Question

PLEASE HELP! (100 POINTS)

A child builds two wooden train sets. The path of one of the trains can be represented by the function y = 2sin2x, where y represents the distance of the train from the child as a function of x minutes. The distance from the child to the second train can be represented by the function y = 3 − sin x. What is the number of minutes it will take until the two trains are first equidistant from the child?

Answer 1

`\\ \rm\Rrightarrow 2sin^2x=3-sinx`

`\\ \rm\Rrightarrow 2(1-cos^2x)=3-1+cos^2x`

`\\ \rm\Rrightarrow 2-2cos^2x=2+cos^2x`

`\\ \rm\Rrightarrow 2cos^2x+cos^2x=0`

`\\ \rm\Rrightarrow 3cos^2x=0`

`\\ \rm\Rrightarrow cos^2x=0`

`\\ \rm\Rrightarrow x=(n\pi)/(2)`

First equidistant=π/2=90°

• Time=15min

Answer 2

The answer is:

π/2 minuets