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2 years ago

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Mathematics

1 answer:

nataly862011 [7]2 years ago

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Step-by-step explanation:

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Jackson wrote the equation below on the whiteboard.

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B = 7

7 x 6 = 42

42 + 6 = 48.

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This graph shows a proportional relationship.<br> What is the constant of proportionality?

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Find the slope given the points (1,4) and (5,9)

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A streetlight sits on top of a 20-foot pole. A six-foot tall man walks away from the pole at a rate of 5 ft/sec. At what rate is

guajiro [1.7K]

Answer:

$\frac{25}{3}ft/s$

Step-by-step explanation:

We are given that

Height of pole,h=20 foot

Height of man,h'=6 foot

$\frac{dx}{dt}=5ft/s$

We have to find the rate at which the man's shadow growing when the man is 10 feet from the pole.

Let x be the distance of man from the pole and y be the distance of tip of man's shadow from the pole.

Distance between man and shadow's tip=y-x

When two triangle are similar then the ratio of their corresponding sides are equal.

$\frac{6}{15}=\frac{y-x}{y}$

$6y=15y-15x$

$15x=15y-6y=9y$

$y=\frac{15}{9}x=\frac{5}{3}x$

Differentiate w.r.t t

$\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}=\frac{5}{3}\times 5=\frac{25}{3}ft/s$

Hence, the man's shadow growing at rate $\frac{25}{3}ft/s$ when the man is 10 feet from the pole.

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