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2 years ago

8

As Juan continued his hitting practice showing off his abilities, one of the balls flew over the center field stands and into th

e parking lot. “Did you see that shot”, he yelled at the girls. “The ball hung in the air for at least 10 seconds”, he exclaimed.
The formula for this hit is:
h(x−) = 16+x2 8+3x 4 where h is the height of the ball and x is the number of seconds the ball is in the air.

I need help with part B

1 answer:

WARRIOR [948]2 years ago

4 0

Answer:

A. Find h(10) = 0 . . . (it is not)

B. h(5.235) = 0; hang time was about 5.235 seconds

Step-by-step explanation:

The hang time of the ball is the value of x in h(x) such that h(x) = 0.

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<h3>A.</h3>

Juan can show the hang time is 10 seconds by finding h(10) = 0. The value of h(10) is ...

h(10) = -16(10²) +83(10) +4 = -1600 +834 = -766 ≠ 0

Juan cannot prove the hang time was 10 seconds.

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<h3>B.</h3>

The hang time is the solution to ...

h(x) = 0

-16x² +83x +4 = 0 . . . . . use the given expression for h(x)

x² -5.1875x = 0.25 . . . . divide by -16

x² -5.1875x +6.7275390625 = 6.9775390625 . . . . add (5.1875/2)²

(x -2.59375)² = 6.9775390625 . . . . . . . . . . rewrite as a square

x = 2.59375 ±√6.9775390625 ≈ {-0.048, 5.235} . . . . square root, find x

The hang time of the ball was about 5.235 seconds.

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We like a graphing calculator for finding a quick solution to questions like this.

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For a moment, let $y=x^2-2x+5$ . Then by the distributive property,

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Again by the distributive property,

$2x^2p=2x^2(x^2-2x+5)=2x^4-4x^3+10x^2$

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Taking everything together, we get

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What is the simplified form of x minus 2 over x squared plus x minus 6divided byx squared plus 5x plus 4 over x plus 4?

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Answer:

$\dfrac{1}{x^2+4x+3}$

Step-by-step explanation:

You have asked for the simpilfied form of ...

$x-\dfrac{2}{x^2}+x-\dfrac{6}{x^2}+5x+\dfrac{4}{x}+4$

That would be ...

$\dfrac{7x^3+4x^2+4x-4}{x^2}$

We suspect that's not what you meant. Parentheses are required for grouping when you write math expressions in text form. They work best using math symbols instead of words. We think you mean

... ((x -2)/(x^2 +x -6))/((x^2 +5x +4)/(x +4))

_____

Maybe you want to simplify ...

$\displaystyle\frac{\left(\frac{x-2}{x^2+x-6}\right)}{\left(\frac{x^2+5x+4}{x+4}\right)}=\frac{(x-2)(x+4)}{(x-2)(x+3)(x+4)(x+1)}\\\\=\frac{1}{(x+1)(x+3)}=\frac{1}{x^2+4x+3}$

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Division of fractions works the same whether you're working with numbers or polynomials (or anything else). Dividing by something is the same as multiplying by its inverse (reciprocal).

(a/b)/(c/d) = (a/b)·(d/c)

I learned this as "invert and multiply". I've recently seen it referred to as "copy dot flip", meaning you copy the numerator, use a dot symbol to indicate multipication, then flip the denominator (make its reciprocal) to become what you're multiplying by.

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----------------------------------

ll = short hair, this is a lowercase L

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==============================================

<h3>Final Answer: A) 1/16</h3>

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