Question

Help! Derivatives application.

Answer 1

@Astrophysics you free? :)

Answer 2

hm? like i'm not even sure how to draw this out o.o

Answer 3

Those are the givens, is that how they should be drawn?

Answer 4

Related rates is what I was saying haha, but we can let x be the distance form the spotlight to the man and then y be his shadow on the wall, which is generic way of dealing with this problem. Then you get the ratio \[\frac{ 2 }{ y } = \frac{ x }{ 12 }\] then you'll have to apply product/ chain rule what ever it is probably both

Answer 5

Note that your \[\frac{ dx }{ dt } = 1.3 \]

Answer 6

so with that ratio what am I solving for?

Answer 7

Oh notice the new diagram, the ratio is from similar triangles, and you want xy, so you can take the derivative which will help you figure out dy/dt essentially as that's what you're looking for

Answer 8

dy/dt is the the length of the shadow decreasing on the building

Answer 9

could it work to use
x^2+y^2=z^2 since it relates all the sides?

Answer 10

and then when we derive that we would get:

x(dx/dt)+y(dy/dt)=z(dz/dt)

Answer 11

or are there too many unknowns there?

Answer 12

haha sorry, I am more used to going about it that way I guess:)

Answer 13

...

Answer 14

Ok so the distance from the spotlight to the man is not 12, we don't know that, so lets represent that as x, and the length of the total triangle is 12 as you have and we'll represent y as the shadow on the wall, so notice we're finding the rate at which the shadow is changing, so we used similar triangles and get \[xy = 24\] take the derivative of this.