column are equal to the values in the B column for all combinations of A and B. This proves the identity (A+B)(A+AB) = B.

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According to the derivative, the critical points are (0,0) and (0,0) along with any point of the form (3y, y) where y is any real number.

Derivatives are an essential concept in calculus that help us analyze the behavior of a function. In this problem, we are given a two-variable function f(x,y) and asked to find its critical points and classify them using the second derivative test. Critical points are the points where the partial derivatives of the function are zero or undefined.

To find the critical points of f(x,y) = x³ – 3x³y, we need to find the partial derivatives with respect to x and y and set them equal to zero.

Taking the partial derivative of f(x,y) with respect to x, we get:

fx = 3x² - 9xy

Similarly, taking the partial derivative of f(x,y) with respect to y, we get:

fy = -3x³

Setting fx and fy equal to zero and solving for x and y, we get:

3x² - 9xy = 0 --> 3x(x - 3y) = 0 --> x = 0 or x = 3y

-3x³ = 0 --> x = 0

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Answer:

If I am correct and you need to find R then R equals 13

Step-by-step explanation:

I got this answer by doing 2 x 1/2 which is 1. Then I did 1 x 13 to get 13 and that is what R is.

To solve this problem using Boolean algebraic manipulation, we can start by using the identity A + AB = A, which is called the absorption law.

We know that AB = 0, which means that either A or B (or both) must be equal to 0. This allows us to simplify the expression A + B = 1 to either A = 1, B = 0 or A = 0, B = 1.

Let's assume A = 1, B = 0 (the other case can be solved similarly).

Substituting these values into the expression (A + C)(A + B)(B + C), we get:
(1 + C)(1 + 0)(0 + C)

Simplifying further, we get:
(1 + C)(0 + C)

Expanding this using the distributive law, we get:
0C + C + 1C + C^2

Simplifying again, we get:
2C + C^2

Now, we need to show that this expression is equal to BC. Using the fact that AB = 0, we can rewrite B as B = AB' (where B' means the complement of B).

Substituting this into the expression BC, we get:
AB'C

Now, using the distributive law again, we get:
A'B'C + AB'C

Since AB = 0, we can simplify this further to:
A'B'C

Comparing this with our previous expression 2C + C^2, we can see that they are equal if C = A'B'.

Therefore, we have shown that (A + C)(A + B)(B + C) = BC if C = A'B'.

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The ladder forms a right triangle with the wall and the ground, with the ladder being the hypotenuse. Let the angle between the ladder and the wall be theta. Then we have:

cos(theta) = adjacent/hypotenuse = x/13
sin(theta) = opposite/hypotenuse = (13-y)/13

We want to find the path followed by point P located 2 feet from the top of the ladder. Let's call the coordinates of point P (x,y). We know that:

y + 2 = 13 sin(theta)

Substituting sin(theta) from above, we get:

y + 2 = 13(1 - cos(theta))

y = 13 - 13cos(theta) - 2

y = 11 - 13cos(theta)

Similarly, we can find x:

x = 13 cos(theta) - 2cos(theta)

x = 11cos(theta)

Therefore, the parametric equations for the path followed by point P are:

x = 11cos(theta)
y = 11 - 13cos(theta)

So the answer is (11cos(theta), 11-13cos(theta)) in terms of the angle theta.

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So the area of the triangle is 3 square units.

To solve this problem, we first need to identify the base and height of the triangle.

The base of the triangle is the line segment connecting the points (5,4) and (8,-1). We can find the length of this base by using the distance formula:

Distance between two points (x1, y1) and (x2, y2) is given by:

[tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

Base length:

[tex]d = \sqrt((8 - 5)^2 + (-1 - 4)^2)[/tex]

[tex]= \sqrt(3^2 + (-5)^2)[/tex]

[tex]= \sqrt(9 + 25)[/tex]

[tex]= \sqrt(34)[/tex]

So the base length of the triangle is sqrt(34).

To find the height of the triangle, we need to find the perpendicular distance from the vertex (2,-1) to the base. We can use the formula for the distance from a point to a line to find the height:

Distance between a point (x1, y1) and a line [tex]Ax + By + C = 0[/tex] is given by:

[tex]h = |Ax1 + By1 + C| / \sqrt(A^2 + B^2)[/tex]

We can find the equation of the line containing the base by using the slope-intercept form:

Slope of the line containing the base:

[tex]m = (y2 - y1) / (x2 - x1)[/tex]

[tex]= (-1 - 4) / (8 - 5)[/tex]

[tex]= -5/3[/tex]

Intercept of the line containing the base:

[tex]y - y1 = m(x - x1)\\\\= y - 4 = (-5/3)(x - 5)\\\\= y = (-5/3)x + (35/3)[/tex]

So the equation of the line containing the base is:

5x + 3y - 35 = 0

Now we can substitute the coordinates of the vertex (2,-1) into the formula for the distance from a point to a line to find the height:

Height:

[tex]h = |5(2) + 3(-1) - 35| / \sqrt(5^2 + 3^2)[/tex]

[tex]= 6 / \sqrt(34)[/tex]

So the height of the triangle is 6/sqrt(34).

Finally, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

Area:

Area = (1/2) * sqrt(34) * (6/sqrt(34))

= 3

So the area of the triangle is 3 square units.

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Answer: (D) - Interest is calculated using average daily balances.

Step-by-step explanation: Credit card companies typically calculate interest using the average daily balance method. This method takes the sum of the outstanding balance at the end of each day in the billing cycle and divides it by the number of days in the cycle to get the average daily balance. The interest is then calculated based on this average daily balance.

a) The corresponding z-score is 0.5 and the direction is to the right.

b) The percentage of adult spiders that have carapace lengths exceeding 19 mm is 30.85%.

If the area under the standard normal curve that lies to the right of nothing is 50%, then the z-score corresponding to this area is 0.

To find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 19 mm, we need to determine the area under the standard normal curve to the right of 19 mm and then find the corresponding z-score using a standard normal distribution table or calculator.

Assuming a normal distribution of carapace lengths of adult spiders, we need to standardize the value of 19 mm by subtracting the mean and dividing by the standard deviation. If we assume that the mean carapace length of adult spiders is 18 mm with a standard deviation of 2 mm, we can calculate the z-score as follows

z = (19 - 18) / 2 = 0.5

This means that a carapace length of 19 mm is 0.5 standard deviations above the mean. To find the area under the standard normal curve to the right of 19 mm, we can use a standard normal distribution table or calculator, which gives us an area of 0.3085.

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The final answer based on the given information, the correct answer is D.

Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values (predictors). This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model). This is appropriate when the response variable has a normal distribution.

The relationship between the data points on the normal probability plot is approximately linear, which suggests that the variable under consideration is not normally distributed. A normal probability plot of a normally distributed variable would show a straight line, but the plot shown in this question appears to have a slight curve. Therefore, the variable is probably not normally distributed.

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To combine the component integrals into a whole vector, you need to integrate each component with respect to the given variable, in this case, 't'. You have provided the components as:

1. 10
2. t^2 * j
3. 9t^8
4. t^9 * k

Now, integrate each component with respect to 't':

1. ∫(10 dt) = 10t
2. ∫(t^2 dt) * j = (t^3/3) * j
3. ∫(9t^8 dt) = (9/9) * t^9 = t^9
4. ∫(t^9 dt) * k = (t^10/10) * k

Now, combine the integrated components into a whole vector:

Vector = 10t * i + (t^3/3) * j + t^9 * k + (t^10/10) * k

Thus, the combined integral vector is:

Vector = 10t * i + (t^3/3) * j + (t^9 + t^10/10) * k

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The z-score for x = 90 is z = 1.50, which means that a value of 90 is 1.50 standard deviations above the mean.

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If X has a mean of 6 and a Poisson distribution. We may determine that k = 4 results in a probability of 0.4098, a value less than 0.45, using a Poisson probability calculator.To guarantee that students have plenty to read during the flight, the professor must bring at least 5 papers.

The professor reads papers for an average of thirty minutes per paper, according to a Poisson process. This indicates that there is an exponential distribution with a mean reading interval of 30 minutes.

The professor will have a period of three hours (180 minutes) to study the papers throughout the journey. The number of papers the professor can read in this amount of time can be predicted using a distribution based on with a mean of 180/30 = 6.

In order to keep the probability that we'll run out of papers to read below 0.45, we need to determine how few pages the professor should bring. Accordingly, we must choose the smallest number k such that: P(X <= k) < 0.45

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the equation you get by taking the Laplace transform of the differential equation and solving for Y(s)=  (-7/74)e^9t + (9/74)e^-5t + (17/74)sin(6t) + (5/37)cos(6t)

To begin, let's take the Laplace transform of both sides of the differential equation:

L{y″} - 4L{y′} - 45L{y} = L{sin(5t)}

Using the properties of the Laplace transform, we can simplify this expression:

s^2 Y(s) - s y(0) - y′(0) - 4(s Y(s) - y(0)) - 45Y(s) = 5/(s^2 + 25)

Substituting in the initial conditions, we get:

s^2 Y(s) + 3s + 7 - 4s Y(s) + 12 - 45Y(s) = 5/(s^2 + 25)

Combining like terms, we get:

Y(s) = (5/(s^2 + 25) + 3s + 19)/(s^2 - 4s - 45)

Now we need to use partial fraction decomposition to simplify this expression:

Y(s) = (A/(s - 9) + B/(s + 5)) + (C s + D)/(s^2 - 4s - 45)

Multiplying both sides by the denominator, we get:

5 = A(s + 5) + B(s - 9) + (C s + D)(s^2 - 4s - 45)

Substituting s = 9, we get:

5 = 14B - 36D

Substituting s = -5, we get:

5 = -4A - 26C - 80D

Solving these equations for A, B, C, and D, we get:

A = -7/74, B = 9/74, C = 17/74, D = -5/37

Substituting these values back into our expression for Y(s), we get:

Y(s) = (-7/74)/(s - 9) + (9/74)/(s + 5) + (17/74)s/(s^2 - 4s - 45) - (5/37)/(s^2 - 4s - 45)

Now we can take the inverse Laplace to transform to get y(t):

y(t) = (-7/74)e^9t + (9/74)e^-5t + (17/74)sin(6t) + (5/37)cos(6t)

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The equation that represents the function is B. f(x) = -2x² - 4x + 7.

A function is a relation between two sets of elements, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the range).

We know that the vertex of the quadratic function is at (-1,9), which means that the axis of symmetry is x = -1. Therefore, the x-coordinate of the two points (-2,7) and (0,7) must be equidistant from the axis of symmetry.

The distance between x=-1 and x=-2 is 1, and the distance between x=-1 and x=0 is also 1. Therefore, the quadratic function must have a symmetric form with respect to the axis x=-1. It must be a quadratic function that has the vertex form:

f(x) = a(x - (-1))² + 9

where "a" is the coefficient that determines whether the parabola opens upward or downward. To find "a", we can use one of the points that the function passes through. Let's use the point (-2,7):

f(-2) = a(-2 - (-1))² + 9 = 7

Simplifying this equation, we get:

a + 9 = 7

a = -2

Therefore, the quadratic function is:

f(x) = -2(x + 1)² + 9

Expanding this equation, we get:

f(x) = -2(x² + 2x + 1) + 9

f(x) = -2x² - 4x + 7

So, the answer is B. f(x) = -2x² - 4x + 7.

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Answer:

m=30

Step-by-step explanation:

Answer: m = 30

Step-by-step explanation: The equation 7m = 210 can be solved for the value of m by isolating m on one side of the equation.

To do this, we can divide both sides of the equation by 7, since dividing by 7 is the inverse operation of multiplying by 7.

So, 7m/7 = 210/7, which simplifies to m = 30.

Therefore, the value of m that makes the equation true is 30.

Answer:

12 cm

Step-by-step explanation:

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Where the above conditions are given with regard to the identity matrix, F(A) = [7 14 31]

To calculate F(A), we need to first compute A² and 5A.

A² = [211013111] x [211013111] = [14 19 36]

[21 33 48]

[21 32 47]

5A = 5 x [211013111] = [10 5 5]

[15 25 10]

[15 20 35]

Now we can substitute these matrices into the expression for F(A):

F(A) = A² - 5A + 3I = [14 19 36] - [10 5 5] + [3 0 0]

[21 33 48] - [15 25 10] + [0 3 0]

[21 32 47] - [15 20 35] + [0 0 3]

F(A) = [7 14 31]

[6 11 41]

[6 12 16]

Therefore, F(A) = [7 14 31]

[6 11 41]

[6 12 16]

To calculate F(x), we simply substitute x = 2, 1, and 3 into the expression for F(x):

F(2) = 2² - 5(2) + 3 = -3

F(1) = 1² - 5(1) + 3 = -1

F(3) = 3² - 5(3) + 3 = 1

Therefore, F(2) = -3, F(1) = -1, and F(3) = 1.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Given matrix A = [211013111]
Can you calculate value of F(A)?
F(A) = A² - 5A + 3I

and

F(x) = x² - 5x +3

Where , I is an Identity matrix.

Maximise p = 3x + y

subject to 2x - 9y ≤0

9x - 2y ≥ 0

x + y ≤11

x ≥0, y≥0

P = 3x + y,  x = 5, y = 6, P = 33

This is possible to rewrite the first restriction, 2x - 9y ≤ 0, as 9y≤ 2x. Since x 0, it follows that y ≤ 2/9x. It is possible to rewrite the second restriction, 9x - 2y ≤  0, as 2y ≤ 9x.

This suggests that y ≤ 9/2x. When these two restrictions are combined, we have y min(2/9x, 9/2x), which is 2/9x.

Now that we have the limits, we may draw the area that is viable. The lines x + y = 11, 9y = 2, and 2y = 9x make up the viable region's boundary. A line with a slope of 3 and a y-intercept of 0 represents the goal function.

At the point when the feasible region's edge meets the goal function, the best solution is found. It is clear that the ideal situation happens when x and y are both equal to six. They are plugged into the goal, yielding p = 3x + y = 33.

Complete Question:

Maximise p = 3x + y

subject to 2x - 9y ≤0

9x - 2y ≥ 0

x + y ≤11

x ≥0, y≥0

p=_____ x=______ y=______

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56.78 (rounded to two decimal places). To evaluate y' at the point (2, 2) for the given equation, we need to find the derivative of y with respect to x and then substitute x=2 and y=2.

To find the derivative of y, we need to use implicit differentiation. Taking the derivative of both sides with respect to x, we get:

e^y(dy/dx) + 0 - 0 = 10x + 4yy'

Simplifying this expression, we get:

e^y(dy/dx) = 10x + 4yy'

Dividing both sides by e^y, we get:

dy/dx = (10x + 4yy')/e^y

Now we can substitute x=2 and y=2:

dy/dx = (10(2) + 4(2)y')/e^2

dy/dx = (20 + 8y')/e^2

So y' at (2, 2) is:

y' at (2, 2) = (20 + 8y')/e^2 = (20 + 8(2))/e^2 = 56.78 (rounded to two decimal places)

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Let A be the event that at least one die lands on a 6, and let B be the event that the two dice land on different numbers. We want to find P(A|B), the conditional probability of A given B.

To start, we can find the probability of B:

P(B) = 1 - P(both dice land on the same number)

Since each die can land on any number from 1 to 6 with equal probability, the probability of both dice landing on the same number is 1/6. Therefore, we have:

P(B) = 1 - 1/6 = 5/6

Next, we can find the probability of A and B:

P(A and B) = P(at least one die lands on a 6 and the two dice land on different numbers)

If one die lands on a 6, then the other die must land on one of the 5 remaining numbers. Therefore, the probability of A and B is:

P(A and B) = P(one die lands on a 6) * P(the other die lands on a number different from the first) = (1/6) * (5/6) = 5/36

Now we can use Bayes' theorem to find P(A|B):

P(A|B) = P(A and B) / P(B)

Plugging in the values, we get:

P(A|B) = (5/36) / (5/6) = 1/6

Therefore, the conditional probability that at least one die lands on a 6 given that the two dice land on different numbers is 1/6.

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the formula for the function's inverse.f(x)=6x where y=f(x).f−1(y)=f(x)=3(2.3)x where y=f(x).f−1(y)=f(x)=log(x21) where y=f(x).f−1(y)=  the inverse function is f^(-1)(y) = (10^y)^(1/21).

the formulas for the inverses of the given functions:

1. For f(x) = 6x, we can find the inverse by setting y = 6x and solving for x in terms of y:

y = 6x
x = y/6

So the formula for the inverse function, f^-1(y), is:

f^-1(y) = y/6

2. For f(x) = 3(2.3)^x, we can use logarithms to find the inverse:

y = 3(2.3)^x
log(2.3)(y/3) = x

So the formula for the inverse function is:

f^-1(y) = log(2.3)(y/3)

3. For f(x) = log(x^2 + 1), we can use the fact that the inverse of a logarithmic function is an exponential function:

y = log(x^2 + 1)
x^2 + 1 = 10^y
x = sqrt(10^y - 1)

So the formula for the inverse function is:

f^-1(y) = sqrt(10^y - 1)

1. For the function f(x) = 6x, we have y = 6x. To find the inverse, we'll solve for x in terms of y:

y = 6x
x = y/6

So, the inverse function is f^(-1)(y) = y/6.

2. For the function f(x) = 3(2.3)^x, we have y = 3(2.3)^x. To find the inverse, we'll solve for x in terms of y:

y = 3(2.3)^x
y/3 = 2.3^x
log(2.3)(y/3) = x

So, the inverse function is f^(-1)(y) = log(2.3)(y/3).

3. For the function f(x) = log(x^21), we have y = log(x^21). To find the inverse, we'll solve for x in terms of y:

y = log(x^21)
10^y = x^21
x = (10^y)^(1/21)

So, the inverse function is f^(-1)(y) = (10^y)^(1/21).

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