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2 years ago

What is the coefficient in the expression? 3(mx)4 + 5

Mathematics

2 answers:

Goryan [66]2 years ago

7 0

3 is the answer to your question

Alex73 [517]2 years ago

3 0

I think its 3 because it is placed before a verable

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What is the first step to writing an equation of a line when given two points?

Alisiya [41]

Find the slope of the line using the two points by plugging them into this formula: m = y2 - y1 / x2 - x1 where the two points are x1, y1 and x2, y2 and m is the slope.

3 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

1 year ago

The ratio of boys to girls in Ms. smith’s class is 3 to 4. If there are 12 boys, how many girls are there?

Lorico [155]

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

Hello!

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

❖ There will be 16 girls.

The relationship is x4. If we multiply 3 x 4, we get 12. What we do to one number we do to the other so 4 x 4 = 16.

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

4 0

2 years ago

PLEASE HELP!!!! ASAP ALMOST DUE

lions [1.4K]

Answer:

idk im not that smart

Step-by-step explanation:

6 0

2 years ago

∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 78° and minor arc CD = 124°, what i

lana [24]

Minor arc AD is 360° -124° -78° = 158°. Then angle ABD is
(158° -78°)/2 = 40°

The appropriate selection is
C) 40°

4 0

2 years ago

Read 2 more answers