Part 2

this activity will you meet these educational goals:

you will create a function to model a fireworks show and examine the attributes of the function.

you’re in charge of planning a fireworks show. the company you hire proposes using fireworks called mortar fireworks. these fireworks are placed in a tube that sits on the ground or a flat surface and are shot from the tube with an initial velocity that propels them into the sky.

mortar fireworks have two fuses that are lit at the same time. the first fuse burns fastest and causes the initial force that launches the firework into the sky. the second fuse takes longer to burn. when the second fuse reaches the middle of the firework, the firework explodes and we see the light show in the sky. this second fuse does not add any extra propulsion to the firework while it’s in the air.

you plan to have the company light the fireworks from the ground. based on information provided by the company, you’ve determined that the fireworks will have an initial velocity of 192 feet/second.

the formula for the vertical motion of an object is h = -16t2 + v0t + h0, where h is the height of the object, h0 is the initial, or starting, height, v0 is the initial velocity, and t is the time in seconds.

using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. interpret what the value represents in this situation.

Step-by-step explanation:

Maximum Value → Parabola opens downward [−A]

Minimum Value → Parabola opens upward [A]

See graph above

I am joyous to assist you anytime.

The maximum value of f(t) is 576, the maximum height of the firework.

Step-by-step explanation:

h = -16t² + v₀t + h₀

Data:

v₀ = 192 ft/s

h₀ = 0

Calculation:

h = -16t² + 192t  

This is the equation of a parabola.

We must solve the equation to find the maximum height.  

The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.

Complete the square

(a) Divide both sides by -16 to make the coefficient of  t² equal to 1.

(-1/16)h = t² - 12t  

(b) Square half the coefficient of t

(-12/2)² = (-6)² = 36

(c) Add and subtract it on the right-hand side

(-1/16)h = t² - 12t  + 36 - 36  

(d) Write the first three terms as the square of a binomial

(-1/16)h = (t - 6)² - 36

(e) Multiply both sides by -16

h = -16(t - 6)² + 576

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 = 6 and k = 576, so the vertex is at (6, 576).

The vertex represents the maximum height of the firework.

The Figure below shows that your firework reaches a maximum height of 576 ft  6 s after ignition.

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

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

(

1

+

20

100

)

=

$

87.12

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

$

87.12

(

1

+

8

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  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

related questions

yes

step-by-step explanation: