Question

At what point do the curves r1(t) = t, 3 - t, 48t² and r2(s) = 8 - s, s - 5, s² intersect? Find their angle of intersection, correct to the nearest degree.

Answer 1

To find the point of intersection and angle of intersection between the given curves, set their coordinates equal to each other and solve for t and s. Then, find the slopes of the curves at the point of intersection and use the formula tan(angle) = (slope1 - slope2) / (1 + slope1 * slope2).

Step-by-step explanation:

To find the point of intersection between the curves r1(t) = t, 3 - t, 48t² and r2(s) = 8 - s, s - 5, s², we need to set their coordinates equal to each other and solve for t and s.

For example, we can set t = 8 - s, 3 - t = s - 5, and 48t² = s².

Solving these equations will give us the values of t and s at the point of intersection. To find the angle of intersection, we can find the slopes of the curves at the point of intersection and use the formula tan(angle) = (slope1 - slope2) / (1 + slope1 * slope2).