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Dennis_Churaev [7]
3 years ago
13

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 15m/s. The ball's height h (in meters) aft

er t seconds is given by the following.
h=1+15t-5t^2
Find all values of t for which the ball's height is 6 meters. Round your answer(s) to the nearest hundredth.
Mathematics
1 answer:
lakkis [162]3 years ago
8 0

\bf \stackrel{\textit{ball's height}~\hfill }{\stackrel{\downarrow }{h}=1+15t-5t^2}\implies \stackrel{\textit{ball's height}~\hfill }{\stackrel{\downarrow }{6}=1+15t-5t^2}\implies 0=-5+15t-5t^2 \\\\\\ ~~~~~~~~~~~~\textit{using the quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-15}t\stackrel{\stackrel{c}{\downarrow }}{+5}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}

\bf t=\cfrac{-(-15)\pm\sqrt{(-15)^2-4(5)(5)}}{2(5)}\implies t=\cfrac{15\pm\sqrt{225-100}}{10} \\\\\\ t=\cfrac{15\pm\sqrt{125}}{10}\implies t=\cfrac{15\pm\sqrt{5^2 \cdot 5}}{10}\implies t=\cfrac{\stackrel{3}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\pm ~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{5}}{\underset{2}{~~\begin{matrix} 10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}

\bf t=\cfrac{3\pm \sqrt{5}}{2}\implies t= \begin{cases} \frac{3+ \sqrt{5}}{2} \approx 2.618\\\\ \frac{3- \sqrt{5}}{2}\approx 0.382 \end{cases}

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Please help math i will give good rating and 5 stars if answer question
Talja [164]

Hey!

Let's walk through this together.

Possible Answers: {5, 7, 9, 11, 13}

Let's start with 5.

5-4<8

1<8

So, 5 is CORRECT.

Next, 7.

7-4<8

3<8

So, 7 is CORRECT.

Next, 9.

9-4<8

5<8

So, 9 is CORRECT.

Next, 11.

11-4<8

7<8

So, 11 is CORRECT.

Last, 13.

13-4<8

11<8

So, 13 is INCORRECT.

Your answers are: {5,7,9,11}

So D.

Hope this helps!

<h2><em>~~~PicklePoppers~~~</em></h2>
4 0
2 years ago
7 - 5x + 1<br>Terms:<br>Like Terms:<br>Constants:<br>Coefficients:​
SOVA2 [1]
Terms : 7 , -5x , 1
like terms : 7 and 1
constants : 1
coefficients : -5
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Answer:

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Step-by-step explanation:

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Answer:

16/9

Step-by-step explanation:

(4/3) ^2

(4/3) * (4/3)

First the numerators

4*4 = 16

Then the denominators

3*3 = 9

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16/9

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Step-by-step explanation:

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