Question

in order to find \\(\frac{dy}{dt}\\), differentiate both sides of the equation (y = \tan(35^{circ})x). substitute \\(\frac{dx}{dt}=14\text{ km/hr}) into \\(\frac{dy}{dt}=\tan(35^{circ})\frac{dx}{dt}) and solve for \\(\frac{dy}{dt}). \\(\frac{dy}{dt}=\tan(35^{circ})\frac{dx}{dt}) \\(\frac{dy}{dt}=\tan(35^{circ})(14\text{ km/hr})\approx\square\text{ km/hr}) (round to two decimal places as needed.)

Explanation:

Step1: Identify given values

We know $\frac{dx}{dt}=14$ km/hr and $\tan(35^{\circ})$ is a constant. The formula for $\frac{dy}{dt}$ is $\frac{dy}{dt}=\tan(35^{\circ})\frac{dx}{dt}$.

Step2: Substitute values

Substitute $\frac{dx}{dt} = 14$ km/hr and $\tan(35^{\circ})\approx0.7002$ into the formula. So $\frac{dy}{dt}=0.7002\times14$.

Step3: Calculate result

$\frac{dy}{dt}=0.7002\times14 = 9.8028\approx9.80$ km/hr.

Answer:

$9.80$ km/hr