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Lorico [155]
3 years ago
9

A 15-ft ladder leans against a wall. The lower end of the ladder is being pulled away from the wall at the rate of 1.5 ft/sec. L

et x be the distance from the bottom of the ladder to the wall, y be the distance from the top of the ladder to the ground and l be the length of the ladder. How fast is the top of the ladder moving along the wall at the instant it is 9 feet above the ground

Mathematics
1 answer:
Aleks [24]3 years ago
7 0

Answer:

The top of the ladder is sliding down at a rate of 2 feet per second.

Step-by-step explanation:

Refer the image for the diagram. Consider \Delta ABC as right angle triangle. Values of length of one side and hypotenuse is given. Value of another side is not known. So applying Pythagoras theorem,

\left ( AB \right )^{2}+\left ( BC \right )^{2}=\left ( AC \right )^{2}

From the given data, L=15\:ft=AC, y=9\:ft=AB and x=BC

Substituting the values,  

\therefore \left ( 9 \right )^{2}+\left ( x \right )^{2}=\left ( 15 \right )^{2}

\therefore 81+x^{2}=225

\therefore x^{2}=225-81

\therefore x^{2}=144

\therefore \sqrt{x^{2}}=\sqrt{144}

\therefore x=\pm 12

Since length can never be negative, so x= 12.

Now to calculate \dfrac{dy}{dt} again consider following equation,  

\left ( y \right )^{2}+\left ( x \right )^{2}=\left ( l \right )^{2}

Differentiate both sides of the equation with respect to t,  

\dfrac{d}{dt}\left(y^2+x^2\right)=\dfrac{d}{dt}\left(l^2\right)

Applying sum rule of derivative,

\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(l^2\right)

\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(225\right)

Applying power rule of derivative,  

2y\dfrac{dy}{dt}+2x\dfrac{dx}{dt}=0

Simplifying,  

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

Substituting the values,  

9\dfrac{dy}{dt}+12\times1.5=0

9\dfrac{dy}{dt}+18=0

Subtracting both sides by 18,

9\dfrac{dy}{dt}=-18

Dividing both sides by 9,

\dfrac{dy}{dt}= - 2

Here, negative indicates that the ladder is sliding in downward direction.  

\therefore \dfrac{dy}{dt}= 2\:\dfrac{ft}{sec}

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butalik [34]

Answer:

choice number 2) 10 in, 18.5 in 31.5 in

Step-by-step explanation:

we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y  with 5 because they are not like terms.

2y +1 + 7y + 3y + 5 = 60

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The 6 crosses the equal sign to the other side because of like terms.And becomes a minus

12y = 60 - 6

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y = 4.5

so,

2y +1= 2 x 4.5 + 1 =10

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Answer is 10 in, 18.5 in, 31.5 in

If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx

Hope this helps and if it does pls mark as branliest answer thx

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3 years ago
Please help 20 points
loris [4]

Answer:

10 4/7

Step-by-step i used photo math

4 0
3 years ago
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Brut [27]
Do you have a better picture?
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2 years ago
9y-5x=20 i dono how to do this x and y intercwpt thingy
bagirrra123 [75]
     9y - 5x = 20
or, (9y - 5x) / 20 = 1
or, 9/20 y - 1/4 x = 1
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y intercept (b) = 20/9

8 0
3 years ago
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