Mathematics, 18.12.2019 05:31 tlperez1230

Afirework is launched upward from the ground at an initial velocity of 60 feet per second.
h = -16t^2 + 60t
how long will it take the fireworks to reach its maximum height?

what is the maximum height that the firework will reach?

when will the fireworks hit the ground?

Answers: 1

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Answer from: JeonTaekook

It will take the fireworks $1\dfrac{7}{8}$ seconds to reach its maximum height.

The maximum height that the firework will reach is $56\dfrac{1}{4}$ feet.

The fireworks will hit the ground in $3\dfrac{3}{4}$ seconds.

Step-by-step explanation:

A firework is launched upward from the ground at an initial velocity of 60 feet per second. The function describing this situation is

h = -16t^2 + 60t

1. Find t-coordinate of the vertex of the parabola:

$t_v\\ \\=\dfrac{-b}{2a}\\ \\=\dfrac{-60}{2\cdot (-16)}\\ \\=\dfrac{15}{8}\ seconds$

It will take the fireworks $\dfrac{15}{8}=1\dfrac{7}{8}$ seconds to reach its maximum height.

2. Find h-coordinate of the vertex of the parabola:

$h(t_v)\\ \\=-16\cdot \left(\dfrac{15}{8}\right)^2+60\cdot \left(\dfrac{15}{8}\right)\ \\=-16\cdot \dfrac{225}{64}+\dfrac{30\cdot 15}{4}\\ \\=\dfrac{-225+450}{4}\\ \\=\dfrac{225}{4}\\ \\=56\dfrac{1}{4}\ ft$

The maximum height that the firework will reach is $56\dfrac{1}{4}$ feet.

3. The fireworks will hit the ground when h = 0:

$-16t^2+60t=0\\ \\4t(-4t+15)=0\\ \\t=0\ \text{or}\ -4t+15=0\\ \\t=0\ \text{or}\ t=\dfrac{15}{4}\ seconds$

The fireworks will hit the ground in $\dfrac{15}{4}=3\dfrac{3}{4}$ seconds.

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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Afirework is launched upward from the ground at an initial velocity of 60 feet per second.
h =...

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