Help me please it’s due today
1 answer:
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.
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Answer:
Price of roses is proportional to the number of roses.
Step-by-step explanation:
Let the price of roses are proportional to the number of roses.
Equation representing this phenomenon will be,
P = k(R) ⇒ k =
where 'P' = price of the roses
R = Number of roses
k = Proportionality constant
If we substitute the values of P and R and we get the same value of constant 'k', then the equation will be true.
For R = 3 and P = $9
k =
k = 3
For R = 6 and R = 18
k =
k = 3
K is same in both the conditions, therefore, Price of roses are proportional to the number of roses.