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Alik [6]
3 years ago
10

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15/ms . The ball's height h (in meters) a

fter t seconds is given by the following. =h+2−15t5t2 Find all values of t for which the ball's height is 7 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Mathematics
1 answer:
Irina-Kira [14]3 years ago
4 0
The height that a ball reaches at a certain time t is given by the equation,
           h = 2 - 15t + 5t²
We are asked to compute for the values of t that would allow the ball to reach a height of 7 meters. 

Substitute the 7 to the equation,
         7 = 2 - 15t + 5t²
Transposing,
               5t² - 15t - 7 + 2 = 0
Simplifying,
               5t² - 15t - 5 = 0
Divide the equation by 5,
               t² - 3t - 1 = 0

The values of t can be calculated through the quadratic formula,
             t = (-b +/- sqrt(b² - 4ac))/2a

Substituting, 
             t = (3 +/-sqrt (9 - 4(-1)) / 2(1)
              t = 3.3 or t = -0.30

Since, we cannot have t as a negative number hence, our final answer is:
      <em> t = 3.3 s</em>
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5 0
3 years ago
How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen
fenix001 [56]

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

n = 6

k = 3

Now we can use the permutation formula:

_{n}P_{k}=\dfrac{n!}{(n-k)!}

_{6}P_{3}=\dfrac{6!}{6-3)!}

_{6}P_{3}=\dfrac{6!}{3!}

_{6}P_{3}=\dfrac{6*5*4*3*2*1}{3*2*1}

The 3*2*1 cancels out and leaves us with:

_{6}P_{3}=6*5*4

_{6}P_{3}=120

So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.

6 0
3 years ago
Read 2 more answers
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