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iragen [17]
3 years ago
6

Can someone explain to me how to do this and what the answer is

Mathematics
1 answer:
Mashutka [201]3 years ago
5 0
Since lines TS and GF are congruent that means that they are the same length.

Use the equation 12=2x-16 and simplify and you get:


X=14 since the side length is 12
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Step-by-step explanation:

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A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed
N76 [4]

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

\dfrac{AD}{AB} = \dfrac{DE}{BC}

\dfrac{8}{12} = \dfrac{2}{y}

8y = 24

y = 24/8

y = 3 meters

Let take an integral look  at the distance of the man from the building as x, therefore the distance from the spotlight to the man is  12 - x

∴

\dfrac{12-x}{12}=\dfrac{2}{y}

1- \dfrac{1}{12}x  = 2* \dfrac{1}{y}

To find the derivatives of both sides ;we have:

- \dfrac{1}{12}dx  = 2* \dfrac{1}{y^2}dy

- \dfrac{1}{12} \dfrac{dx}{dt}  = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}

During that time ;

\dfrac{dx}{dt }= 1.4 \ m/s   and y = 3

So; replacing the value into above ; we have:

-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}

\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 }  }{  \dfrac{2}{9}}

\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 }  }*{  \dfrac{9}{2}}

\dfrac{dy}{dt} =0.525 \ m/s

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

7 0
3 years ago
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