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Darya [45]
3 years ago
14

A café's annual income depends on x, the number of customers. The function /(x) = 4x2 – 20x

Mathematics
2 answers:
kotegsom [21]3 years ago
7 0
The correct answer is letter B
Cloud [144]3 years ago
7 0

Answer:B

Step-by-step explanation:

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5th grade math. Correct answer will be marked brainliest.
vitfil [10]

Answer: The answer would be (0,3)

4 0
3 years ago
Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2
exis [7]

The Jacobian for this transformation is

J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}

with determinant |J| = 12, hence the area element becomes

dA = dx\,dy = 12 \, du\,dv

Then the integral becomes

\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv

where R' is the unit circle,

\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1

so that

\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}

Then

\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}

3 0
2 years ago
The following question has two parts. First, answer part A. Then, answer part B.
Pie

Answer:

When you're talking factors, you're talking about some sort of integer; that's because “factors” depends on the concept of divisibility, which are virtually exclusive to integers. When you're talking “greater than”, you're excluding complex numbers (where the concept of ordering doesn't exist) and you're probably assuming positive integers. If you are, then no; no positive integer has factors that are larger than it.

If you go beyond positive numbers, that changes. 0 is an integer, and has every integer, except itself, as factors; since its positive factors are greater than zero, there are factors of zero that are greater than zero. If you extend to include negative numbers, you always have both positive and negative factors; and since all positive integers are greater than all negative integers, all negative integers have factors that are greater than them.

Beyond zero, though, no integer has factors whose magnitudes are greater than its own. And that's a principle that can be extended even to the complex integers

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
A piece rate worker is paid _____.
Alchen [17]

Answer:

The answer is  on the quantity they produce per hour.

Step-by-step explanation:

If they produce more, they will be paid more, based on the rate per finished item

5 0
2 years ago
Read 2 more answers
The red shape has been translated into the blue shape. The translation is
MAXImum [283]
Answer is (A). (X’ , Y’) = (x, y-6)
7 0
3 years ago
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