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hram777 [196]
3 years ago
12

Benjamin threw a rock straight up from a cliff that was 48 ft above the water. If the height of the rock​ h, in​ feet, after t s

econds is given by the equation h = -16 t² + 52 t + 48, how long will it take for the rock to hit the​ water?
Mathematics
1 answer:
fomenos3 years ago
5 0

Answer: It will take 4 seconds  for the rock to hit the​ water.

Step-by-step explanation:

Given : Benjamin threw a rock straight up from a cliff that was 48 ft above the water.

If the height of the rock​ h, in​ feet, after t seconds is given by the equation

h = -16 t^2+ 52 t + 48

To find : Time taken for the rock to hit the​ water.

When rock hit the water height becomes zero , i.e. put h = 0 , we get

-16 t^2+ 52 t + 48 =0

Divide equation by 2 , we get

-8t^2+26t+24=0

The Laue of x for ax²+bx+c =0 is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

So , t=\frac{-26\pm\sqrt{(26^{2}-4(-8)(24))}}{2(-8)}

t=\dfrac{-26\pm 38}{-16}\\\\ t=-\dfrac{-26+38}{-16}=-0.75\ \ t=\dfrac{-26-38}{-16}=4

Since t cannot be negative , so t= 4

Hence, it will take 4 seconds  for the rock to hit the​ water.

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someone please help :( a sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Ore
Volgvan

Answer:

Oregon:

Median: 467.5

Mean: 451.33

Standard Deviation: 113.6

Washington:

median: 380

Mean: 396.6

Standard deviation: 56.3

Step-by-step explanation:

To calculate the median, we need to organize the price and select the value that is in the middle position.

To calculate the mean, we need to sum all the values and divide them by the number of values

To calculate the standard deviation, we need to square the distances between every price and the mean, sum it all and divide them by the number of values less 1 and finally calculate the square root.

So, for Oregon, the organized values are:

$295, $345, $460, $475, $538, $595

The median is a value between $460 and $475. it is calculated as:

\frac{460+475}{2}=467.5

The mean is:

\frac{295+475+345+595+538+460}{6}=451.33

The standard deviation is:

\sqrt{\frac{(295-451.3)^2+(475-451.3)^2+(345-451.3)^2+(595-451.3)^2+(538-451.3)^2+(460-451.3)^2}{6-1}}=113.6

At the same way, we can calculate the median, mean, and standard deviation for Washington and get:

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3 0
2 years ago
Which angle measures create a triangle with three different side lengths?
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Answer:

C

Step-by-step explanation:

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A: In the case of A, The angles do not add up to 180 so this is not possible. Even if it was, the angles are all the same and the side lengths would be as well.

B: Two angles are the same, therefore, 2 sides will be the same, even though the two sides added together will be larger than the side opposite.

D: Two angles are the same. The angles add to 180. The triangle will have 2 equal sides.

C: Answer. The three given angles add to 180. They are different. Unless the side opposite 93 exceeds the length of the other 2 sides, this forms a triangle with 3 different  sides. Using other methods to calculate the answer the other 2 sides do exceed the the base length so everything is fine.  

3 0
2 years ago
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