Hey i need help! Its due soon

To find the extreme values of a function f(x,y) on a curve xequalsx(t), yequalsy(t), treat f as a function of the single vari

pychu [463]

Answer:

Absolute maximum is 2

Absolute minimum at -2

Step-by-step explanation:

The given parametric functions are:

$x=2\cos t,y=2\sin t$

By the chain rule:

$f'(t)=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$\frac{df}{dt} =\frac{2 \cos t}{-2\sin t} =-\cot(t)$

At fixed points, $f'(t)=0$

$\implies -\cot (t)=0$

This gives $t=\frac{\pi}{2} ,\frac{3\pi}{2}$ on $0\le t\le 2\pi$

This implies that the extreme points are $(2\cos \frac{\pi}{2}, 2\sin \frac{\pi}{2})=(0,2)$ and $(2\cos \frac{3\pi}{2}, 2\sin \frac{3\pi}{2})=(0,-2)$

By eliminating the parameter, we have $x^2+y^2=4$

This is a circle with radius 2, centered at the origin.

Hence (0,2) is an absolute maximum ,at $t=\frac{\pi}{2}$ and (0,-2) is an absolute minimum at $t=\frac{3\pi}{2}$

7 0

3 years ago

the sum of three number number in an artithmetic product is 21. if second number isreduced by 1 and third term is increased by 1

grin007 [14]

The three numbers will be 12, 7, 2 and 3, 7, 11.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

Let the three consecutive numbers be a, a + d, and a + 2d

The sum of three numbers which are consecutive terms of an A.P. is 21.

a + a + d + a + 2d = 21

3(a + d) = 21

a = 7 - d

If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.

Then the number will be a, a + d − 1, a + 2d + 1. Then we have

$\rm \dfrac{a + d - 1}{a} = \dfrac{a + 2d + 1}{a + d - 1}$

On simplifying, we have

36 = a (8 + d)

a² - 15a + 36 = 0

On factorizing, the value of a will be

a² - 15a + 36 = 0

a² - 12a - 3a + 36 = 0

(a - 12)(a - 3) = 0

a = 3, 12

If a = 12, then the value of d will be

d = 7 - 12

d = -5

If a = 3, then the value of d will be

d = 7 - 3

d = 4

Then the three numbers will be 12, 7, 2 and 3, 7, 11.

More about the sequence link is given below.

brainly.com/question/21961097

#SPJ1

7 0

2 years ago

Maria has baked a cake for Cathy's birthday. The dimensions of the cake are 13 1/2 inches by 6 3/4 inches. The cake is going to

ycow [4]

Answer:

Step-by-step explanation:

Given:

Length = 27/4 in

Width = 27/2 in

5.55% of the cake = 5.55/100

= 1/18

Therefore, 18 equal squares of cake where 1 piece is 5.55 % of the cake

Since, the cake is twice as long as it is wide, so that means cut half the cake (27/4 × 27/4) into 9 pieces.

Therefore, each has a side of 1/3 * 27/4

= 9/4 inches.

8 0

3 years ago

Find the volume of a box 24 in. x 20 in x 23 in.

kaheart [24]

<span>The definition for discovering the volume of a box is when the person takes the length, the width, and the height of the box. And because we have those values here, there is no math that is necessary to do other than multiplying the numbers together and creating a new unit of inches cubed. The answer is 11040 inches cubed.</span>

8 0

3 years ago

Use complete sentences to describe how measurements of position in two directions (vertical and horizontal) are sufficient enoug

posledela

Answer:

We know that our world is in 3 dimensions i.e. there are three directions and so, three co-ordinates are required.

Now, if we have to find a position of an object lying on a flat surface, this means that there are only two directions and so, two co-ordinates are needed.

So, we can define the domain ( xy-axis ) in such a way that there are two axis - horizontal where right area have positive values & left area has negative values and vertical where upward side have positive values & downward side has negative values.

For e.g. if we want to find the position of a pen on the table. We will make our own xy-axis and see in which quadrant the pen lies.

Let us say that the pen lies at (2,3), this means that the position of pen is in the first quadrant or it is 2 units to the right of y-axis and 3 units up to the x-axis.

This way we can see that two directions are sufficient to find the position of an object placed on a flat surface.

5 0

3 years ago