Find d 2 y over d x squared for the curve given by x = 2t + 5 and y equals 3 times t over 2 . (4 points) 3 over the quantity 4 times t plus 10 the quantity 4 times t plus 10 ove…

Question

asked Oct 14, 2020 18.9k views

1 Answer

Rick Rat · Answer 1 · 2020-10-18T09:02:57+0000

Answer:

(d^2y)/(dx^2)=0

D is correct.

Explanation:

Given:
x(t)=2t+5

y(t)=(3t)/(2)

To find:
(d^2y)/(dx^2)

As we know,

(dy)/(dx)=((dy)/(dt))/((dx)/(dt))

This is parametric equation. Differentiate both function separately and substitute into formula.

x(t)=2t+5 and
y(t)=(3t)/(2)

(dx)/(dt)=2,(y)/(dt)=(3)/(2)

Substitute into derivative

$(dy)/(dx)=(3)/(2\cdot 2)=(3)/(4)$

For double derivative differentiate w.r.t x

(d^2y)/(dx^2)=0

Hence, The value of
(d^2y)/(dx^2)=0