For every $2 Pam saves, her brother saves $7. If Pam has $20 in her account how much does her brother have?

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(

jasenka [17]

9514 1404 393

Answer:

7.5 ft
32.5 ft, 5 ft
10.7 ft

Step-by-step explanation:

a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.

The irrigation system is positioned <u> 7.5 </u> feet above the ground

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b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...

h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet

The spray reaches a maximum height of <u> 32.5 </u> feet at a horizontal distance of <u> 5 </u> feet from the sprinkler head.

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c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.

The spray reaches the ground at about <u> 10.7 </u> feet away.

3 0

2 years ago

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Please Please Please help with this math problem

katovenus [111]

The revenue as a function of x is equal to -x²/20 + 920x.
The profit as a function of x is equal to -x²/20 + 840x - 6000.
The value of x which maximizes profit is 8,400 and the maximum profit is $3,522,000.
The price to be charged to maximize profit is $500.

<h3>How to express the revenue as a function of x?</h3>

Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.

Mathematically, the revenue can be calculated by using the following expression:

R(x) = x × P(x)

Revenue, R(x) = x(-1/20(x) + 920)

Revenue, R(x) = x(-x/20 + 920)

Revenue, R(x) = -x²/20 + 920x.

Expressing the profit as a function of x, we have:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = -x²/20 + 920x - (80x + 6000)

P(x) = -x²/20 + 840x - 6000.

For the value of x which maximizes profit, we would differentiate the profit function with respect to x:

P(x) = -x²/20 + 840x - 6000

P'(x) = -x/10 + 840

x/10 = 840

x = 840 × 10

x = 8,400.

For the maximum profit, we have:

P(x) = -x²/20 + 840x - 6000

P(8400) = -(8400)²/20 + 840(8400) - 6000

P(8400) = -3,528,000 + 7,056,000 - 6000

P(8400) = $3,522,000.

Lastly, we would calculate the price to be charged in order to maximize profit is given by:

P(x) = -1/20(x) + 920

P(x) = -1/20(8400) + 920

P(x) = -420 + 920

P(x) = $500.

Read more on maximized profit here: brainly.com/question/13800671

#SPJ1

3 0

1 year ago

PLEASE LOOK AT PHOTO! WHOEVER ANSWERS CORRECTLY I WILL MARK BRAINIEST!!

8_murik_8 [283]

Step-by-step explanation:

let m2 be x

then m1 = 4x

Since, m1+m2 = 115

therefore x + 4x = 115

5x = 115

x = 23

so , m2 = 23°

3 0

2 years ago

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Can someone help me :(( thank you so so much if u do <33:)

Keith_Richards [23]

Answer:

13

Step-by-step explanation:

8-13=-5

4 0

2 years ago

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Please Help Me!! Its for tomorrow and i rlly need help pls pls pls pls

DanielleElmas [232]

Answer:

perimeter = 6x + 15

Step-by-step explanation:

The perimeter of the triangle is the distance around the triangle.

We need to apply our ability to convert word problems in to mathematical expressions.

We were told that the bottom of the triangle is x units.

From the diagram perimeter 4x + 12 + x + 3 + x = 6x + 15

Four times the length of the bottom will be 4x .

12 more than 4 times the bottom will be 4x + 12.

Hence another side of the triangle is 4x + 12.

Finally we were told that the last side is 3 more than the bottom, that will be x + 3.

4 0

2 years ago

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For every $2 Pam saves, her brother saves $7. If Pam has $20 in her account how much does her brother have?​

For every $2 Pam saves, her brother saves $7. If Pam has $20 in her account how much does her brother have?