if $v = 1148 \sqrt{p}$ $v=1148sqrt(p)$ where $p$ $p$ is a function of $t$ $t$ then find $\frac{d v}{d t}$ $(dv)/dt$ when $p = 44.0$ $p=44.0$ and $d \frac{p}{d t} = 0.307$ $dp/dt=0.307$ ?

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Answer 1 · 2017-07-21T14:10:52

$[(dv)/(dt)]_(p=44.0) = 26.3 \ ft (s^(-2))$ to three significant figures

We have:

$v = 1148sqrt(p)$
$\ \ = 1148p^(1/2)$

Differentiating wrt $p$ we get:

$(dv)/(dp) = 1/2(1148)p^(-1/2)$
$" " = 574/sqrt(p)$

We are also give that:

$(dp)/dt =0.307$

By the chain rule we have:

$(dv)/(dt) = (dv)/(dp) * (dp)/(dt)$
$" " = 574/sqrt(p) * 0.307$
$" " = 176.218/sqrt(p)$

So when $p=44.0$ we have:

$[(dv)/(dt)]_(p=44.0) = 176.218/sqrt(44)$
$" " = 26.565863 ... ft \ s^(-2)$

if v=1148sqrt(p)v=1148√pv=1148sqrt(p) where ppp is a function of ttt then find (dv)/dtdvdt(dv)/dt when p=44.0p=44.0p=44.0 and dp/dt=0.307dpdt=0.307dp/dt=0.307?