Oct 16, 10:30:54 AMA rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer 1

Answer:

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function $f(x)=-16x^2+64x+8$ which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

$f(0)=-16(0)^2+64(0)+8$

Evaluate:

$f(0)=8$

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

$(-(b)/(2a),f(-(b)/(2a)))$

Let's label our coefficients. We have $-16x^2+64x+8$

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

$x=-(64)/(2(-16))\n\Rightarrow x=64/32=2$

Now, to find the maximum height, substitute 2 back into our function f(x):

$f(2)=-16(2)^2+64(2)+8$

Evaluate:

$f(2)=-16(4)+64(2)+8\n\Rightarrow f(2)=-64+128+8\n\Rightarrow f(2)=72\text{ feet}$

Therefore, the rocket reaches a maximum height of 72 feet.

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Let’s use a sample set.
Let’s use 5 and 7.
5•5=25
7•7=49
49+25=74
The integers are 5 and 7. The way I found this was by thinking of 9 and 11 at first. I knew that it would be entirely way too much, but 3 and 1 would be too little. 5 and 7 fit in the middle of those two samples.

Your answer is 5 and 7.

Can someone Help plz!!

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Step-by-step explanation:

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Because according to pytheorem

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