Question

A galvanized iron sheet 64 cm wide is to be bent to form a gutter by turning up vertical strips along each side. How many centimeters should be turned up at each side in order to give a gutter with the maximum cross-sectional area?

Answer 1

Your teacher must really hate giving out details for problems ._.

Answer 2

Yep :) It really gives me a headache >.<

Answer 3

I could imagine these are table flipping problems

Answer 4

Which luckily I can help you :p

Answer 5

Two dimensions:
v = the vertical height of the turned up edge
b = the width of the remaining base.

2*v + b = 64
v * b = A (objective Amax)

Let's simplify the second equation by substituting b from the 1st:
b = 64 - 2*v, so
v * (64 - 2*v) = A, or
64*v - 2*v^2 = A(v)

We want to know the maximum A(v), which can be found where the derivative of A(v) with respect to v is 0:
d[A(v)] = 64 - 4*v,
where 64 - 4*v = 0, v = 16

Test this: using equation 1, 2*v + b = 64, or 2 * 16 +b = 64, b = 32

So Amax would be v * b, or 16 * 32 = 512 cm^2, (whereas dividing the sheet in 3rds, giving height and width of 21.33 cm will only provide 455 cm^2)

Answer 6

455 cm^2<<< Basically the answer

Answer 7

Basically the short cut to reading all dem words

Answer 8

Thank you so much! @DarkBlueChocobo :)

Answer 9

Anything I can help you with I shall try :D Even though I must say I want to flip at least 12 tables at your teacher >.<

Answer 10

Hahaha xD I would like to do that too but I can't >.< @DarkBlueChocobo

Answer 11

*sigh* Well someone needs too I can contact my table flipping friend if you need me too XD

Answer 12

Really? Haha xD Who?

Answer 13

Well my friend Eliot and I can teach him a lesson. Dem Table Flips hurt people. ._. Just tie him up in the middle of the night and put him in a room full of tables. That is my dream.

Answer 14

Dem Tables be hurting

Answer 15

Not to mention those tables would be made out of MAHOGANY

Answer 16

It would really hurt

Answer 17

Me and my friend would be like ┻━┻ ︵ヽ(`Д´)ﾉ︵ ┻━┻

Answer 18

Then after that we would flip your teacher (╯°□°）╯ /(.□. \）

Answer 19

Great! Really. It will the best show I will ever see! xD

Answer 20

Yes :p xD o.o Sparkles (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧*:･ﾟ✧

Answer 21

Well my table flipping friend any more evil math questions you would like me to help you conquer

Answer 22

Sure! No problem! :)

Answer 23

It will be an honor

Answer 24

Also here have some sparkles It will do you some good with a teacher like that (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧*:･ﾟ✧

Answer 25

Amazing! ^_^

Answer 26

^-^ mhm the magic of sparkles

Answer 27

Yes, the magic of sparkles!

Answer 28

*poke* ._.

Answer 29

By the way, I would like to say, thank you for helping me today. I need to go. See you! :)

Answer 30

Alright :3 Bye It has been a pleasure helping you out