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antiseptic1488 [7]
3 years ago
11

A model rocket is launched with an initial upward velocity of 202 ft/s. The rocket's height h (in feet) after t seconds is given

by the following.
h= 202t-16t^2
Find all values of t for which the rocket's height is 82 feet.

Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Mathematics
1 answer:
7nadin3 [17]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

The rocket will reach a height of 82 feet at:

t1=0.42s

and

t2=12.21s

<h2>Why?</h2>

We are asked to find the value(s) of t for which the rocket's height is 82 feet, so, we need to replace the height value (82 feet) into the given quadratic equation, and then, isolate "t" making the equation equal to 0.

So, writing the quadratic formula, we have:

\frac{-b+-\sqrt{b^{2} -4ac} }{2a}

The given function is:

-16x^2+202x=h

Substituting h equal to 82 feet, we have:

-16x^2+202x=82

-16x^2+202x-82=0

Where,

a=-16\\b=202\\c=-82

Then, substituting it into the quadratic equation we have:

\frac{-b+-\sqrt{b^{2} -4ac} }{2a}=\frac{-202+-\sqrt{202x^{2} -4*-16*-82} }{2*-16}\\\\\frac{-202+-\sqrt{202x^{2} -4*-16*-82} }{2*-16}=\frac{-202+-\sqrt{40804-5248} }{-32}\\\\\frac{-202+-\sqrt{40804-5248} }{-32}=\frac{-202+-\sqrt{35556} }{-32}=\frac{-202+-(188.56) }{-32}\\\\t1=\frac{-202+(188.56) }{-32}=0.42\\\\t2=\frac{-202-(188.56) }{-32}=12.205=12.21

So, the rocket will reach a height of 82 feet at:

t1=0.42s

and

t2=12.21s

Have a nice day!

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Step-by-step explanation:

Since there is no picture attached to depict the house and its dimension, I am taking values of a similar problem.

<em><u>Dimensions of Shed</u></em>

2 walls with dimensions of 15 ½ ft. by 12 ft.

2 walls with dimensions of 25 ¼ ft. by 12 ft.

Ceiling with dimensions of 15 ½ ft. by 25 ¼ ft.

2 windows that are each 2 ft. by 4½ ft. as well as an 8-ft. by 5-ft. door

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We need to find the total wall area and ceiling area which when combined will give us the total area shed's outer surface that needs to be painted.

For total area of the wall, we need to first find the sum of area for each wall and subtract area of windows and door

Wall Area = Area of 1st two walls+Area of other two walls-Area of 2 windows-Area of door=[15.5(12)(2)] + (25.25) (12) (2) - (2)(2) (4.5) -(8)(5)

Wall Area = 371 + 606 - 17 - 40

Wall Area = 920 square ft = 102.2 square yards

Ceiling Area is just the area of the ceiling

Ceiling Area = (15.5) (25.25 )

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Which is the area paul needs to cover with paint.

<em>Note: Converted Square foot to square yard as the problem requires that.</em>

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