Question

In exercises 23-38, find parametric equations for the given curve.

A) Determine the slope of the curve
B) Express the curve in terms of x and y
C) Represent the curve using vectors
D) Find equations for the tangent lines

Answer 1

To find the tangent line to the curve at t = 25 s, determine the endpoints using the given positions at different times and then calculate the slope of the tangent line using the slope equation.

Step-by-step explanation:

The tangent line to a curve at t = 25 s can be found by determining the endpoints of the tangent, which correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s. To find the slope of the tangent line, we can plug these endpoints into the slope equation:

slope = (change in y) / (change in x)

where (change in y) = (3120 - 1300) and (change in x) = (32 - 19). By calculating these values, we can find the slope of the tangent line.