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