MATHEMATICS COLLEGE

Please answer ASAP. due tomorrow.
please answer ASAP. due tomorrow. - 1

Answers

Answer 1
Answer:

Answer:1: 36milimeters 2. 3,6 centimeters 3. 5milimeters 4.   .5centimeters  5. 50milimeters 6. 5centimeters

Step-by-step explanation:

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You are measuring the height of a statue. You stand 17 feet from the base of the statue. You measure the angle of elevation from the ground to the top of the statue to be 61º. Find the height h of the statue to the nearest foot.

A soup can has a height of 4 inches and a radius of 2.5 inches. What's the area ofpaper needed to cover the lateral face of one soup can with a label?
OA) 62.8 in?
B) 15.7 in?
C) 78.5 in2
125.7 in2

Answers

Answer:

  1. The lateral surface can be thought of as the crossectional area of the surface integral over dA such that
  2. lateral \: = 2\pi * r * h \n given \: that \: formula \: : \n </li><li>lateral = 2\pi * (2.5)(4) \n \n 2\pi * 10 \n 20 * \pi \n \n lateral=62.8

Answer: 62.8

Step-by-step explanation: took the test, hope this helps (;

A gym has yoga classes each class has 14 students if there are c classes write an equation to represent the total number of students s taking yoga

Answers

Answer:

14 times c = s

Step-by-step explanation:

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month betore. Explain to Jo howto represent his first 20 payment n sigma notation.Then esplain how to tind the sum of his frst 20 pyments, using complete sentences. Esplain why this series is convergent or divergent

Answers

Since each term of the series is 1.1 times the previous one, the series is geometric. The generic term of a geometric series is
  a_(n)=a_(0)\cdot r^((n-1))

The sum in sigma notation simply adds these terms. The leading factor of 100 can be factored out.
sum=\displayform{100\cdot\sum\limits_(n=1)^(20){1.1^((n-1))}}

The sum can be found by adding the terms or by using the formula for the sum of a geometric series. In the latter case, we have
sum=100\cdot(1.1^(20)-1)/(1.1-1)\approx5727.50

The series is divergent because the common ratio of terms is greater than 1. (Of course, any finite number of terms will have a finite sum.)

Please help! Thank you

Answers

Answer:

-294

Step-by-step explanation:

Find the next three terms in the geometric sequence. 2,-16,128,-1024,...

Answers

Answer:8192,-65536,524288

Step-by-step explanation:

2,-16,128,-1024,....

First term=a=2

Common ratio=r=-16/2=-8

Using the formula

Tn=a x r^(n-1)

T5=2 x (-8)^(5-1)

T5=2x (-8)^4

T5=2x4096

T5=8192

T6=2x(-8)^(6-1)

T6=2x(-8)^5

T6=2x-32768

T6=-65536

T7=2x(-8)^(7-1)

T7=2x(-8)^6

T7=2x262144

T7=524288

Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf= Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= i+ j Note: Your answers should be numbers

Answers

Answers:

  • Gradient of f:    \nabla f = y\hat{i} + x\hat{j}
  • Gradient of f at point p: \nabla f = -4\hat{i} -4\hat{j}
  • Directional derivative of f and P in direction of v: \nabla f(P)v = -20\n
  • The maximum rate of change of f at P:  | \nabla f(P)| = 4√(2)
  • The (unit) direction vector in which the maximum rate of change occurs at P is:  v = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

Step by step solutions:

Given that:

  • f(x,y) = xy
  • P = (-4,4)\n
  • v = 2i + 3j

A: Gradient of f

\nabla f = ((\partial f)/(\partial x), (\partial f)/(\partial y)) = (y,x) = y\hat{i} + x\hat{j}

B: Gradient of f at point P:

Just put the coordinates of p in above formula:

\nabla f = -4\hat{i} -4\hat{j}

C: The directional derivative of f and P in direction of v:

The directional derivative is found by dot product of \nabla f(P) \: \rm and \: \rm v:

\nabla f(P)v = [-4,4][2,3]^T = -20\n

D: The maximum rate of change of f at P is calculated by evaluating the magnitude of gradient vector at P:

| \nabla f(P)| = √((-4)^2 + (-4)^2) = 4√(2)

E: The (unit) direction vector in which the maximum rate of change occurs at P is:

v = ((-4)/(4√(2)), (-4)/(4√(2))) = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

That vector v is the needed unit vector in this case.

we divided by 4√(2) to make that vector as of unit length.

Learn more about vectors here:

brainly.com/question/12969462

Answer:

a) The gradient of a function is the vector of partial derivatives. Then

\nabla f=((\partial f)/(\partial x), (\partial f)/(\partial y))=(y,x)=y\hat{i} + x\hat{j}

b) It's enough evaluate P in the gradient.

\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}

c) The directional derivative of f at P in direction of V is the dot produtc of \nabla f(P) and v.

\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\n3\end{array}\right] =(-4)2+(-4)3=-20

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

||\nabla f(P)||=√((-4)^2+(-4)^2)=√(32)=4√(2)

e) The maximum rate of change occurs in the direction of the gradient. Then

v=(1)/(4√(2))(-4,-4)=((-1)/(√(2)),(-1)/(√(2)))= (-1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

is the direction vector in which the maximum rate of change occurs at P.
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