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3 years ago

PLEASE ANSWER!!!!! I WILL MARK YOU AS BRAINLIEST!!!!! IT IS HIGHLY APPRECIATED!!! :)

Mathematics

1 answer:

kkurt [141]3 years ago

3 0

Answer:

A number less than 4 was rolled 18 times.

The number cube was rolled 50 times. The relative frequency of rolling a number less than 4 is 36%.

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Help plz! (a + b - c)(a + b + c) multiplying polynomials

saul85 [17]

Answer:

a^2 + 2ab + b^2 - c^2

Step-by-step explanation:

When you multiply all the terms together you get a^2 + ab + ac + ab + b^2 + bc - ac - bc - c^2. Then you can just combine like terms and simplify it to a^2 + 2ab + b^2 - c^2. Hope this helps :)

5 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

-PLeAse HeLP-

ExtremeBDS [4]

This question is tricky.

I think there would be B)24 people that would prefer Yellow :)

4 0

3 years ago

There are 8 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being

Natalija [7]

Well, the keyword here is One of the performers insist on being the last.

So, the amount of performers that we can arrange freely is 7 performers.

Different ways we can schedule their appearance is :

7 ! = 7 x 6 x 5 x 4 x 3 x 2 x 1

= 5040

hope this helps

5 0

3 years ago

7. In each case, write an equation that models the situation described. a) An antique is purchased for $5000 in 1990. It appreci

balandron [24]

A) A= 5000 x .0325 ( 31)
A= 5,037.50

.0325 = 3.25%
31 years 2021-1990 = 31

3 0

3 years ago