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2 years ago

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A moving company needs to replace a circualr glass mirror that it broke during a move. The dimensions of a piece of the broken m

irror are shown in the figure. What was the diameter of the original mirror? Round your answer to the nearest tenth if an inch.

1 answer:

dmitriy555 [2]2 years ago

4 0

Is there a picture that goes with this?

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F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.

Whitepunk [10]

Take partial derivatives and set them equal to 0:

$\nabla F(x,y)=\langle2x+4,2y-4\rangle=\mathbf 0$

We find one critical point within the boundary of the disk at $(x,y)=(-2,2)$ . The Hessian matrix for this function is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite, and incidentally independent of $x$ and $y$ , so $F(x,y)$ attains a minimum $F(-2,2)=-8$ .

Meanwhile, we can parameterize the boundary by $\mathbf r(t)=\langle9\cos t,9\sin t\rangle$ with $0\le t\le2\pi$ , which gives

$F(x,y)=F(x(t),y(t))=f(t)=81\cos^2t+81\sin^2t+36\cos t-36\sin t=81+36(\cos t-\sin t)$

with critical points at

$f'(t)=0\implies 36(-\sin t-\cos t)=0\implies\sin t+\cos t=0\implies t=\dfrac{3\pi}4,\dfrac{7\pi}4$

At these points, we get

$f\left(\dfrac{3\pi}4\right)=81-36\sqrt2\approx30.0883$
$f\left(\dfrac{7\pi}4\right)=81+36\sqrt2\approx131.9117$

so we attain a maximum only when $t=\dfrac{7\pi}4$ , which translates to $(x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right)$ .

3 0

2 years ago

How many quarter-acre lots can be made from 6 1/2 acres of land?

Reptile [31]

26! A quarter is 1/4 and so you time the 4 (one whole) times 6 which leaves you with 24 and there’s still have an acre which is two quarter acres and so you add to to 24 and get tour final answer of 26 :)

3 0

2 years ago

Read 2 more answers

For the first year of his car insurance policy, Tom pays $77 per month. Tom's payments are reduced to $65 per month in the secon

Tcecarenko [31]

77/65=1.18
round 1.18 to 1.2

6 0

2 years ago

Read 2 more answers

Math 9:The floor of conference hall can be covered completely with tiles. Its length is 36 ft longer than its width. The area of

valentina_108 [34]

What is the question?
I'm assuming it is to find the length and width.
+_= plus or minus
(X+36)
____________
| |
(X) | |
|____________|

X^2+36X-2040<0
X<-36+_(36^2-4*-2040)^(1/2)
-----------------------------------
2
X<-18+_2((591)^(1/2))
This is probably not what you wanted, sorry

8 0

2 years ago

With an 18% discount, Joan was able to save $13.23 for a coat. What was the original price of the coat?

strojnjashka [21]

Hi there!

First we need to realise that the 18% discount equals John's savings. Therefore 18% of the original price is $13.23.

When we know 18% of the price, we can also find 1% of the total price.

18% = $13.23
Divide both sides by 18.

1% = $0.735
To find the total price, which equals 100%, we know only need to multiply both sides by 100.

100% = $73.50.
Therefore, the original price for the coat is $73.50.

~ Hope this helps you!

5 0

2 years ago