x = t^3 + 2t
y = t^2
dx/dt = x velocity = 3 t^2 + 2
dy/dt = y velocity = 2 t
tangent slope = dy/dt / dx/dt
= 2t/(3t^2+2)
now what is t when x = 3 and y = 1?
t^2 = 1 = 1
so t = 1 (or -1 but we will see that won't work:)
1^3 + 2*1 = 3, sure enough
so slope = 1/4
y = (1/4) x + b
1 = (1/4)(3) + b
4/4 = 3/4 + b
b = 1/4
so
4y = x + 1
Find the equation of the line tangent to the path of a particle traveling in the xy-plane with position vector r(t)=<t^3 +2t, t^2> at the point (3, 1).
6 answers
But the answer choices are
y=2/5x + 11/5
y=6/11x - 7/11
y=y=2/5x + 13/5
y=2/5x - 1/5
y=6/11x - 18/11
y=2/5x + 11/5
y=6/11x - 7/11
y=y=2/5x + 13/5
y=2/5x - 1/5
y=6/11x - 18/11
Why didn't you post the answer choices before? Damon went to all of this work without having all of the necessary information.
Well shouldn't Damon have known what to do and not need answer choices?
Oh, the slope is 2/4 = 1/2
You can do it from there I think
You can do it from there I think
tangent slope = dy/dt / dx/dt
= 2t/(3t^2+2)
when t = 1
that is 2/(3+2) = 2/5
= 2t/(3t^2+2)
when t = 1
that is 2/(3+2) = 2/5