Question

Calculus Optimization
Picture attached
A rectangle is inscribed in a circle of radius 2 m. Find the maximum area of this rectangle.

Answer 1

@wio I hope you can still help me with this problem

Answer 2

Okay.

Answer 3

Thanks in advance for all of your help

Answer 4

Find the radius in terms of x and y. That is your secondary equation. Use pythagorean theorem.

Answer 5

I don't see it

Answer 6

a is y b is 2x and c is 2 correct

Answer 7

ok I think I got it

Answer 8

ok so I got 2 times the square root of (1-x^2) is that correct for my secondary equation

Answer 9

something is wrong with my worksheet. I am not finding the equation at all. Thanks, I think I will skip this one.

Answer 10

width = 2x
heigt = 2sqrt(4-x^2)

A = 4x sqrt(4-x^2).

Answer 11

how did you get square root (4-x^2)?

Answer 12

because the radius is 2.

Answer 13

That is the correct equation according to the puzzle. What am I overlooking?

Answer 14

sqrt(4-x^2) is the upper semicirlce

Answer 15

you're given radius = 2. (not 1)

Answer 16

Yes I am given that radius is 2. Am I not to use Pythagorean Thm?

Answer 17

just how did you get sqrt(1-x^2)

Answer 18

y^2 + 4x^2 =4
y^2=4-4x^2
y=square root (4-4x^2)
y=2 times square root (1-x^2)

Answer 19

your solution is one listed on my puzzle worksheet. I thought it was a typo but now I think I overlooked something

Answer 20

y^2 + 4x^2 = 4 is not a cirlce. It's an ellipse

Answer 21

you should have had x^2 + y^2 = 4

Answer 22

yes, you are correct........

Answer 23

Thanks, I got it now.......

Answer 24

to answer the question, maximum area is 8

Answer 25

yes, now one more quick question. You are putting the 2 in front to cover the entire circle in your height, correct?

Answer 26

not sure what you mean by cover the entire circle, but sqrt(4-x^2) is only half the height of the rectangle. So to get the total height, i multiplied by 2.

Answer 27

ok yes semantics...