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2 years ago

According to the Venn diagram how many students like all three colors evenly.

Mathematics

1 answer:

earnstyle [38]2 years ago

4 0

Answer:

the answer is 1 and if not nine

Step-by-step explanation:

trust me sorry if im incorrect

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Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15. How much money did Chris spend on her new

ollegr [7]

Answer:

Christ spent $51 on her new school clothes.

Step-by-step explanation:

12 * 3 = 36

36 + 15 = 51

3 0

3 years ago

Read 2 more answers

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Consider the function below.

vovangra [49]

An inverse function reverses (x, f(x)) to make it (f(x), x).

The 1st selection does that.

5 0

3 years ago

Read 2 more answers

Please help it’s my final

Kryger [21]

Answer:

Step-by-step explanation:

5 0

2 years ago

The ratio of the width to the length of a painting is 3 to 7. If the painting is 42 in. long how wide is it

belka [17]

If length is 42 inches, then width is 18 inches.

Step-by-step explanation:

We are given ratio of width to the length of a painting i.e 3 to 7. If the painting is 42 inches long, then how wide it is?

Solving:

$\frac{width}{length}=\frac{width}{length}\\ \frac{3}{7}=\frac{w}{42}\\ Cross\,\,multiply:\\3*42=w*7\\126=w*7\\w=\frac{126}{7}\\w=18$

So, If length is 42 inches, then width is 18 inches.

Keywords: Ratio

Learn more about Ratio at:

#learnwithBrainly

8 0

3 years ago