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13 days ago

A baseball is thrown up in the air. The table shows the heights y (in feet) of the baseball after x seconds.

Mathematics

1 answer:

lawyer [4K]13 days ago

7 0

Answer:

Alright, we can express the baseball's motion with an equation like:

h(x) = a*x^2 + b*x + c

Here, x denotes time, while h(x) indicates height.

Let’s construct this:

The acceleration is:

a(t) = a

For velocity, integrating over time results in:

v(x) = a*x + v0

Where v0 signifies the initial vertical velocity.

Subsequently, we can determine position or height by integrating once more:

h(x) = a*x^2 + v0*x + h0

Here, h0 is the initial height.

h(x) = a*x^2 + v0*x + h0.

When x = 0s, h(0s) = 6ft

<pthus:>

h(0s) = a*0s^2 + v0*0s + h0 = 6ft

h0 = 6ft.

It’s also noted that:

h(2s) = h(4s)

a*x^2 + b*x + c

The symmetry line is given by:

x = -b/2a

b = v0

a = a

3s = -v0/(2*a)

v0 = -3s*(2a)

h(x) = a*x^2 - 6s*a*x + 6ft

h(2s) = 22ft = a*(2s)^2 - 6s*a*2s + 6ft

h(x) = (-2ft/s^2)*x^2 + (12ft/s)*x + 6ft

b) The height after 5 seconds is expressed as:

h(5s) = (-2ft/s^2)*(5s)^2 + (12ft/s)*5s + 6ft = 16ft

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6 days ago

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 1

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Question:

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B) Asymptotes exist at x = 7 and.

C) Asymptotes exist at x = –7 and.

D) Gaps are present at (–7, 0) and.

Answer:

B) Asymptotes exist at x = 7 and $(x = \frac{-4}{3})$

Step-by-step explanation:

Given:

$f(x) = \frac{x-5}{3x^2-17x-28}$

Goal:

Identify the correct statement

$f(x) = \frac{x-5}{3x^2-17x-28}$

We need to factor the denominator first.

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Divide both sides by 3:

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lim f(x) as $(x = \frac{-4}{3})$ = ±∞

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3 days ago

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Answer:

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