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riadik2000 [5.3K]
2 years ago
8

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine

burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet
Mathematics
1 answer:
Free_Kalibri [48]2 years ago
3 0
The maximum height is 144 feet.

The maximum height is the y-coordinate of the vertex.  To find the vertex, we first use x = -b/2a.  For our information, that is x=-64/2(-16) = -64/-32 = 2.

Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144
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<em>The point where a function (for our problem its the cubic function shown)</em>

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<u>and/or</u>

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<em>is a zero of the function.</em>

From the graph shown, we can clearly see that it cuts the x-axis at -1 and touches the x-axis at 2.

So the zeros are at -1 and 2.


ANSWER: {-1,2}


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Cody's rent is increasing by $51 per month starting next year. That is an increase of 15% from his current monthly rent. Let r r
Inessa05 [86]

Answer:

r = 43.35

Step-by-step explanation:

Given

Current\ Rent = r

Increment = 15\%

New\ Rent = \$51

Required

Determine the value of r

The value of r can be set up percentage increase formula as follows:

\%Increment  = \frac{New\ Rent - Current\ Rent}{Current\ Rent}

Substitute values in the above equation

15\% = \frac{51 - r}{51}

Cross Multiply

51 - r = 15\% * 51

Convert percentage to decimal

51 - r = 0.15 * 51

51 - r = 7.65

And the value of r\ is\ calculated\ using:

r = 51 -7.65

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Hence, Cody's current rent is $43.35 monthly

8 0
3 years ago
Keegan leans an 18-foot ladder against the top of a wall. The bottom of the ladder is 4.5 feet from the base of the wall. What i
zaharov [31]

Answer: C. 17.5 feet

Step-by-step explanation:

The attached photo shows the triangle ABC formed by the ladder and the wall. It is a right angle triangle because one of its angles is 90 degrees. The ladder is the hypotenuse of the triangle. To determine the height of the wall, we would find BC by applying Pythagoras theorem

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BC = √303.75 = 17.5 feet.

3 0
3 years ago
Evan enjoys eating fresh fruits and vegetables. This
Arlecino [84]

Answer:

2304 \ in^3

Step-by-step explanation:

Given the surface dimensions of the garden as 24 inches by 48 inches:

#Calculate surface area of the garden's top:

A=lw\\\\=48\times 24\\\\=1152 in^2

Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:

V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3

Hence, the amount of soil used is 2304 cubic inches.

4 0
3 years ago
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