anonymous
  • anonymous
Help with related rate problem please! (DISTANCE)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
hint -> you want dy/dt so: dy/dt = (dy/dx) * (dx/dt)
anonymous
  • anonymous
which formula do i use?

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