Answer: maximum height of the football = 176 feet
Step-by-step explanation:
We want to determine the maximum height of the football from the ground. From the function given,
h(t) = -16t^2+96t +32, it is a quadratic function. Plotting graph if h will result to a parabolic shape. The maximum height of the football = the vertex of the parabola. This vertex is located at time, t
t = -b/2a
b = 96 and a= -16
t = -b/2a = -96/2×-16= 3
Substituting t = 3 into the function if h
h(t) = -16×3^2+96×3 +32
=-16×9 + 96×3 +32
= -144+ 288+32
=176 feet
Aprox 14.663
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Answer:
a) 81
b) 16,807
c) 100
d) 78125
Step-by-step explanation:
a)
3^2 x 3^2
Step 1. Simplify the exponents
3^2 = 3 x 3 = 9
Step 2. Multiply
9 x 9 = 81
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b)
7 x 7^4
Step 1. Simplify the exponent
7^4 = 7 x 7 x 7 x 7 = 2401
Step 2. Multiply
7 x 2401 = 16,807
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c)
10^9 divided by 10^7
Step 1. Simplify the exponents
10^9 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1000000000
10^7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10000000
Step 2. Divide
1000000000 divided by 10000000 = 100
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d)
5^8 divided by 5
Step 1. Simplify the exponent
5^8 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 390625
Step 2. Divide
390625 divided by 5 = 78125
Keep in mind that, the directrix is "p" distance units away from the vertex, and the focus point is also "p" distance units from the vertex but in the opposite direction, so in short the vertex is half-way between both of them.
in this case the vertex is at the origin, and the directrix 5 units above it, so that means the parabola is vertical and opening downwards, like the one in the picture below, and the focus point is 5 units the other way.
