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Dennis_Churaev [7]
3 years ago
8

The height, h, in feet of a rock above the ground is given by the equation h = -16t^2 + 24t + 16, where t is the time in seconds

after the rock is thrown. At what time does the rock hit the ground?
Please show all work and not just the answer.
Mathematics
1 answer:
boyakko [2]3 years ago
8 0

The rock will hit the ground at 2 seconds.

Explanation:

Given that the height, h, in feet of a rock above the ground is given by the equation h=-16t^2+24t+16, where t is the time in seconds after the rock is thrown.

We need to determine the time at which the rock will hit the ground.

To determine the time, let us equate the height h = 0 in the equation h=-16t^2+24t+16, we get,

0=-16t^2+24t+16

Switch sides, we have,

-16 t^{2}+24 t+16=0

Let us solve the equation using the quadratic formula.

Thus, we have,

t=\frac{-24 \pm \sqrt{24^{2}-4(-16) 16}}{2(-16)}

Simplifying, we get,

t=\frac{-24 \pm \sqrt{576+1024}}{-32}

t=\frac{-24 \pm \sqrt{1600}}{-32}

t=\frac{-24 \pm 40}{-32}

Hence, the two values of t are

t=\frac{-24 + 40}{-32}   and   t=\frac{-24 -40}{-32}

Simplifying the values, we get,

t=\frac{16}{-32}  and  t=\frac{-64}{-32}

Dividing, we get,

t=-\frac{1}{2}  and  t=2

Since, t cannot negative values, we have,

t=2

Thus, the rock will hit the ground at 2 seconds.

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Answer:

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Answer:

We have a quotient between a 2 digit number and a 4 digit number.

The usual rule for this type of problems is:

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For example, if we divide 10 by 100 we have:

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The denominator has one more digit than the numerator, then n = 1.

this means that the first digit of the quotient, will be on the first place at the left of the decimal point.

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4 Find a formula for the exponential function passing through the points (-2, 4/9) and (3, 108)​
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9514 1404 393

Answer:

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Dividing the second equation by the first gives ...

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