Question

CHECK MY WORK PLEASE? Calculus Rate of Change:

Answer 1

Indy is 6 feet tall and is walking at a rate of 3 feet per second towards a lamppost that is 18 feet tall. At what rate is his shadow due to the lamppost shortening when he is 6 feet from the base of the lamppost?

Answer 2

I got -6 ft/sec

Answer 3

\[\frac{ 18 }{ w+s }=\frac{ 6 }{ w }\]

Answer 4

\[12\frac{ dw }{ dt }=6\frac{ ds }{ dt }\]

Answer 5

\[\frac{ ds }{ dt }= -6ft/\sec\]

Answer 6

what grade r u in

Answer 7

a higher grade than i am XP

Answer 8

i am in 7

Answer 9

same

Answer 10

lol
@shyguy1026 will you be my fan please

Answer 11

ssssssooooooorrrrrrryyyyyy

Answer 12

@kisses what u tryin to figure out?

Answer 13

I had asked you what grade you were dont be so mean man

Answer 14

sorry i would help but cant :C

Answer 15

I'm trying to find dh/dt

Answer 16

oookkk lemme see...

Answer 17

Ooops sorry not that lol

Answer 18

****I'm looking for the rate of change in which the shadow is shortening.

Answer 19

Similar triangles

Answer 20

sorry i have to do my school work see youll in a bit :P

Answer 21

ummm....do have the triangles so i can see them?

Answer 22

I found this online http://img.sparknotes.com/figures/6/6feb2790f92651105afa8c668bf0b7ba/figure3-2p-3.gif

Answer 23

But I used different variables s for x(t) and w for y(t)

Answer 24

woow...um lemme see if i can find one of my ppl to help u cuz i dont wanna do it wrong

Answer 25

ok

Answer 26

That's what I got. I may be wrong though let me double check

Answer 27

yea the andwer is right

Answer 28

try to picture things
the shadow is changing with time when Indy gets closer and closer to lamppost

Answer 29

Oh you get the picture above! now you need to connect the dots
what do you think you need to connect x(t) with y(t)

Answer 30

Hint: use triangle similarity

Answer 31

Yes I used triangle similarity, ratios

Answer 32

\[\frac{ x(t)+y(t) }{ 18 }=\frac{ x(t) }{ 6 }\]

Answer 33

so \[ 6\frac{ dy(t) }{ dt }=12\frac{ dx(t) }{ dt }\]

Answer 34

ok good
but remember that dx/dt is negative

Answer 35

decreasing means you are having a negative slope

Answer 36

\[\frac{ dx(t) }{ dt }= -2 ft/\sec\]

Answer 37

ooops I forgOt tO plUg IN LOL

Answer 38

i didn't do the calculations so I'm not sure what it is
but as long as you did those ratios step the right way and put the right givens then you should be good. I'm out of time so i won't be able to check your math to see it is correct
good luck

Answer 39

yes you need to plug in the givens

Answer 40

So yea the rate of change of the shadow is -6 ft/sec

Answer 41

Ok Thank you :D

Answer 42

Yes it should be sloping down so negative is good

Answer 43

Have a nice day!

Answer 44

You are welcome and thank you!