Question

A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross sectional area to allow the greatest amount of water to flow

Answer 1

this was the other question you were asking about?

Answer 2

yes^-^ i dont get at all i been trying to do it for the next hour but i dont get it>.<

Answer 3

\[2x + y = 20\]

Answer 4

\[A = xy\]

Answer 5

yeahhh see now this is where it gets tricky cuz if you dont use some basic calculus... it gets really annoying...

Answer 6

im screwed then>.< idk anything about calculus

Answer 7

lol do you know or heard of derivatives?

Answer 8

not at all! im not there yet>.<

Answer 9

o crap... okk did your teacher teach something similar to this yet?

Answer 10

nop i only know this becuse my friend help me on friday but i didnt finish-_-

Answer 11

ok..... sooo ima give u a quick lesson on derivatives to make life SOOOOOO much easier... cuz if not... we're gonna prob have to go old fashion trial and error...

Answer 12

okay then^-^

Answer 13

ok.... so a derivative of fucntion is the rate of change of the function
so lik the derivative of a distance would be the speed... and the derivative of the speed would be acceleration.... does that make somewhat sense?

Answer 14

alittle>.< so we're gonna look for the derivative of distance no?

Answer 15

well in this case... the derivative of the area.... in which the derivative of the area would mean the change in area... and since if the area is at its maximum.... it cant get any bigger so the change is equal to 0... or in short.... the derivative of the area is zero...

Answer 16

this is too much derivative>.< but i kinda of get you

Answer 17

okkk basically...... just think lik... if im expanding a square with a certain amount of material... the square can only have so much area before it reaches it max...

Answer 18

so in this case there is gonna be alot of material in the squared so it could reach the maximized then right

Answer 19

either way.... wats interesting about the derivative.... is that it has a strange relationship with the orignial function... such that.... if the function was lik.... \[x^{2}\] the 2 would come down and the exponent would minus one.... to make \[2x^{1}\] or just \[2x\]

Answer 20

so thats why its 20xx-2x^2 right

Answer 21

sooo in your case... where the equation is.... \[20x-2x^{2}\]...the derivative would just equal \[20(1)x^{0} - 2(2)x^{1}\] which equals \[20-4x\] and since you want to that to equal zero.... you get \[20-4x=0\]

Answer 22

that should make life easy

Answer 23

so then it would be x=-5 pr +5?

Answer 24

x=5

Answer 25

which then u can easily find y.. by using \[20=2x+y\]

Answer 26

idk how to do that>.< wait is it like this 20=2(5)+y

Answer 27

yuppp :D

Answer 28

so then y= 10?

Answer 29

yuppp :D

Answer 30

wait then what's this? the maximum area cross sectional area? or the depth of the gutter that will maximized its cross sectional area? & finally i got somehting!!!!!!!!!:D

Answer 31

soooo now u know the width and the height (x and y) soooo u can easily get the area.. XD

Answer 32

so then its going to be 50?^-^

Answer 33

yuppp XD

Answer 34

wait then whts the depth?:O

Answer 35

thats ur max area.... and ur width is ur y... so your depth (or height) is ur x

Answer 36

so my depth is 5^-^

Answer 37

yup

Answer 38

thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! you're probably gonna kill me right now though>.<

Answer 39

vacationeer!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 40

lolol its fine XD

Answer 41

dude can you help me with one last problem pleased i swear its the last one!>.<