374,512 views
33 votes
33 votes
Hi I just saw that I was going back to the

Hi I just saw that I was going back to the-example-1
User Jose Rui Santos
by
2.6k points

1 Answer

23 votes
23 votes

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}

User Astrotim
by
2.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.