Ask question

Ask question

All categories

Black_prince [1.1K]

3 years ago

5

No Links!! A tissue box has a height of 4 inches, a width of 8 inches and a length of 5.5 inches. What is the volume in inches c

ubed?

1 answer:

ANEK [815]3 years ago

7 0

Answer:

Step-by-step explanation: bey said yass

So it’s 89

You might be interested in

the sum of the first 6 terms of a geometric series is 15624 and the common ratio is 5. what is the first term of the series?

9966 [12]

Answer:

first term a=4

Step-by-step explanation:

Sum of the first 6 terms S6 = 15624

common ratio r= 5

n= 6

first term a=?

Formula: S6= a(r^n-1)/r-1

15624 = a( 5^6-1)/5-1

15624 = a(15625-1)/4

15624= a( 15624)÷4

15624= 15624a÷4

Cross multiply

15624×4 = 15624a

62496 = 15624a

divide both sides by 15624

62496÷15624 = 15624a÷15624

4 = a

a= 4

7 0

3 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

H E L P P P P P P P PP P P P P P P P P P P P PP. PP. P PP P P P P P P P P P P P P P P P P PP P. PP P P P P P P P. P P

Anni [7]

X=69 for the second one

5 0

3 years ago

Read 2 more answers

Can anyone help me with this equation 19 + 19 equals X ???

dezoksy [38]

Answer:

19+19= x

So x, is 38. Just add 19 and 19

8 0

3 years ago

Read 2 more answers

Which graph corresponds to the equation: y=−3x−6 ?

Nonamiya [84]

Answer:

Step-by-step explanation:

An insurance company has provided you with a sample of paid claims. The sample includes the following claims: 192, 113, 200, 287, and 225. What are the mean and the variance respectively of this sample rounded to the nearest whole number?

4 0

2 years ago

Read 2 more answers