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2 years ago

Find the quotient. Round to the nearest hundredth,5,434 divided by 12

Mathematics

1 answer:

Volgvan2 years ago

5 0

Answer:

452.83

Step-by-step explanation:

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erica [24]

Answer: 67.725feet²

Step-by-step explanation:

A heptagon consist of 7 sides and Its area is calculated using the formula

= 1/2 × nsr

n = number of sides = 7

s = side length = 4.3

r = apothem = 4.5

Area = 1/2 × nsr

= 1/2 × 7 × 4.3 × 4.5

= 0.5 × 7 × 4.3 × 4.5

= 67.725feet²

7 0

2 years ago

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

Find the slope of the line

lakkis [162]

Answer:

Step-by-step explanation:

Rise / Run

= 4/2

= 2

8 0

3 years ago

Read 2 more answers

Is y=3x+b a linear relationship

Nataly_w [17]

Yes it is a linear relationship

5 0

2 years ago

If you have 40hr/week of class how many hours should you study outside of class

kozerog [31]

There is 24 hours a day with 7 days a week which equals 168 hours total in a week. You will subtract 168 from 40 which will equal 128 hours left.

24 x 7 = 168

168 - 40 = 128

Answer: 128

6 0

3 years ago