Principal: $4,000
Rate: 7.25%
Time: 8 years
How much money will need to be paid back to the bank for this loan?

Answer:

angle mkn and okn

Step-by-step explanation:

beacuse both of them are 90 degree to each other and hence the sum of two 90 degree angle is 180 which is supplementary

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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The vectors uvt and vut are related by a simple matrix transposition.

In other words, if we consider u, v, and t as columns of a matrix, say A, then uvt is simply the product of A and the vector [1 0 1] (a column vector with 1's in the first and third rows and 0 in the second row).

On the other hand, vut is the product of the transposed matrix of A (denoted as A^T) and the vector [1 0 1]. Therefore, uvt and vut are related as follows:

vut = (A^T) [1 0 1]

In summary, uvt and vut are related through a matrix transposition, with vut being the product of the transposed matrix of A and the vector [1 0 1].

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The given statement "the quantity represented by x is a function that changes over time i.e. is not constant" is false.

The statement "the quantity represented by x is a function that changes over time i.e. is not constant" is not true. A function is a set of ordered pairs of numbers (x, y) such that each x corresponds to exactly one y value.

In other words, for a given value of x, there is only one corresponding value of y, which implies that it cannot change over time. Therefore, if x is a function, it is constant. Hence the statement is false.

Conclusion :The given statement "the quantity represented by x is a function that changes over time i.e. is not constant" is false. A function is a set of ordered pairs of numbers (x, y) such that each x corresponds to exactly one y value. Therefore, if x is a function, it is constant.

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It took both Sandy and Tom 54 seconds to cover the same distance.

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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To make a stem-and-leaf display, we will separate the ages into stems based on the tens digit and leaves based on the ones digit.

Therefore, the stem-and-leaf display of the age distribution is:

1 | 6

2 | 6 8 9

3 | 3 7 8

4 | 1 3 6 7 8 9

5 | 3 5

6 | 3 4 5 8

A stem-and-leaf display is a graphical representation of a set of data. It is a way to organize and display data in a way that allows for easy interpretation and comparison of the data.

In a stem-and-leaf display, the data is separated into two parts: the stem and the leaf. The stem represents the tens digit of each data point, and the leaf represents the ones digit. For example, the number 47 would be represented as a stem of 4 and a leaf of 7.

The stems are listed vertically, and the leaves are listed horizontally next to their respective stems. The leaves are usually listed in increasing order.

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Answer:

z = -70

Explanation:

-12.2z-13.4z=1792

-25.6z=1792

Divide both sides by (-25.6)

z = -70

Answer:

16 or 8

Step-by-step explanation:

I'm not sure if this are right

Answer:

x=-6

Step-by-step explanation:

For the function f(x,y)=x3−3x+3xy2,

(0,0) - a critical point of undetermined nature

(0,1) - a saddle point

(0,-1) - a saddle point

and there are no local maxima or local minima.

To find the local maximum and minimum values and saddle points of the function f(x,y)=x3−3x+3xy2, we need to first find its critical points.

To find the critical points of f(x,y), we need to solve the system of equations given by setting the partial derivatives of f(x,y) with respect to x and y equal to zero:

∂f/∂x = 3x2 - 3 + 3y2 = 0

∂f/∂y = 6xy = 0

From the second equation, we get either x=0 or y=0.

If x=0, then the first equation becomes 3y^2-3=0, which gives y=±1. Substituting these values of x and y back into f(x,y), we get the critical points (0,1) and (0,-1).

If y=0, then the second equation becomes x=0. Substituting this value of x back into f(x,y), we get the critical point (0,0).

So, we have three critical points: (0,0), (0,1), and (0,-1).

Now, we need to classify these critical points as local maxima, local minima, or saddle points. To do this, we can use the second partial derivative test.

The Hessian matrix of f(x,y) is given by:

H(x,y) =

[6x 6y]

[6y 6x+6]

At the critical point (0,0), we have H(0,0) =

[0 0]

[0 6]

The determinant of H(0,0) is 0, and the eigenvalues are 0 and 6. Since the determinant is 0, we cannot conclude whether (0,0) is a local maximum, local minimum, or saddle point using the second partial derivative test. Instead, we can use other methods to determine the nature of this critical point.

At the critical point (0,1), we have H(0,1) =

[0 6]

[6 6]

The determinant of H(0,1) is -36, and the eigenvalues are approximately -4.59 and 10.59. Since the determinant is negative and the eigenvalues have opposite signs, we can conclude that (0,1) is a saddle point.

At the critical point (0,-1), we have H(0,-1) =

[0 -6]

[-6 6]

The determinant of H(0,-1) is 36, and the eigenvalues are approximately -10.59 and 4.59. Since the determinant is positive and the eigenvalues have opposite signs, we can conclude that (0,-1) is also a saddle point.

Therefore, the critical points of f(x,y) are:

(0,0) - a critical point of undetermined nature

(0,1) - a saddle point

(0,-1) - a saddle point

So, there are no local maxima or local minima for the function f(x,y)=x3−3x+3xy2.

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Answer:

it increases by 6 cents for every mile driven plus the initial 105 dollars

Step-by-step explanation:

brainliest plzzzz

Answer:

Hope this helps.

The lengths of the sides are: AP = 7cm BC = 6cm BX = 28/3 cm and

QN = 12cm.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since triangles P and Q are similar, their corresponding sides are proportional. That means:

AP/PN = BX/QN

We know that AP = 7cm and PN = 9cm, so we can substitute those values:

7/9 = BX/QN

We also know that QC = 6cm, so we can find QN by subtracting CN from QC:

QN = QC - CN

QN = 18cm - 6cm

QN = 12cm

Now we can solve for BX:

7/9 = BX/12

Multiplying both sides by 12, we get:

BX = 84/9

Simplifying, we get:

BX = 28/3 cm

Therefore, the lengths of the sides are:

AP = 7cm

BC = 6cm

BX = 28/3 cm

QN = 12cm

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Complete question:

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer:

well that's already the slope and your i-intercept would be -6

Step-by-step explanation:

It takes 4 weeks at minimum for each pair to hug at least once if they sit in random order.

Analyzing the Given Information

As per the given information,

Number of people = 8

It is given that they sit in random order every week.

W e assume that the order is not repeated.

There are 4 pairs and since a person hugs both the persons on his immediate left and right.

Determining the Number of Weeks

Total number of people to be hugged by each person = 7

Number of people hugged by a person in one week = 2

So, number of weeks taken by each to huge every other person = 7/2

⇒ It will take (3 +1) for every pair to hug.

It takes 4 weeks at a minimum for every pair to hug if we assume that  their order is not repeated.

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Answer:

1170 m^3

Step-by-step explanation:

Just compute 13x18x5. The formula for volume of a rectangular prism is length times width times height.

Answer:

E (The product of seven and the difference of b minus two)

Step-by-step explanation:

Answer:

tru

Step-by-step explanation:

Answer:

9 No explanation needed

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{24}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{24}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 16 }{ 2 } \implies 8\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 8}(x-\stackrel{x_1}{1}) \\\\\\ y-8=8x-8\implies {\Large \begin{array}{llll} y=8x \end{array}}\)

Answer:

\(y=8x\)

Step-by-step explanation:

We can see that this line has a constant of proportionality. That is — x is proportional to y and vice versa. This means that the equation for the line's equation will be in the form:

\(y = mx\)

where \(m\) is the ratio of x to y.

This ratio is also known as the line's slope. We can solve for the slope using the equation:

slope = rise / run

slope = \(\Delta\)y / \(\Delta\)x

slope = 8 / 1

slope = 8

\(m=8\)

So, the equation of the line is:

\(y=mx\)

\(\boxed{y=8x}\)

Answer:

y ≤ 11

Step-by-step explanation:

7y ≤ 33 + 4y

3y ≤ 33

y ≤ 11

So, the answer is y ≤ 11

Answer:

Consider the original trapezoid and the reduction. A trapezoid has corresponding side lengths of 13. 5 centimeters and 9 centimeters. Side A corresponds to a side with length 3 centimeters. Figures not drawn to scale. What is the length of side A, in centimeters, on the reduced trapezoid? 1 1. 5 2 2004. 5.

Step-by-step explanation:

Answer:

165 minutes is how long it would take

Answer:

11×15

lbs× minutes per lbs

Answer:

\(5m+8=16\)

Step-by-step explanation:

\(5m+8=16 \\ \\ 5m=8 \\ \\ m=1.6 \neq 2\)

Answer:

I think it is 4 white and 3 blue

Step-by-step explanation:

Because they have 3 cups of white then 6 cups of white so i think they multiplied it. Then they have 4 cups of blue then 8 cups of blue. So if you multiply it, it will give you the answer. I hope this is right and it helped and can you mark me brainliest!!!!!!!!

it is estimated that approximately 4032 carrots out of the 5000 measured fall between 10 cm and 13 cm in length.

To calculate the estimated number of carrots between 10 cm and 13 cm, we need the values of z1 and z2. Let's calculate them:

Lower bound:

z1 = (10 - 11.5) / 1.15 = -1.3043

Upper bound:

z2 = (13 - 11.5) / 1.15 = 1.3043

Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores.

P(Z < -1.3043) ≈ 0.0968

P(Z < 1.3043) ≈ 0.9032

To find the probability of a carrot falling between 10 cm and 13 cm, we subtract the lower probability from the upper probability:

P(-1.3043 < Z < 1.3043) ≈ 0.9032 - 0.0968 ≈ 0.8064

Finally, we multiply this probability by the total number of carrots (5000) to estimate the number of carrots between 10 cm and 13 cm:

Estimated number of carrots = 0.8064 * 5000 ≈ 4032

Therefore, it is estimated that approximately 4032 carrots out of the 5000 measured fall between 10 cm and 13 cm in length.

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Answer:

THE SLOPE OF THE GRAPH

Step-by-step explanation:

Answer:

the slope of the graph of y = mx+b

Step-by-step explanation

The equation of any straight line can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.