SOLUTION: Find the tangent to each curve at the point where t = 3: x = 5(t)^2, y = 10t answer is y = (1/3)x + 15

Algebra ->  Equations -> SOLUTION: Find the tangent to each curve at the point where t = 3: x = 5(t)^2, y = 10t answer is y = (1/3)x + 15      Log On


   

Question 1180307: Find the tangent to each curve at the point where t = 3:
x = 5(t)^2, y = 10t


answer is y = (1/3)x + 15
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The point of tangency is (x(3),y(3)) = (45,30)

The slope of the tangent is the derivative of the curve at t=3.

dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29+=+%2810%29%2F%2810t%29+=+1%2Ft

So at t=3 the slope is 1/3.

Use basic algebra with a slope of 1/3 and a point (45,30) to confirm the correctness of the answer you show.