in order to find \\(\\frac{dy}{dt}\\), differentiate both sides of the equation (y = \\tan(35^{circ})x)…

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.)

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.)

Answer

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