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sveta [45]
3 years ago
7

A community theater uses the function p(d)=−4d2+200d−100 to model the profit (in dollars) expected in a weekend when the tickets

to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Show your reasoning. At what price would the theater make the maximum profit, and what is that maximum profit. Show your reasoning.
Mathematics
1 answer:
bixtya [17]3 years ago
8 0

Answer:

price = $25

maximum profit is $2400

Step-by-step explanation:

Given the function modeled by the community theatre as

p(d)=−4d^2+200d−100

The maximum profit will be ,ade at dP/dd = 0

dP/dd = -8d + 200

0 = -8d + 200

8d = 200

d = 200/8

d = 25

hence he theatre will make maximum profit at a price of $25

Substitute d = 25 to get the maximum profit

p(25)=−4(25)^2+200(25)−100

p(25) = -2500+5000-100

p(25) = 2400

Hence the maximum profit is $2400

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Ln how many ways 5 person sitted in a round table having 8 seats?
kvasek [131]

Answer: First consider the case that ‘just’ 5 persons are seated around a round table.

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Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

Step-by-step explanation:

First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

5 0
3 years ago
The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triang
kipiarov [429]

Answer:

The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Step-by-step explanation:

The image related to the exercise is necessary, to be able to solve therefore the attached one.

We have the following information:

Perimeter of the triangle = 58 units

Hypotenuse = 24 units

We have that the other two sides are equal and have x units, therefore we have the following:

x + x + 24 = 58

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Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.

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4 0
2 years ago
(Worth 30 points) What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term
kolbaska11 [484]

Answer:

a_n=5-2(n-1), all integers where n≥1

Step-by-step explanation:

we know that

The explicit equation for an arithmetic sequence is equal to

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a_n is the th term

a_1 is the first term

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n is the number of terms

we have

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Remember that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference.

To find out the common difference subtract the first term from the second term

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substitute the given values in the formula

a_n=5-2(n-1)

The domain is all integers for n\geq 1

3 0
3 years ago
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