question suppose that the length l, width w, and perimeter p of a rectangle are differentiable functions of…

question suppose that the length l, width w, and perimeter p of a rectangle are differentiable functions of t. suppose also that the length is always two times and twenty - three more than the width. write an equation that relates dp/dt to dw/dt. enter your answers using exact values. provide your answer below: dp/dt = □ dw/dt

question suppose that the length l, width w, and perimeter p of a rectangle are differentiable functions of t. suppose also that the length is always two times and twenty - three more than the width. write an equation that relates dp/dt to dw/dt. enter your answers using exact values. provide your answer below: dp/dt = □ dw/dt

Answer

Explanation:

Step1: Write the relationship between length and width

Given $l = 2w+ 23$.

Step2: Write the perimeter formula

The perimeter of a rectangle is $P=2(l + w)$. Substitute $l = 2w + 23$ into it, we get $P=2((2w + 23)+w)=2(3w + 23)=6w+46$.

Step3: Differentiate both sides with respect to $t$

Differentiating $P = 6w+46$ with respect to $t$ using the chain - rule. $\frac{dP}{dt}=\frac{d}{dt}(6w + 46)$. Since $\frac{d}{dt}(6w+46)=6\frac{dw}{dt}+\frac{d}{dt}(46)$, and $\frac{d}{dt}(46) = 0$, we have $\frac{dP}{dt}=6\frac{dw}{dt}$.

Answer:

$6$