Help with related rate problem please! (DISTANCE)

- anonymous

Help with related rate problem please! (DISTANCE)

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- anonymous

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- anonymous

hint ->
you want dy/dt
so:
dy/dt = (dy/dx) * (dx/dt)

- anonymous

which formula do i use?

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- anonymous

you have dx/dt at this point and you have the point itself. that should help you

- anonymous

right.

- anonymous

got that.

- anonymous

dy/dt = (dy/dx) * (dx/dt)

- anonymous

dy/dx means derivative of y with respect to x
dx/dt is given at this point

- anonymous

i know.

- anonymous

so?

- anonymous

but what formula should i use, for example there are problems for volume, circle, triangle, etc.

- anonymous

distance formula?

- anonymous

ok
so distance from the origin is
s = sqrt(x^2 + y^2)
so you want
ds/dt = (ds/dy) * (dy/dt) + (ds/dx) * (dx/dt)

- anonymous

what does s symbolize?

- anonymous

right.

- anonymous

s - distance

- anonymous

so that is it. now you have it all

- anonymous

thanks let me try

- anonymous

you can, as well, to express y in terms of x in the distance formula
and then find
ds/dt = (ds/dx) * (dx/dt)
it will be much more simple

- anonymous

right the whole 5*sqrt(2x+2) is throwing me off though,

- anonymous

im not sure if i should find the derivative of that function with respect to time.

- anonymous

and the whole distance formula too.

- anonymous

ok so if we do it the way i said at the end :
"you can, as well, to express y in terms of x in the distance formula
and then find
ds/dt = (ds/dx) * (dx/dt)
it will be much more simple"
then you dont have to do much

- anonymous

cause
s=sqrt(x^2 + y^2) = sqrt(x^2+50x+50)
now
ds/dt = (ds/dx) * (dx/dt)

- anonymous

you just need to find ds/dx

- anonymous

i did this:
i found s=10.0499
then i found the derivative which i got 5/sqrt(2x+2) *dx/dt

- anonymous

i got ds/dt as 10 but i know it's wrong.

- anonymous

you dont need to find s.
you need to find ds/dx

- anonymous

ds/dx=10

- anonymous

what about dy?

- anonymous

since we express y in terms of x
we dont need to worry about it anymore.

- anonymous

ok

- anonymous

ds/dx = (x + 25)/sqrt(x^2+50x+50)
at the point x=1 it is
ds/dx = 26 / sqrt(101)
so ds/dt = (26 / sqrt(101))* 4
i might done some mistake though

- anonymous

yeah im not sure what's happening.

- anonymous

why?
s = sqrt(x^2+y^2) = sqrt(x^2+50x+50)
so we want ds/dt
ds/dt = ds/dx * dx/dt
ds/dx = (x + 25)/sqrt(x^2+50x+50)
ds/dx at this point = 26/sqrt(101)
so ds/dt at this point = 26 * 4 /sqrt(101)

- anonymous

plugged into the derivative x=1 and dx/dt = 4

- anonymous

understand what i did ?

- anonymous

sqrt(x^2+50x+50) ?

- anonymous

this is the distance..
s=sqrt(x^2 + y^2) = sqrt(x^2 + 50x + 50)

- anonymous

i know, how'd you come up with this sqrt(x^2+50x+50)

- anonymous

x^2+50x+50)

- anonymous

plugged y=5sqrt(2x+2)

- anonymous

10=10

- anonymous

50x+50?

- anonymous

i plugged in y and x

- anonymous

what ?

- anonymous

y=5sqrt(2x+2)
y^2 = 50x+50

- anonymous

plugged y=5sqrt(2x+2). i plugged in y and x.
10=10

- anonymous

so now
s = sqrt(x^2 + y^2)
but since y^2 = 50x+50
s = sqrt(x^2+50x+50)

- anonymous

not the value of y at the point. plug y as a function of x

- anonymous

okay thanks alot.

- anonymous

i got it

- anonymous

are you sure ?

- anonymous

s = sqrt(x^2+y^2) = sqrt(x^2+50x+50)
so we want ds/dt
ds/dt = ds/dx * dx/dt
when we calculate ds/dx we calculate is using s as a function of x. not plugging numerical values yet.
ds/dx = (x + 25)/sqrt(x^2+50x+50)
now plug x=1
ds/dx at this point = 26/sqrt(101)
so ds/dt at this point = 26 * 4 /sqrt(101)

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