I’m multiplying polynomials. And have no idea where to start. Please help, it’s almost 2 AM and it was due days ago!!
1 answer:
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Answer:
49 ft
Step-by-step explanation:
h(t) = 56t - 16t²
This is the equation of a parabola.
We must solve the equation to find the time (t) when the ball reaches its maximum height (h).
The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.
One way to solve this problem is to convert the equation to the vertex form.
We do that by completing the square.
Calculation:
h = -16t² + 56t
Divide both sides by -16 to make the coefficient of t² equal to 1.
(-1/16)h = t² - ⁷/₂t
Square half the coefficient of t
(-7/4)² = 49/16
Add and subtract it on the right-hand side
(-1/16)h = t² - ⁷/₂t + 49/16 - 49/16
Write the first three terms as the square of a binomial
(-1/16)h = (t - ⁷/₄)² - 49/16
Multiply both sides by -16
h = -16(t - ⁷/₄)² + 49
You have converted your equation to the vertex form of a parabola:
y = a(t - h)² + k = 0,
where (h, k) is the vertex.
h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).
The time to reach maximum height is ⁷/₄ s = 1.75 s.
The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.
Answer:
16 people
Step-by-step explanation:
First subtract the cost of the rental from the amount of money:
$400-$150 = $250
Therefore Tia has $250 to spend for additional people. Then if each person is $15, divide the remaining amount of money by the amount of money per person:
$250/$15 = 16.67
Since you can't have 0.67 of a person she can have 16 people go with her.
This can also be modeled by this inequality: