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Leviafan [203]
3 years ago
14

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)
(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec

20 feet away from the wall
_____ ft/sec

24 feet away from the wall
_____ ft/sec

...?
Mathematics
1 answer:
Soloha48 [4]3 years ago
5 0

last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez

<span><span>x2</span>+<span>y2</span>=25</span>

calculus says

<span>2x<span>x′</span>+2y<span>y′</span>=0</span>

and you are told that

<span><span>y′</span>=2</span>

so you know

<span>2x<span>x′</span>+4y=0</span>

or

<span><span>x′</span>=−<span><span>2y</span>x</span></span>

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What is the answer to this question I am really having trouble ??
masya89 [10]
<h3>Answer: Choice B</h3><h3>y = x^2 + 7x + 1</h3>

======================================

Proof:

A quick way to confirm that choice B is the only answer is to eliminate the other non-answers.

If you plugged x = 1 into the equation for choice A, you would get

y = -x^2 + 7x + 1

y = -1^2 + 7(1) + 1

y = -1 + 7 + 1

y = 7

We get a result of 7, but we want 9 to be the actual output. So choice A is out.

-----------

Repeat for choice C. Plug in x = 1

y = x^2 - 7x + 1

y = 1^2 - 7(1) + 1

y = 1 - 7 + 1

y = -5

We can eliminate choice C (since again we want a result of y = 9)

-----------

Finally let's check choice D

y = x^2 - 7x - 1

y = 1^2 - 7(1) - 1

y = 1 - 7 - 1

y= -7

so choice D is off the list as well

-----------

The only thing left is choice B, so it must be the answer. It turns out that plugging x = 1 into this equation leads to y = 9 as shown below

y = x^2 + 7x + 1

y = 1^2 + 7(1) + 1

y = 1 + 7 + 1

y = 9

And the same applies to any other x value in the table (eg: plugging in x = 3 leads to y = 31, etc etc).

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3 years ago
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