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andrezito [222]
3 years ago
15

Which term of ap 30,27,24is0

Mathematics
1 answer:
son4ous [18]3 years ago
8 0

Answer:

11th term is 0

Step-by-step explanation:

30, 27 , 24 ,......0

a = first term = 30

Common difference = second term - first term = 27 - 30 = -3

nth term = a+(n-1)*d

a + (n-1)d = 0

30 + (n - 1) *(-3) = 0

30 + n*(-3) -1*(-3) = 0

30 - 3n + 3 = 0

      -3n + 33 = 0

               -3n = -33

                   n = -33/-3

n = 11

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The theater make the maximum profit at d = $25. Then the maximum profit of the theatre is $ 900.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It may be increasing or decreasing.

A community theater uses the function P(d) = (− 4d + 40) (d − 40) to model the profit (in dollars) expected on a weekend when the tickets to a comedy show are priced at d dollars each.

Then the maximum profit of the theatre will be

The function is P(d) = (− 4d + 40) (d − 40)

Differentiate the function with respect to d and put it equal to zero for maximum or minimum profit.

\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= 0\\\\\dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) &= 0\\\\(-4d+40) -4 (d-40) &= 0\\\\-8d + 200 &= 0\\\\d &= 25 \end{aligned}

Then the checking for maximum or minimum, again differentiate, we have

\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(-8d + 200) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= -8\\\\ \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) & < 0\end{aligned}

The value is less than zero hence maximum value will occur at d = 25.

Then maximum profit will be

P(d) = (− 4×25 + 40) (25 − 40)

P(d) = (− 100 + 40) (−15)

P(d) = (− 60) (− 15)

P(d) = $ 900

More about the differentiation link is given below.

brainly.com/question/24062595

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