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Delvig [45]
3 years ago
12

A baseball player swings and hits a pop fly straight up in air to the catcher. the height of the baseball in meters t seconds af

ter it is hit is given by the quadratic function h(t)=-4.9t^(2)+34.3t+1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
Mathematics
1 answer:
Ludmilka [50]3 years ago
3 0
h(t)=-4.9t^{2}+34.3t+1
\\h'(t)=(-4.9t^{2}+34.3t+1)'=-9.8t+34.3
\\h'(t)=0
\\-9.8t+34.3=0
\\
\\t= \frac{34.3}{9.8} =3.5
\\
\\h_{max}=h(3.5)=-4.9\times3.5^{2}+34.3\times3.5+1=61.025

The ball reaches its maximum height after 3.5 seconds, and the maximum height is 61.025 meters.
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andrew-mc [135]

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<h2>y = 2.8</h2><h2>x = 14</h2>

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3 years ago
What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?​
Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

 Given the equation:

\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}

Follow these steps to solve it:

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\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}

- Using the Difference of squares formula (a^2-b^2=(a+b)(a-b)) we can simplify the denominator of the right side of the equation:

\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}

- Multiply both sides of the equation by (m+3)(3-m) and simplify:

\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}

- Multiply both sides by m-3:

(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)

- Apply Distributive property and simplify:

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- Divide both sides of the equation by -6:

\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0

- Factor the equation and solve for "m":

(m-3)^2=0\\\\m=3

In order to verify it, you must substitute m=3 into the equation and solve it:

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<em>NO SOLUTION</em>

7 0
3 years ago
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