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Papessa [141]
3 years ago
11

Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t2 - 28t + 60, where t is the

time in seconds and h(t) is the height of his head, in inches.
How many seconds will it take for Daniel's head to reach the surface of the pool?
Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0
So, h(t) is how far is Daniel's head from the surface of the water, namely the surface itself is when the height is nill, so his head is at the surface and the height of it is just 0, thus h(t)  = 0.  Namely, what is "t" when h(t) is 0?

\bf h(t)=-8t^2-28t+60\implies \stackrel{h(t)}{0}=-8t^2-28t+60
\\\\\\
0=-2t^2-7t+15\implies 2t^2+7t-15=0\implies (2t+3)(t-5)=0
\\\\\\
\begin{cases}
2t+3=0\implies 2t=-3\implies &t=-\frac{3}{2}\\\\
t-5=0\implies &\boxed{t=5}
\end{cases}

clearly the seconds cannot be a negative unit, so is not -3/2.
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Answer:

The third choice is the one you want

Step-by-step explanation:

If we are to write the equation of a line perpendicular to WX, we first must determine what the slope of the WX is, because the line perpendicular to WX has a slope that is the flip of the slope of WX with the opposite sign.  Solving for y takes care of finding the slope of WX:

2x + y = -5 so

y = -2x - 5

The slope is -2.  That means that the reciprocal slope is 1/2.  Using that slope along with the coordinates x = -1 and y = -2, we first write the line using point-slope form and then solve it for y.  Start by filling in the m, the x value and the y value:

y - (-2) = \frac{1}{2}(x-(-1))

Getting rid of the double negatives gives us:

y+2=\frac{1}{2}(x+1)

Distributing then gives us:

y+2=\frac{1}{2}x+\frac{1}{2}

And finally solving for y (I am going to express the 2 on the left as 4/2 when I move it by subtraction in order to add those fractions):

y=\frac{1}{2}x+\frac{1}{2}-\frac{4}{2}

And the final equation in slope-intercept form is:

y=\frac{1}{2}x-\frac{3}{2}

8 0
2 years ago
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7 0
3 years ago
Read 2 more answers
Find the percent of change. Round to the nearest percent.
katovenus [111]

Answer:

<u> -54.5%</u>

Step-by-step explanation:

You will have to use this formula

\frac{new value-oldvalue}{oldvalue}

When substituted in you have \frac{30-66}{66}

30-66=-36

-36/66= -0.54 (54 repeating)

Then you have to convert this into a percentage, -54.54(repeating) percent

To the nearest hundredth you would round down to<u> -54.5%</u>.

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8 0
3 years ago
Drag a statement or reason into the blank to complete this proof;
sergiy2304 [10]
\left[x \right] = \left[ 5\right][x]=[5]2(x+1)/−2 = 8−2 _________
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6 0
3 years ago
A golfer keeps track of his score for playing nine holes of golf​ (half a normal golf​ round). His mean score is 8080 with a sta
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Answer:

Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and 11\sqrt2 respectively.

Step-by-step explanation:

Given that,

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E(X) = 80

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For the second 9 holes Y:

E(Y) = 80

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For the sum W=X+Y, the following properties holds for means , variance and standard deviation :

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            and

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Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and 11\sqrt2 respectively.

                                               

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