Respuesta :
Answer:
[tex]\displaystyle\frac{dR}{dt} \approx 0.107[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]R = \displaystyle\frac{T}{W}[/tex]
where, R is the tip speed, T is the speed tip of blade and W is the speed of wind.
We have to find [tex]\frac{dR}{dt}[/tex], whem W = 75 km per hour, [tex]\frac{dW}{dt} = -4\text{ km per hour}[/tex], T = 150 km per hour
Formula:
[tex]\displaystyle\frac{dR}{dt} = \displaystyle\frac{dR}{dW}\displaystyle\frac{dW}{dt} + \displaystyle\frac{dR}{dT}\displaystyle\frac{dT}{dt}\\\\= \displaystyle\frac{dR}{dW}\displaystyle\frac{dW}{dt}\\\\\text{ as T is constant with respect to t}\\\\= -\displaystyle\frac{T}{W^2}\displaystyle\frac{dw}{dT}[/tex]
Putting all the value, we have:
[tex]\displaystyle\frac{dR}{dt} = -\displaystyle\frac{150\times -4}{75\times 75} = 0.106666666667 \approx 0.107[/tex]
