Question

Toricelli's theorem states that if there is a hole in a container of liquid h feet below the surface of the liquid, the the liquid will flow out at a rate given by R(h)= sort(ugh) where g = 32 ft/sec. Find a linear function that can be used to approximate this rate for holes that are close to 25 ft below the surface of the water

Answer 1

*Torricelli's *then *sqrt(rgh)

Answer 2

@SolomonZelman @FibonacciChick666 @DanJS

Answer 3

sorry for all the typos btw :/

Answer 4

lol I thought they were funny

Answer 5

just use the valuses they gave you

Answer 6

its real that simple?

Answer 7

you might like to read this: http://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx

Answer 8

and Torricelli's theorem says ...velocity = (2*g*h)^1/2

Answer 9

I believe it is, \(\large\color{black}{ L(h) \approx R(25)+ R'(25)(h-25) }\), but I can be wrong.

Answer 10

but yes, all of the above first, plug in your values given then apple

Answer 11

okay! i'll read the notes… hang on. We did linear approximation during the first weeks of the smemester so I'm a bit foggy on it now; Im studying for my final

Answer 12

yea, but do we know r?

Answer 13

i don't believe so; they just gave me g

Answer 14

it says 25 ft below the surface?

Answer 15

you are given this ya? \[R(h)=\sqrt{rgh}\]

Answer 16

we have to define r first, before we can just plug in

Answer 17

Which as solomon pointed out, is done by reading between the lines in the wuetion

Answer 18

oh shoot! no ! its R(h)= square root(2gh)

Answer 19

that makes a difference

Answer 20

it sure does

Answer 21

and makes it easier haha

Answer 22

ok so can you find \[R'(h)=?\]

Answer 23

remember we have \[\sqrt{2*32*h}=R(h)\]

Answer 24

so i just find the derivative and then do the whole linear approximation equation..? or am i missing something

Answer 25

nope, that's it

Answer 26

oh okay! thats not bad at all :) i always freak out when i see word problems and my mind freezes and forgets everything i know haha lol

Answer 27

just remember to relax, write your givens, what you want, then how your gonna get it have a really nice outliine, it helps

Answer 28

I'm going to try doing that from now on. Whenever i see related rates or optimization problems i tend to freak out just because they're a bit lengthy, but the outline would help a lot

Answer 29

That is a good hint to apply the linear approx. "Close to" the number.

Answer 30

I teach it for algebra to physics to calc to everything, a game plan helps reduce anxiety

Answer 31

and even if you're clueless, you may get a point or two

Answer 32

yes, draw pictures, free body diagrams, givens