Question

A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.

Answer 1

@hackworthaustin123 can you help me?

Answer 2

yeah let me think about this.

Answer 3

Okay. the answer choices are..

A. 5 inches
B. 4 inches
C. 4.5 inches
D. 5.5 inches

Answer 4

@robtobey think maybe you can help?

Answer 5

okay so the area of this has to be length times width.
So, I'm thinking the answer is 5.5.
you take 18 and subtract it from 5.5. That will give you 12.5.
Then you take 12.5 and divide it by 2. That'll give you 6.25.
Then, you'll take 6.25 and multiply it by 2, and it'll give you 34.375, which is the largest area of all the answer choices you have.

Answer 6

you want the highest area of all.

Answer 7

Hmm okay can you explain why you chose to do those steps? And what do you think @robtobey ?

Answer 8

Let x be the height of one side.
Cross sectional area is x(18-2x)
Set the derivative of x (18 - 2 x) to zero and solve for x.
x = 9/2, 18-2x = 9

Answer 9

Okay but 9 isn't one of my choices..

Answer 10

x is the depth or the height of one side.
x = 9/2 or C. 4.5 inches.

Answer 11

Oh okay I get it now, thank you guys so much.

Answer 12

A plot is attached.

Answer 13

And your welcome.

Answer 14

Ok thank you