17.02.2022 the following question

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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17.02.2022, solved by verified expert
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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 per second from a platform 24 feet high. the pumpkins height, h, at time --------(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 per second from a platform 24 feet high. the pumpkins height, h, at time

Again differentiating above equation with respect to t,

We get,   Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

For maximum or minimum,    Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

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 per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

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

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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 per second from a platform 24 feet high. the pumpkins height, h, at time --------(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 per second from a platform 24 feet high. the pumpkins height, h, at time

Again differentiating above equation with respect to t,

We get,   Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

For maximum or minimum,    Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

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 per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time

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

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Explanation:
Please refer to the attached table.  
The total cost includes the cost of the room and the cost of buffet dinner.
From the given table hotel 5,
The cost of the room for 120 people is found to be $166 per hour.
The conference will last for 5 hours so the total cost of the room is:
Cost of room=5*$166=$830.
From the given table hotel 5,
The cost of the buffet dinner per head is found to be $30.
Since there are total 120 people so the total cost of dinner is:
Cost of dinner=120*$30=$3600;
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We are given that hotel 5 has recently increased the total chargers by 10%:
Total cost=$4430*1.10;.
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Therefore, the booking cost of hotel 5 would be $4,873.

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The answer is in the image 
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The answer is in the image 

The answer is in the image 

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The solution is in the image given below

The solution is in the image given below