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Dennis_Churaev [7]
2 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]2 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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fgiga [73]

Answer:

The answer is x > 2

Step-by-step explanation:

to solve this inequality:

5x+7 > 17

Put "-7" on both sides

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divide by 5 on both sides

your answer should be 2.

8 0
1 year ago
the first group of students consists of 10 and their average age was 13 years old the next group consisted of 30 students and th
Kazeer [188]

Answer: The average was 9 years old find the average age of both groups is 10 years old.

Step-by-step explanation:

Formula foe average : \text{Average} =\dfrac{\text{Sum of all observations}}{\text{Number of observations}}

Given : The first group of students consists of 10 and their average age was 13 years old.

i.e. 13=\dfrac{\text{Sum of ages of students of first group}}{10}\\\\\Rightarrow\ \text{Sum of ages of students of first group}=13\times10=130      (1)

The next group consisted of 30 students and their average was 9 years old.

i.e. 9=\dfrac{\text{Sum of ages of students of next group}}{30}\\\\\Rightarrow\ \text{Sum of ages of students of nextgroup}=9\times30=270      (2)

Then from (1) and (2) , the sum of both groups (first group and next group )students = 130+270 =400

Combined students of both groups (first and next group )= 10+30=40

Now , the average of both groups =\dfrac{\text{Sum of combined students}}{\text{combined students}}

=\dfrac{400}{40}=10

Hence, the average was 9 years old find the average age of both groups is 10 years old.

4 0
3 years ago
A rectangular prism has a length of 114 yards, a width of 212 yards, and a height of 4 yards.
drek231 [11]

Answer: 96,672 yards cubed

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114yds × 212yds × 4yds = 96,672yds^3

Its already in simplest form since its all yards

But, you can also convert it into miles

In which 1 mile = 1760 yards

So you'd divide 96670 by 1760, and what ever answer youget would be the answer in miles

8 0
3 years ago
Read 2 more answers
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vivado [14]
12w+15r=18.30 /*2
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From the first equation we have
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3 0
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mash [69]

Answer:

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