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erastova [34]
3 years ago
14

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the bui

lding at a speed of 1.8 m/s, which is taken as the given dx/dt, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Mathematics
1 answer:
Sedbober [7]3 years ago
8 0

Answer:

0.675 m/s

Step-by-step explanation:

Let height of shadow= y,CD=x

Height of man=2 m

Speed of man= \frac{dx}{dt}=1. 8 m/s

\triangle ABD\sim\triangle ECD

Therefore, \frac{AB}{EC}=\frac{BD}{CD}

\frac{y}{2}=\frac{12}{x}

xy=24

Differentiate w.r.t t

x\frac{dy}{dt}+y\frac{dx}{dt}=0

x\frac{dy}{dt}=-y\frac{dx}{dt}

\frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}

When the man is 4 m from  the building

Then, we have x=12-4=8 m

\frac{dx}{dt}=1.8 m/s

Substitute the values in above equation then, we get

8y=24

y=\frac{24}{8}=3

Substitute the values then we get

\frac{dy}{dt}=-\frac{3}{8}\times 1.8=-0.675 m/s

Hence, the length of his shadow on the building decreasing at the rate 0.675 m/s.

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Alex17521 [72]
3.8 is the answer you already figured it out
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3 years ago
What's -1.55 as a fraction? show work please help
expeople1 [14]

Answer:

hope it's help you dear

Step-by-step explanation:

The decimal part of your number seems to have the repeating digit 5 in it.

Your original number to convert is 1.550000. Let's slide the decimal point in this number to the right 1 place(s) (the same number of digits in the number 5).

If we do this, we'll get a 15.500000 (slide the decimal in the 1.550000 right 1 places, you'll get 15.500000).

So what? Well now, we have two numbers with the same repeating decimal parts, 15.500000 and 1.550000.

Now let's just work a little algebra into all of this. Let's call your original number x. And in this case, x=1.550000. The number with the decimal point slid over can be called 10x, because 10x=15.500000

What if we subtracted these two equations (that is, subtract the items on the left of the equal sign

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10x = 15.5

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----------

9x = 13.95.

Now here's the important result of doing all of this: Notice how all of the repeating decimal parts have subtracted away to zero! We are left with a nice, simple 14 on the right side of the equal sign.

Now, solving 9x=14 for x by dividing both sides of it by 9, we'll get that x=14/9. And this is your answer.

How is this your answer? Well remember that above, x was originally set equal to 1.550000 via x=1.550000, and now we have that x is also equal to 14/9, so that means 1.550000=14/9..and there's 1.550000 written as a fraction!

The fraction is an improper fraction (the numerator is greater than the denominator).

While there is nothing incorrect about this, an improper fraction is typically

simplified further into a mixed number.

The whole number part of the mixed number is found by dividing the 14 by the 9.

In this case we get 1.

The fractional part of the mixed number is found by using the remainder of the division,

which in this case is 5 (14 divided by 9 is 1 remainder 5).

So your final answer is: 1.550000 can be written as the fraction

7 0
3 years ago
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Step-by-step explanation:

First find the difference between the amounts.

7,400, 000 - 6, 900,000 = 500, 000  

Now divide the obtain number by  the original number which is 6,900,000

500, 000/ 6,900,000 = 0.07246  

Multiply 0.07246 by 100 to convert it to a percent.

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Round it to the nearest tenth of a percent.

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Answer:

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Step-by-step explanation:

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alukav5142 [94]

Answer:

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280 - 160 = 168x - 160x

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