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Korvikt [17]
2 years ago
5

Help please and thanks

Mathematics
1 answer:
STALIN [3.7K]2 years ago
8 0

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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