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2 years ago

15

Heyy! i’ll give brainliest please help

1 answer:

Vsevolod [243]2 years ago

5 0

I found the answer on a quiz!!!

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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

1 year ago

Approximate the value of each of the irrational numbers below to the nearest thousandth.

Marta_Voda [28]

ANSWER

$\sqrt{13} = 3.606$

to the nearest thousandth.

EXPLANATION

The given irrational number is

$\sqrt{13}$

We use the calculator to evaluate this to obtain,

$\sqrt{13} = 3.605551...$

To round to the nearest thousandth means we are rounding to 3 decimal places.

The third decimal place is 5.

The next number is 5 so we round up.

$\sqrt{13} = 3.606$

4 0

2 years ago

Solve for b, i already solved for A <br> will give brainliest

larisa86 [58]

Answer:

b=23 degrees

Step-by-step explanation:

a was 66 degrees so b=23 degrees 180-90-66=23

6 0

2 years ago

Algebraic expressions

Ede4ka [16]

Answer:

10y^2-3xy+6x

Step-by-step explanation:

7 0

2 years ago

Forty-five roses, plus some number of daffodils and tulips, are blooming in a garden.

stellarik [79]

The maximum number of of bouquets the gardener could have made is 3

<h3>How to find unknown parameter</h3>

Total = 45

let

number of daffodils = x
number of tulips = y

Roses = 4x

Tulips = 4x + 15

Total = roses + daffodils + tulips

45 = 4x + x + (4x + 15)

45 = 5x + 4x + 15

45 = 9x + 15

45 - 15 = 9x

30 = 9x

x = 30/9

x = 3.33333333333333

Approximately,

x = 3

Let more about equation:

brainly.com/question/16863577

4 0

1 year ago