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REY [17]
2 years ago
6

Question 11 Multiple Choice Worth 1 points)

Mathematics
1 answer:
Viefleur [7K]2 years ago
8 0

Answer:

x = 35

Step-by-step explanation:

First, we need to add the angles on a straight line and subtract them by 180 (because angles on a straight line adds up to 180)

56 + 51 = 107

180 - 107 = 73

Now that we have found the angle of y, we can find the angle of x now. Because angles in a triangle adds up to 180, we have to add 72 and 73 now.

72 + 73 = 145

And now subtract it from 180

180 - 145 = 35

So x = 35

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A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6
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Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

           Length of street light AB = 25 ft

           Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate (\frac{dw}{dt}) of the tip (D) of the girl's shadow (BD) moving away from th

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Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, \frac{dx}{dt}=6 feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

\frac{x}{21}=\frac{x+y}{25}

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = \frac{4x}{21}

Now we take the derivative on both the sides,

\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}

= \frac{4}{21}\times 6

= \frac{8}{7}

≈ 1.14 ft per sec.

Since w = x + y

Therefore, \frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}

\frac{dw}{dt}=6+1.14

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

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