6- A particle moves in teh xy-plane so that dx/dt =3t-cos(t^2) ....

Question

6- A particle moves in the xy-plane so that dx/dt =3t-cos(t^2) and dy/dt=4t+sin(t). (For 0 less that or equal to t which is less than equal to 1), what is the value of t at which line tangent to the path of the particle is vertical

Answer 1

dy/dx = (4t + sint)/(3t - cost²).

Tangent line vrtical where dy/dx undefined. So, 3t - cost² = 0.

We solve this equation using TI-84.

t = 0.33132683