Victor bought a Nintendo Game Boy that cost $68. He received $32 in change.

A community theater uses the function p (d) = (-4d+40) (d−40) to model the profit (in dollars) expected in a weekend when the ti

fomenos

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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7 0

2 years ago

If a group of distinct objects can be arranged in 120 different ways, how many objects are there? 3 4 5 6

igomit [66]

<span>Look At The Picture.</span>

5 0

3 years ago

Read 2 more answers

Find the solution set for this equation:<br> -a2+4a=0<br> (Separate the two values with a comma)

Rashid [163]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: \{ 0,4 \}$

____________________________________

$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0$

$\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0$

$\qquad \tt \rightarrow \: {a}^{2} - 4a = 0$

$\qquad \tt \rightarrow \:a(a - 4) = 0$

The two cases are :

a = 0

or

a -4 = 0, that leads to a = 4

We can conclude :

$\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

5 0

2 years ago

Read 2 more answers

Which of the following statements are true? Select all that apply. This is Algebra Nation

natita [175]

Answer:

241

Step-by-step explanation:

3 0

3 years ago

Alex wrote the expanded form for the number 165.038 as "100 60 5 30 8." was he correct? if not, give the correct expanded form.

grin007 [14]

The expanded form for the number 165.038 is 100+60+5+0.03+0.008.

<h3>What is the expended form of decimal numbers?</h3>

Writing decimals in expanded form simply means writing each number according to its place value. This is done by multiplying each digit by its place value and adding them together. Let's look at an example: 2.435. In words, we would say this as two and four hundred thirty-five thousandths.

In the given question expended form 100+60+5+30+8 is wrong.

After decimal point the first digit is at the tenth place and second digit at the hundredth place and third is at the thousandth place and so on....

165.038 = 100+60+5+ $\frac{0}{10}$ + $\frac{3}{100}$ + $\frac{8}{1000}$

= 100+60+5+0.03+0.008

Hence, The correct expended form of the given number is 100+60+5+0.03+0.008.

To learn more about expended form from the given link:

brainly.com/question/603715

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5 0

2 years ago