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.

16

17.02.2022, solved by verified expert

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,

--------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,

Again differentiating above equation with respect to t,

We get,

For maximum or minimum,

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

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

And, the maximum value is,

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

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,

--------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,

Again differentiating above equation with respect to t,

We get,

For maximum or minimum,

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

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

And, the maximum value is,

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

### Faq

Mathematics

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
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

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

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

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Mathematics

The solution is in the following image

Mathematics

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

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

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