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IrinaK [193]
2 years ago
15

The height of water shooting my fountain is modeled by the function f(x)= -4x^2 +24x -29 where x the distance from the spout in

feet. Complete the square to determine the maximum height of the path of the water.
Mathematics
1 answer:
Doss [256]2 years ago
7 0

By the use of the completing the square method, the maximum height is 3 ±√29/4 + 9 m.

<h3>What is the maximum height of the water?</h3>

The maximum height has been modeled by the use of the equation f(x)= -4x^2 +24x -29. Now we know that f(x)= h so we can write;

h = -4x^2 +24x -29

Now we have;

0 = -4x^2 +24x -29

-4x^2 +24x -29= 0

x^2 - 6x = -29/4

(x - 3)^2 = -29/4 + 3^2

(x - 3)^2 =  -29/4 + 9

x = 3 ±√29/4 + 9 m

Learn more about completing the square:brainly.com/question/4822356

#SPJ1

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Find the slope of the line passing through the given points (-5, 14) and (-1,2).
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Simplify this expression.
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2 years ago
Tina is saving to buy a notebook computer. She has two options. The first option is to put $500 away initially and save $10 ever
Alexxandr [17]

Answer:

Tina would save the same amount using either option after 20 months.

With either option, Tina would save $700.

Step-by-step explanation:

This problem can be modeled by a first order equation:

Where Tina's saved money after n months is:

S(n) = S(0) + rn, where S(0) is the money put away initially and r is how much she saves every month.

The first option is to put $500 away initially and save $10 every month, so:

S_{1}(n) = 500 + 10n

The second option is to put $100 away initially and save $30 every month, so:

S_{2}(n) = 100 + 30n

After how many months would Tina save the same amount using either option?

It will happen at the month n in which S_{1}(n) = S_{2}(n), so:

S_{1}(n) = S_{2}(n)

500 + 10n = 100 + 30n

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20n = 400

n = \frac{400}{20}

n = 20.

Tina would save the same amount using either option after 20 months.

How much would she save with either option?

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S_{1}(20) = 500 + 10(20) = 500 + 200 = 700

With either option, Tina would save $700.

3 0
3 years ago
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