12.08.2022

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time t seconds can be represented by the equation h(t) = -16t^2+ 72t +24.find the maximum height of the pumpkin and the time it takes to reach this point.

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Step-by-step answer

17.02.2022, solved by verified expert
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3 students found this answer . helpful

Maximum height =  105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03 --------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,    Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Again differentiating above equation with respect to t,

We get,   Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

For maximum or minimum,    Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds

It is was helpful?
Unlock the full answer

Maximum height =  105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03 --------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,    Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Again differentiating above equation with respect to t,

We get,   Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

For maximum or minimum,    Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Apumpkin is launched directly upwards at 72 feet, №15221510, 12.08.2022 18:03

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds

It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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