What is the volume of the rectangular solid below?

Find where the two curves intersect:

y = 6x - 2x ²

y = x ²

6x - 2x ² = x ²   →   3x ² - 6x = 3x (x - 2) = 0   →   x = 0 and x = 2

Now, for a shell of radius x units away from the axis of revolution, the height of the shell would be the vertical distance between the upper curve and the lower curve. For 0 ≤ x ≤ 2, we have 6x - x ² ≥ x ², so the height of any given shell is (6x - x ²) - x ² = 6x - 2x ².

Then volume of the solid is

[tex]\displaystyle 2\pi \int_0^2 x(6x-2x^2)\,\mathrm dx = 2\pi \left(2x^3-\frac{x^4}2\right)\bigg|_0^2 = \boxed{16\pi}[/tex]

Answer:

Every gene has many types of gene variants, which are called alleles. These alleles help the body prouperly code different types of variants. Humans have many different traits in their body, and that is how we have so many features. Genes are stored in chromosomes.

Answer:

Human variability, or human variation, is the range of possible values for any characteristic, physical or mental, of human beings. As the human species exhibits sexual dimorphism, many traits show significant variation not just between populations but also between the sexes.

Step-by-step explanation:

Answer:

J. 19.7

Step-by-step explanation:

SOH(sine = opposite side/hypotenuse) CAH TOA

sin 80° = RS/20

=> 0.985 = RS/20

=> RS = 20 × 0.985 = 19.7

9514 1404 393

Answer:

  D.  6

Step-by-step explanation:

The height of the larger cylinder is 15/5 = 3 times the height of the smaller one. Because the cylinders are similar, you know that the radius of the larger one will have the same multiplier of the radius of the smaller one.

The larger radius is 3 × 2 = 6.

Answer:

Correct answer is 4,2.

So go through it.

Answer:

81.8 kg

Step-by-step explanation:

Answer:

81.8

Step-by-step explanation:

Decimals work just like basic addition.

Line it up at the decimal point.

  46.2

+ 35.6

_______

81.8

Answer:

I would think it would be 4 because dont you add the 2 sides?

Step-by-step explanation:

9514 1404 393

Answer:

  B.  -2/3

Step-by-step explanation:

Each small division on this number line is 1/3 unit. Point A is 2 small divisions left of 0, so corresponds to the value -2/3.

Answer:

A, A, B

Step-by-step explanation:

Answer:

15) 5    b. color the objects on the chalkboard green

Step-by-step explanation:

15)

This question needs the Pythagorean Theorem, which is a^2 + b^2 = c^2

a is a leg (opposite line to hypotenuse)

b is a leg (base line)

c is the hypotenuse (the diagonal line.)

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

then you square root the number to the left to find c

square root of 25 is 5, since 5 x 5 is 25.

Answer:

All you have to do is find out what 7.5 percent of 650 is.

Step-by-step explanation:

The answer would be 48.75 in sales taxes

Answer:

y=(x-4)(x-1)

Step-by-step explanation:

We need y to be 0 and x must equal 4 and 1

The only way to make y=0

is to swap 9 and 5 for -4 and -1

Answer:

10 times

Step-by-step explanation:

If you are talking about division, then we would do 87/8=10

Answer:

It can go 10.875  times.

Step-by-step explanation:

87/8 = 10.875

≈ 11

Hope this helps; have a great day!

Answer:

The distance from the tetherball pole is the edge of the circle is 5 feet. What is the circumference of the circle

31.416

Step-by-step explanation:

The distance from the tetherball pole is the edge of the circle is 5 feet. What is the circumference of the circle

2 times Pi (3.14) times the radius (5)

Answer:

31.416

Step-by-step explanation:

2 times Pi (3.14) times the radius (5)

Answer:

(x-2)(x-2) or (x+2)(x+2)

Step-by-step explanation:

since you are squaring it, technically the terms are negative, but the product will be positive. when you multiply two negative factors, you get a positive answer. so either both can be negative or both can be positive.

Answer:

1491.5

Step-by-step explanation:

radius is 5in so pi * 5 squared * 19 will get you this answer

Answer:

i think its four..not sure though <3

Step-by-step explanation:

you take two fingers and take another set of two fingers and mash them together making 4 fingers!!!!

I honestly don't know at this point.

Using lateral limits, the correct option is:

The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9.

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For a limit of a function f(x) to exist at a point a, it is needed that:

[tex]\lim_{x\rightarrow a^-} f(x) = \lim_{x\rightarrow a^+} f(x)[/tex]

That is, it has to approach a from both sides toward the same value, it cannot be oscillating.

These limits found, approaching a from close but smaller values, [tex][tex]\lim_{x\rightarrow a^-} f(x)[/tex], and from close but greater values, [tex]\lim_{x\rightarrow a^+} f(x)[/tex], are called lateral limits.

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Since the lateral limits are different, the limit does not exist, and the correct option is:

The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9.

A similar question is given that https://brainly.com/question/23630768

Answer:

A

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The height of the actual tree when on a scale drawing with a scale of 1 cm:0.75 ft, the height of a mailbox is 6.5 cm, is 4.875 ft.

Scale factor is the factor which is used to enlarge or smaller the original figure.

Scale factor is the ratio of representation measurement of the figure to the original figures.

On a scale drawing with a scale of 1 cm:0.75 ft, the height of a mailbox is 6.5 cm. Here, the scale factor is,

[tex]k=\dfrac{1\rm\; cm}{0.75\rm\; ft}[/tex]

The height of a mailbox is 6.5 cm. Let suppose, the actual tree is x meter long. Thus, the ratio of this factor is,

[tex]k=\dfrac{6.5}{x}[/tex]

Comparing both factors,

[tex]\dfrac{1\rm\; cm}{0.75\rm\; ft}=\dfrac{6.5}{x}\\x=6.5\times0.75\\x=4.875[/tex]

Thus, the height of the actual tree when on a scale drawing with a scale of 1 cm:0.75 ft, the height of a mailbox is 6.5 cm, is 4.875 ft.

Learn more about the scale factor here;

https://brainly.com/question/10253650

#SPJ2

Answer:

H0 : μD = μN

H0 : μD > μN

Test statistic = 2.192

Pvalue = 0.017

there is strong evidence that healthy adult eat more cookies for a snack when they are distracted with a computer game during lunch than when they are not.

Step-by-step explanation:

Given the data:

n1 = 22 ; x1 = 52.1 ; s1 = 45.1

n2 = 22 ; x2 = 27.1 ; s2 = 26.4

H0 : μD = μN

H0 : μD > μN

The test statistic :

(x1 - x2) ÷ (Sp*√(1/n1 + 1/n2))

Sp = (n1 - 1)s1² + (n2 - 1)s2²] ÷ (n1 + n2 - 2)

Sp = √[((21 * 45.1^2) + (21 * 26.4^2)) ÷ 42]

Sp = 36.952469

Test statistic :

(52.1 - 27.1) ÷ Sp * √(1/21 + 1/21))

25 ÷ (36.952469 * 0.3086066)

25 ÷ 11.4037758196954

Test statistic = 2.192

Using the Pvalue from Test statistic calculator :df = 42, Tscore = 2.192

Pvalue = 0.017

α = 0.05

Pvalue < α

Hence, there is strong evidence that healthy adult eat more cookies for a snack when they are distracted with a computer game during lunch than when they are not.

Answer:

the answer is 16x2 - 16

Step-by-step explanation:

:)))

Answer: 5/6

Step-by-step explanation:

because if you get velocity and multiply it by the term which is 5/12 you half the denominator.

Answer:

44

Step-by-step explanation:

12 = r - (34 - 2)

12 = r - 32

12+32 = r

r=44

Answer:

yEE-

Step-by-step explanation:

I need help with this please graphing is too complicated. If anyone can help I would be very happ.

Answer:

270

Step-by-step explanation:

Convert 15% into a decimal: .15

Then multiply 1800* 0.15

This gives you 270

Answer:

270

Step-by-step explanation:

Answer:

5 cm

Step-by-step explanation:

Volume of a cylinder = π*radius^2*height

675π = π * radius^2 * 27

radius^2 = 25

radius = 5 cm

Answer:

Step-by-step explanation:

V=pi x r^2 x h

r^2 = 675pi / (pi x 27) = 25

r = 5

Answer:

-10x

Step-by-step explanation:

multiply -5 with 2x

-5×2x= -10x

Answer:

Basically, you have to multiply the term at the top with the one on the left of the corresponding box. In this case you have to multiply -5 with 2x.

[tex]-5\cdot \:2x=-10x[/tex]

Answer:

solution given:

height [h]=7ft

side 1=7ft

side2=8ft

it is trapezium

so

area of trapezium=[tex] \frac{1}{2} 7(7 + 8)[/tex]

=52.5ft²

Answer:

C. Solving this equation results in the statement -48 = 48. Because this is a false statement, the equation has no solution.

Step-by-step explanation:

8(3x - 6) = 6(4x + 8)

24x - 48 = 24x + 48

minus 24x from both sides and you get -48 = 48

A false statement means one side does not equal the other. False statement always means no solution

you can solve this equation for x, but looking at the answers it's not what the question is asking for