Question

Hi I just saw that I was going back to the

Answer 1

Given:

`\sin\theta=(x)/(z)`
`\begin{gathered} (dx)/(dt)=-60mph \\ \\ z=2miles \\ \\ \theta=(\pi)/(6) \\ \\ (dz)/(dt)=-55mph \end{gathered}`

Required:

To find the value of

`(d\theta)/(dt)`

Step-by-step explanation:

Consider

`\sin\theta=(x)/(z)`

Differentiate with respect to t, we get

`\cos\theta(d\theta)/(dt)=(x(dz)/(dt)-z(dx)/(dt))/(z^2)`

Now by substituting the values,

`\begin{gathered} \cos(\pi)/(6)(d\theta)/(dt)=(x(-55)-2(-60))/(2^2) \\ \\ (√(3))/(2)(d\theta)/(dt)=(-55x+120)/(4) \\ \\ (d\theta)/(dt)=(2)/(√(3))((-55x+120)/(4)) \\ \\ (d\theta)/(dt)=(-55x+120)/(2√(3)) \end{gathered}`