What is the first 5 common multiples of 7 and 20

Mathematics

1 answer:

alisha [4.7K]3 years ago

4 0

The first 5 common multiples of 7 and 20:
140
280
420
560
700

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Let R be the region enclosed by the y-axis, the line y=1 and the curve y=x^3. A solid is generated by rotating R about the line

scZoUnD [109]

Answer:

The volume of the solid is 19. $\overline{142857}$ unit³

Step-by-step explanation:

The given function is y = x³

The solid is created by revolving R about the line y = 1

We have that when y = 1, x = 1

Taking the end point as x = 2, we have the volume given by the washer method as follows;

$V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx$

Where;

a = 1, and b = 2, we have;

g(x) = 1

$V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}$

The volume of the solid, V = $19\dfrac{1}{7}$ unit³ = 19. $\overline{142857}$ unit³

6 0

3 years ago

Mr. Morales purchases 6 boxes of pencils, 12 boxes of pens, and 4 cases of notebook paper for his classroom. Each box of pencils

Darina [25.2K]

Answer:

$522.60

Step-by-step explanation:

pencils: $4.10 * 6 ===> $24.60

pens: $6.50 * 12 ===> $78

notebook paper: $105 * 4 ===> $420

pencils + pens + notebook paper = total cost

24.60 + 78 + 420 = 522.60

5 0

3 years ago

Question 1 (1 point)

insens350 [35]

Answer:

1. q = p - mn

2. c = -6

3. 10

Step-by-step explanation:

$mn=p-q\\\textsf{add q to both sides}\implies mn + q = p\\\textsf{subtract mn from both sides}\implies q = p-mn$

$5c+23=c-1\\\textsf{subtract 23 from both sides}\implies5c=c-24\\\textsf{subtract c from both sides}\implies4c=-24\\\textsf{divide both sides by 4}\implies c=-6$