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3 years ago

Simplify the following c^2+4c-12

Mathematics

1 answer:

Artemon [7]3 years ago

5 0

Have a nice days..................

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Calculus Application

Fiesta28 [93]

<h3>Answer:</h3>

-8/3 ft/s

<h3>Step-by-step explanation:</h3>

<u>We are given:</u>

distance of the top of the ladder from the ground (h) = 12 ft

height of the ladder = 20 ft

rate of change of the distance of the base of ladder from the wall (dx/dt):

2 ft/s

<u>Finding the distance of the base of the ladder from the wall:</u>

From the Pythagoras's Theorem, we know that:

hypotenuse² = height² + base²

<em>replacing the given values</em>

20² = 12² + x²

400 = 144 + x²

x² = 256 [subtracting 144 from both sides]

x = 16 ft [taking the square root of both sides]

<u>The rate of change of the height of the Ladder from the ground:</u>

We know that:

h = 12 ft

( $\frac{dh}{dt}$ ) = ?

x = 16 ft

( $\frac{dx}{dt}$ ) = 2 ft/s

According to the Pythagoras's Theorem:

20² = x² + h²

<em>differentiating both sides with respect to time</em>

$\frac{d(400)}{dt} = \frac{d(x^{2} + h^{2})}{dt}$

$0 = \frac{d(x^{2})}{dt} + \frac{d(h^{2})}{dt}$

$0 = \frac{d(x^{2})}{dx}(\frac{dx}{dt}) + \frac{d(h^{2})}{dh}(\frac{dh}{dt})$

$0 = 2x(\frac{dx}{dt}) + 2h(\frac{dh}{dt})$

<em>replacing the variables</em>

$0 = 2(16)(2) + 2(12)(\frac{dh}{dt})$

$0 = 64 + 32(\frac{dh}{dt})$

$-64 =32(\frac{dh}{dt})$ [subtracting 64 from both sides]

$\frac{-64}{32} =(\frac{dh}{dt})$ [dividing both sides by 32]

$\frac{dh}{dt} = \frac{-8}{3} ft/s$

Hence, the ladder will slide down at a speed of 8/3 feet per second

7 0

3 years ago

Solve this algebraic expression:<br> 5x-2(3x)

Aleonysh [2.5K]

5x - 2(3x)

5x - 6x

-1x

6 0

3 years ago

Read 2 more answers

Which is the best unit to use for measuring the length of an eyelash millimeters C centimeters B meters or D kilometers

myrzilka [38]

I believe it is centimeters

5 0

3 years ago

For the function f(x) =<br> x 1/3/4<br> find f-1(x).

AnnyKZ [126]

Answer:

You can model a data using a linear function when the dependent variable is a multiple of the independent formula plus another constant by the y-intercept. The constant multiple is represented by the slope. In real life problems, linear function is applied when you want to determine the cost given with a slope which is represented by cost per unit time. For example, the cost of wifi connection is $10/month plus $2 inclusive for phone charges. The linear function would be:

C = 10t + 2

where C is the cost and t is time in months

Step-by-step explanation:

7 0

3 years ago

if 9 people share 5 pizzas equally each person receives a fraction of the whole what fraction describes what each person receive

kari74 [83]

Answer:

5 slices

Step-by-step explanation:

7 0

3 years ago