The diameter of a planet is 1280 mi. Find the volume of the planet ?

The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

To learn more about Simplification link is here brainly.com/question/19691064

#SPJ4

Answer:

number 1

Step-by-step explanation:

faster way to it to try to multiple the first to the 2nd one .

(7x+3)(7x-3)

( 7x .7x - 7x.3 ) + ( 3 .7x - 3.3)

49x^2 -21x + 21x - 9

it take you back to the original equation

Answer:

A is correct

Step-by-step explanation:

Total cost function is C(x) = 35x + 2500

Total revenue function is R(x) = 60x

a)

Recall,

total profit = total revenue - total cost

Total profit function would be

P(x) = R(x) - C(x)

P(x) = 60x - (35x + 2500)

P(x) = 60x - 35x - 2500

P(x) = 25x - 2500

b) The break even point is the point where revenue - cost = 0

Revenue = cost

60x = 35x + 2500

60x - 35x = 2500

25x = 2500

x = 2500/25

x = 100

The break even occurs when x = 100

To maximize the integral ∫(b-1)x^2(3-x)dx for b > -1, you need to find the value of b that results in the largest integral value. First, integrate the given function with respect to x:

∫x^2(3-x)dx = ∫(3x^2 - x^3)dx = x^3 - (1/4)x^4 + C

Now, evaluate the definite integral from b-1 to b:

[x^3 - (1/4)x^4] evaluated from b-1 to b.

Substitute the limits of integration:

(b^3 - (1/4)b^4) - ((b-1)^3 - (1/4)(b-1)^4)

To maximize this expression, take the derivative with respect to b:

3b^2 - b^3 - 3(b-1)^2 + (b-1)^3

Now, find the critical points by setting the derivative equal to zero and solving for b:

3b^2 - b^3 - 3(b-1)^2 + (b-1)^3 = 0

Solving this equation for b, you will find the value that maximizes the integral. However, due to the complexity of the equation, it's recommended to use numerical methods or a graphing calculator to find the approximate value of b that maximizes the integral.

To find the value of b that maximizes the integral ∫b−1x2(3−x)dx, we need to use the concept of optimization. First, let's integrate the given function:

∫b−1x2(3−x)dx = [x3/3 - x4/4]b−1 = (1/3)[(b−1)3 − (b−1)4/4]

Now, to find the value of b that maximizes this integral, we need to take the derivative of the integrated function with respect to b and set it equal to zero:

d/dx [(1/3)[(b−1)3 − (b−1)4/4]] = (1/3)[3(b-1)2 - 4(b-1)3/4] = (1/3)(b-1)(3-2b)

Setting this equal to zero and solving for b, we get:

(b-1)(3-2b) = 0
b = 1 or b = 3/2

However, we need to ensure that b > -1, so the only valid solution is:
b = 3/2
Therefore, the value of b that maximizes the integral ∫b−1x2(3−x)dx is b = 3/2.

To know more about value click here

brainly.com/question/30760879

#SPJ11

Explanation:

Factor using the difference of squares rule

\(a^2 - b^2 = (a-b)(a+b)\\\\(13x)^2 - (8)^2 = (13x-8)(13x+8)\\\\169x^2 - 64 = (13x-8)(13x+8)\)

The rectangular pool has dimensions of 13x-8 units by 13x+8 units.

Answer:

D.) 5 x 25 = 125

Step-by-step explanation:

The two numbers are 25 and 5. If you take 1/5 of 25, or simply divide by 5, you will get 5.

Answer:

A) X + Y = 30

B) X = .2Y OR X - .2Y = 0

We subtract B) from A)

1.2Y = 30

Y = 25  X = 5

X * Y = 125

Answer is d.) 125

Step-by-step explanation:

Answer:

s = -3.39

Explanation:

First, we need to apply distributive property on the right side as:

Then, adding like terms, we get:

Subtracting 3s from both sides:

Subtracting 240 from both sides:

Finally, dividing by 69, we get:

Therefore, the answer is s = -3.39

An ordered rooted tree is a tree data structure in which each node has a specific parent-child relationship with its adjacent nodes. Each node in the tree has an address or path that specifies its location in the tree.

Given an ordered rooted tree T with vertex v at address 3.4.5.2.4, we can answer the following questions:

The level of a vertex in a tree is the number of edges on the path from the root to that vertex. In this case, the root is at address 3, and the path from the root to v has four edges: 3->4, 4->5, 5->2, and 2->4. Therefore, v is at level 5.

The parent of a vertex is the node that is immediately above it in the tree. In this case, the parent of v is the node at address 3.4.5.2. Therefore, the address of the parent of v is 3.4.5.2.

The siblings of a vertex are the nodes that have the same parent as the vertex. In this case, we do not have enough information to determine the number of siblings of v. We only know the address of v and its parent, but we do not know the structure of the tree beyond that.

The number of vertices in a tree can be calculated using the formula n = m + 1, where n is the total number of vertices and m is the number of edges. In this case, we know that the path from the root to v has four edges, so there are at least five vertices in the tree (including the root). However, we do not have enough information to determine the exact number of vertices in T, as there may be additional branches and nodes that are not specified.

Based on the address of v, we can determine some of the other addresses that must occur in the tree. For example, the address 3.4.5 must occur in the tree, as this is the parent of v. Additionally, the address 3.4 must occur in the tree, as this is the parent of 3.4.5. However, we cannot determine all of the other addresses that must occur in the tree without additional information about its structure.

To learn more about vertex click:

https://brainly.com/question/31159105

#SPJ1

Answer:

it should be b

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

Answer:

I dont know what your supposed to do but i can tell you that x = 5 because if you simplify the equation you get 3x + 5 = 4x. Using this you can infer that a single x is equivalent to 5 since you need 5 to get from 3x to 4x.

Answer:

thxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Step-by-step explanation:

Answer:

You need them both

Step-by-step explanation:

Without the amount of flowers you wouldn't know what to multiply 8 by (and vice versa)

The total number of flowers is 45 and multiplication helps us to find the total number of flowers.

Given,

8 students have 5 flowers each.

We need to find which helps us to find the total number of flowers.

If 1 person has 5 apples then the total number of apples for 9 people is:

Number of people x number of apples for 1 people

= 9 x 5

= 45 apples.

Find the total number of flowers for 8 students.

We have,

5 flowers = 1 student

So,

We will multiply 8 and 5.

= Number of people x Number of flowers each person has

= 8 x 5

= 45 flowers.

Thus the total number of flowers is 45 and multiplication helps us to find the total number of flowers.

Learn more about finding the total number of flowers grown here:

https://brainly.com/question/23848847

#SPJ2

Answer:

To find out how much money Denzel made per hour, you can divide the total amount of money he made by the number of hours he worked. In this case, you can divide $72 by 7.5 hours to find out how much he made per hour:

72 / 7.5 = $<<72/7.5=9.6>>9.6 per hour

To find out how much money Denzel would make after working 45 hours at this rate, you can multiply the number of hours he works by the amount of money he makes per hour:

45 hours * $9.6 per hour = $<<45*9.6=432>>432.

So if Denzel works for 45 hours at a rate of $9.6 per hour, he will make a total of $432.

Step-by-step explanation:

To find the number that exceeds its square by the greatest amount, we can use these terms: "number" and "square."

Let "n" represent the number.
The square of the number is "n^2."

We are looking for the greatest difference between the number and its square, which can be represented as:

Difference (D) = n - n^2

To find the number that maximizes this difference, we can use calculus to find the critical points (where the derivative is zero or undefined). However, since you asked not to solve it, I'll provide the necessary equations for solving:

1. D = n - n^2
2. Find the derivative of D with respect to n: dD/dn

By following these steps, you can solve for the number that exceeds its square by the greatest amount.

To learn more about Derivative

https://brainly.com/question/30466081

#SPJ11

The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

Learn more about slope of a line here:

https://brainly.com/question/3493733

#SPJ1

Answer: first blank: jen

second blank: mean

Step-by-step explanation:

N/A

Answer:

Q (- 1, 6 )

Step-by-step explanation:

use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M

P (11, - 10) and let Q = (x, y ) , then

\(\frac{11+x}{2}\) = 5 ( multiply both sides by 2 )

11 + x = 10 ( subtract 11 from both sides )

x = - 1

and

\(\frac{-10+y}{2}\) = - 2 ( multiply both sides by 2 )

- 10 + y = - 4 ( add 10 to both sides )

y = 6

coordinates of Q = (- 1, 6 )

Answer: 7

Step-by-step explanation:

The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

To learn more about hyperbola link is here

brainly.com/question/19989302

#SPJ4

Answer:

20

Step-by-step explanation:

This triangle can be solved using the Pythagorean theorem. 16^2+12^2=x^2. 16^2+12^2=400. If we set 400 equal to x^2, x=20.

The evaluation of a definite integral and the solution of a differential equation are two distinct concepts in calculus. A definite integral calculates the accumulated value of a function over a specific interval.

The solution of a differential equation involves finding a function that satisfies a given equation containing derivatives.

A definite integral is represented as ∫[a,b] f(x) dx, where f(x) is a function and [a, b] is the interval over which the integral is evaluated. It helps in calculating quantities like area under a curve, total distance, and volume. Definite integrals are computed using techniques such as the Fundamental Theorem of Calculus or numerical methods like Simpson's rule.

On the other hand, a differential equation is an equation that relates a function with its derivatives. It can be an ordinary differential equation (ODE) or a partial differential equation (PDE), depending on the number of independent variables. The main goal is to find a function, called the solution, that satisfies the given equation. Solving differential equations may involve methods like separation of variables, substitution, or employing numerical techniques like Euler's method.

In summary, evaluating a definite integral focuses on calculating the accumulated value of a function over a specific interval, while solving a differential equation aims to find a function that satisfies an equation involving derivatives.

To know more about Function visit :

https://brainly.com/question/30721594

#SPJ11

Answer:

4608

Step-by-step explanation:

4x4x4x6x12

The linear transformation T defined by T(x) = ax is given, and we need to find the kernel, nullity, range, and rank of this transformation.

The kernel of a linear transformation T is the set of all vectors x such that T(x) = 0. In this case, T(x) = ax, so we need to find all vectors x such that ax = 0. If a is nonzero, then the only solution is x = 0, so ker(T) = {0}. If a = 0, then \(ker(T)\)is the set of all nonzero vectors.

The nullity of T is the dimension of the kernel, which is 0 if a is nonzero, and 2 if a = 0.

The range of T is the set of all vectors of the form ax, where x is any vector in the domain of T. If we assume that the domain of T is the vector space of all 2-dimensional vectors, then the range of T is the line spanned by the vector (5,-3) if a is nonzero, or the entire plane if a = 0.

The rank of T is the dimension of the range, which is 1 if a is nonzero, and 2 if a = 0.

The matrix A is not directly related to T, but we can use it to find a if we assume that T maps the standard basis vectors (1,0) and (0,1) to the columns of A. In this case, we have T((1,0)) = 5(1,0) + 1(0,1) + 1(0,8) = (5,1), and\(T((0,1))\) = -3(1,0) + 1(0,1) + (8-1)(0,8) = (-3,1). Therefore, a = \([\begin{array}{cc} 5 & -3 \\ 1 & 1 \\ 1 & 8-1 \end{array}\right].\)

Learn more about basis here:

https://brainly.com/question/30451428

#SPJ11

Answer: (1, 3)

Step-by-step explanation:

Answer:

6x+4y+2x-4y = 18+(-10)

8x = 8

x = 1

6x+4y = 18

6*1+4y = 18

4y = 18-6

4y = 12

4y/4=12/4

y= 3

Answer:

see the attachment photo!

Answer:

the answer is 7! hope this helps

Step-by-step explanation:

if p is the probability that some bin ends up with 3 balls and q is the probability that every bin ends up with 4 balls. pq is 16.

First, let us label the bins with 1,2,3,4,5.

Applying multinomial distribution with parameters  n=20  and  p1=p2=p3=p4=p5=15  we find that probability that bin1 ends up with 3, bin2 with 5 and bin3, bin4 and bin5 with 4 balls equals:

5−2020!3!5!4!4!4!

But of course, there are more possibilities for the same division  (3,5,4,4,4)  and to get the probability that one of the bins contains 3, another 5, et cetera we must multiply with the number of quintuples that has one 3, one 5, and three 4's. This leads to the following:

p=20×5−2020!3!5!4!4!4!

In a similar way we find:

q=1×5−2020!4!4!4!4!4!

So:

pq=20×4!4!4!4!4!3!5!4!4!4!=20×45=16

thus, pq = 16.

To learn more about Probability visit: https://brainly.com/question/29508225

#SPJ4

Answer is attached

hope it helps you ⬆️

Answer:

30

Step-by-step explanation: