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wel
3 years ago
5

A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32

t + 6. Describe in detail (using formulas and/or specific steps needed) TWO ways to find the maximum height reached by the ball.
Mathematics
1 answer:
olga2289 [7]3 years ago
4 0

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

       32*t = 32

            t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

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The morning temp. In Atlanta, Georgia is 21 1/4 degrees. During the day it warms up 6 2/7 degrees. What is the new temp
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Answer:

27 15/28 degrees

Step-by-step explanation:

Since we are adding 21 1/4 to 6 2/7, we need to find the LCD, or, least common denominator, so that we can add 1/4 and 2/7 together.

1*4=4             1*7=7

2*4=8           2*7=14

3*4=12          3*7=21

4*4=16          <u>4*7=28</u>

5*4=20

6*4=24

<u>7*4=28</u>

Since we had to multiply 7 four times to get it equal to 28, we need to take 2/7 * 4/4. This will give you 8/28. Then, since we multiplied 4 seven times to get it equal to 28, we need to take 1/4 *7/7. This will give you 7/28. Finally, you need to add 8/28 and 7/28 since they now share the same denominator.

8/28 + 7/28=15/28

For our last step, we need to add the whole numbers together so the answer is complete.

21+6=27

27+15/28= 27 15/28 degrees

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2 years ago
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