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Help with related rate problem please! (DISTANCE)

Mathematics
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hint -> you want dy/dt so: dy/dt = (dy/dx) * (dx/dt)
which formula do i use?

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Other answers:

you have dx/dt at this point and you have the point itself. that should help you
right.
got that.
dy/dt = (dy/dx) * (dx/dt)
dy/dx means derivative of y with respect to x dx/dt is given at this point
i know.
so?
but what formula should i use, for example there are problems for volume, circle, triangle, etc.
distance formula?
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)
what does s symbolize?
right.
s - distance
so that is it. now you have it all
thanks let me try
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
right the whole 5*sqrt(2x+2) is throwing me off though,
im not sure if i should find the derivative of that function with respect to time.
and the whole distance formula too.
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
cause s=sqrt(x^2 + y^2) = sqrt(x^2+50x+50) now ds/dt = (ds/dx) * (dx/dt)
you just need to find ds/dx
i did this: i found s=10.0499 then i found the derivative which i got 5/sqrt(2x+2) *dx/dt
i got ds/dt as 10 but i know it's wrong.
you dont need to find s. you need to find ds/dx
ds/dx=10
what about dy?
since we express y in terms of x we dont need to worry about it anymore.
ok
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
yeah im not sure what's happening.
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)
plugged into the derivative x=1 and dx/dt = 4
understand what i did ?
sqrt(x^2+50x+50) ?
this is the distance.. s=sqrt(x^2 + y^2) = sqrt(x^2 + 50x + 50)
i know, how'd you come up with this sqrt(x^2+50x+50)
x^2+50x+50)
plugged y=5sqrt(2x+2)
10=10
50x+50?
i plugged in y and x
what ?
y=5sqrt(2x+2) y^2 = 50x+50
plugged y=5sqrt(2x+2). i plugged in y and x. 10=10
so now s = sqrt(x^2 + y^2) but since y^2 = 50x+50 s = sqrt(x^2+50x+50)
not the value of y at the point. plug y as a function of x
okay thanks alot.
i got it
are you sure ?
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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