Question

step 3
now find $\frac{dy}{dt}$.
$\frac{dy}{dt}=-\frac{24}{x^{2}}-\frac{24}{x^{2}}cdot\frac{dx}{dt}$
step 4
substituting $x = 8$ gives us the following. (round your answers to one decimal place.)
$\frac{dy}{dt}=\frac{(-24)(space)\text{x your answer cannot be understood or graded. more information}}{64}$
$=\text{x}$
the shadow is decreasing at a rate of $\text{x}$ m/s.

Explanation:

Step1: Recall the derived formula

We have $\frac{dy}{dt}=-\frac{24}{x^{2}}\cdot\frac{dx}{dt}$.

Step2: Substitute $x = 8$

Substitute $x = 8$ into $-\frac{24}{x^{2}}$. When $x = 8$, $x^{2}=64$, and $-\frac{24}{x^{2}}=-\frac{24}{64}=-\frac{3}{8}$. Assume $\frac{dx}{dt}=1$ (since it is not given in the problem - if there was a value for $\frac{dx}{dt}$ we would multiply by that value). Then $\frac{dy}{dt}=-\frac{3}{8}\times1=- 0.4$ (rounded to one decimal place).

Answer:

$-0.4$