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2 years ago

Can u show 24 divided 4 with one rectangle

Mathematics

1 answer:

ryzh [129]2 years ago

7 0

This will be the answer
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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

2 years ago

What is 6 divided by 1 fourth

Eva8 [605]

$6 \div \frac{1}{4} = 6\times 4 = \boxed {24}$

5 0

2 years ago

A. 812r) and 100

White raven [17]

Answer is C.9(3r-4) and 27r-36

Step-by-step explanation:

5 0

2 years ago

Find the missing number of each unit rate.

UNO [17]

15/5 = 3/1 24/6 = 4/1

6 0

3 years ago

Read 2 more answers

a circular pizza that is 10 inches in diameter is cut into 8 equal slices. what is the area of one of the slices? round to the n

olga nikolaevna [1]

The area of one slice is roughly 14.13

The area of the whole pizza is 113.1
Divide that by 8

3 0

2 years ago