What is the value of 2|2-9|-3(4+2)?<br> A. -32<br> B. -26<br> C. -15<br> D. -5 <br> E. -4

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

Round 5,836,197 to the nearest humdred

Olenka [21]

5,836,200 Is the answer :) Have a Great day!!!

4 0

3 years ago

Read 2 more answers

For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Th

Reptile [31]

Answer:

(a) (x-2)^2 +(y-2)^2 = 16

(b) r = 2

Step-by-step explanation:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)^2 +(y -k)^2 = r^2

The given circle is ...

(x -2)^2 +(y -2)^2 = 16

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(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

r = 2

6 0

3 years ago

What is the value of 2|2-9|-3(4+2)? A. -32 B. -26 C. -15 D. -5 E. -4