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
The answer for the first question is D.
here's why: John goes 60 miles an hour so to go 240 miles is 4, and to 30 miles is 30 minutes. so that would mean it would take him 4.5 hours ( 4 hours and 30 minutes. )
The answer to the second question is C.
here's why: since each of the workers mow at the same speed, there's no need to worry about the 9. now you just need to divide 45 by 10 ( 4.5 ) to see how many lawns he mows in an hour ( 4.5 )
Pedro had 1487 hits
Ricky had 1202 hits
2688/2=1344.5
285/2=142.5
1344.5-142.5=1202 (Ricky)
1344.5+142.5=1487 (Pedro)
1487-1202=285
1487+1202=2689
Answer: C) Sometimes positive; sometimes negative
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Explanation:
Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5
Plug this into f(x)
f(x) = x(x+3)(x+1)(x-4)
f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)
f(-0.5) = -0.5(2.5)(0.5)(-4.5)
f(-0.5) = 2.8125
We get a positive value.
This shows that f(x) is positive on the region of -1 < x < 0
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Now pick a value between x = 0 and x = 4. I'll use x = 1
f(x) = x(x+3)(x+1)(x-4)
f(1) = 1(1+3)(1+1)(1-4)
f(1) = 1(4)(2)(-3)
f(1) = -24
Therefore, f(x) is negative on the interval 0 < x < 4
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In short, f(x) is both positive and negative on the interval -1 < x < 4
It's positive when -1 < x < 0
And it's negative when 0 < x < 4