2 years ago

Ok so i hope this app works

Mathematics

1 answer:

castortr0y [4]2 years ago

6 0

36 times 24 equals 864.

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STALIN [3.7K]

Answer:

Rate of change of length of shadow is $\frac{15}{7} ft/s$

Step-by-step explanation:

Consider the figure

We have

$\begin{aligned}&\frac{d x}{d t}=\text { rate of person walking } \\&\frac{d y}{d t}=\text { rate of change of shadow length } \\&\frac{d x}{d t}+\frac{d y}{d t}=\text { rate of change of tip of shadow }\end{aligned}$

$\begin{aligned}&\frac{6}{20}=\frac{y}{x+y} \\&6(x+y)=20 y \\&6 x+6 y=20 y \\&6 x=14 y\end{aligned}$

$6\left(\frac{d x}{d t}\right)=14\left(\frac{d y}{d t}\right)\\\\6(5)=14\left(\frac{d y}{d t}\right)\\\\\frac{30}{14}=\frac{d y}{d t}\\\\\frac{15}{7}=\frac{d y}{d t}\\\\$

Rate of change of length of shadow is $\frac{15}{7} ft/s$

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