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The volume of the solid formed by rotating the region about the y-axis is 6π/7 cubic units.

To find the volume of the solid formed by rotating the region bounded by the curves y = x³/4, x = 0, y = 1 in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

[tex]\mathrm V = \int\limits^a_b {2\pi \mathrm x \times \mathrm f(x)} \, dx[/tex]

Where:

a and b are the limits of integration (in this case, a = 0 and b = 1 since we are rotating in the first quadrant).

f(x) is the height of the shell at the given x-value.

2πx is the circumference of the shell at the given x-value.

In this case, we need to express y = x³/4 in terms of x to find the function f(x).

Given: y = x³/4

To find the function in terms of x, solve for x:

[tex]x = (4y)^{(1/3)[/tex]

Now, the function f(x) becomes:

[tex]\mathrm f(x) = (4x)^{(1/3)[/tex]

Now, let's calculate the volume using the cylindrical shell method:

[tex]\mathrm V = \int\limits^1_0 {2\pi \mathrm x \times \mathrm 4x^{1/3}} \, dx[/tex]

[tex]\mathrm V = 2\pi \int\limits^1_0 { x^{4/3}} \, dx[/tex]

To integrate, add 1 to the exponent and divide by the new exponent:

[tex]\mathrm V = 2\pi \times (3/7) \times x^{(7/3)} |^0_1[/tex]

Now, evaluate the expression at the limits of integration:

[tex]\mathrm V = 2\pi \times (3/7) \times (1)^{(7/3)} - 2\pi \times (3/7) \times (0)^{(7/3)[/tex]

[tex]\mathrm V = 2\pi \times (3/7) - 0[/tex]

[tex]\mathrm V = 6\pi/7[/tex]

So, the volume of the solid formed by rotating the region about the y-axis is 6π/7 cubic units.

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Answer:

D. uv = 1.71 and vu = 3.16

Step-by-step explanation:

The scalar projections are uv = 1.71 and vu = 3.16

The correct option is (D)

The definition of scalar projection is the length of the vector projection.

Given: u = ⟨2, 1⟩,  = ⟨4, –1⟩, and θ = 40°

Proj u_v = |u| cosθ

= 2.25 * cos 40

= 2.25 * 0.7660

=1.72

and, Proj v_u = |v| cosθ

= 4.123 * cos 40

= 4.123 * 0.7660

= 3.16

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Answer:

0.222 as a decimal

111/500 as a fraction

22.2 as a %

Answer:

62.50 or 0.625

Step-by-step explanation:

The decimal form of  [tex]62\frac{1}{2}[/tex] percent is 0.625.

The given percentage is [tex]62\frac{1}{2}[/tex] %

This fraction is in a mixed fraction.

Convert it into an improper fraction

So,

[tex]62\frac{1}{2}[/tex] %  = (62x2 + 1)/2

           = (124+1)/2

           = 125/2 %

Now divide 125 by 2 to get the decimal form

2) 125 ( 62.5

-  12

 _____

     x 5

  -     4

______________

          1  0

 -        1   0

 _________

            x

Therefore,

 [tex]62\frac{1}{2}[/tex] %  =  62.5 %

We can write,

62.5 % = 62.5/100

           = 0.625

Hence the required decimal form is 0.625.

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Answer:

Choice A

Step-by-step explanation:

Answer:

Ok so I've had braces and it doesn't really hurt getting put in but it does hurt when they tighten them but you have nothing to worry about :)

Step-by-step explanation:

Answer:

They don't hurt when they put them in however you will feel mild soreness and discomfort as your mouth adjusts to them as with anything, for example, fillings, they feel gritty and uncomfortable at first but your mouth adjusts to it.

" There will be mild soreness or discomfort after the orthodontic wire is engaged into the newly placed brackets, which may last for a few days to a week."

I know its can be scary at first but its for the health of your teeth and not everyone gets that privilege, just make sure to take care of them properly.

Step-by-step explanation:

Answer:

43.75%

Step-by-step explanation:

80-45=$35 off

35 is 43.75% of 80

Answer: of each shape? 3 & 4?

Step-by-step explanation:

Lilian worked 24 hours last week

Answer:

Step-by-step explanation:

3x^4+2x^3

Answer:

30 quizzes

Step-by-step explanation:

12 quizzes in 2 weeks means that there were 6 per week and 6 (quizzes per week) times 5 (number of weeks) would be 30.

Hope this helped!!

Answer:

30, or 42

Step-by-step explanation:

If they took 12 quizzes over the course of 2 weeks, then we can assume that they take 6 quizzes each week (12/2 = 6).

Over the course of 5 weeks, they'll have taken 30 quizzes if the above is true. However, the 'or' is there because I don't know if they're including the past 12 or not. If they are including the 12 quizzes taken over 2 weeks, then the answer is 42. If they are only referring to the 5 weeks of school, then the answer is 30.

Answer:

-pi over 6 or B.

Step-by-step explanation:

I plugged it into desmos and this is what I got

Using the inverse of the sine function, it is found that the value of x is:

[tex]x = -\frac{\pi}{6}[/tex]

It is the function described by:

[tex]y = \arcsin{x}[/tex]

And means that sine of y is equals to x, that is:

[tex]x = \sin{y}[/tex]

In this problem, the function is:

[tex]x = \arcsin{-\frac{1}{2}}[/tex]

Which means that we have to solve for x, considering that the sine of x is of -1/2. Hence:

[tex]\sin{x} = -\frac{1}{2}[/tex]

[tex]x = -\frac{\pi}{6}[/tex]

Hence, the value of x is given by:

[tex]x = -\frac{\pi}{6}[/tex]

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Answer:

Marisa has made 6 sandwiches.

Step-by-step explanation:

The pounds of roast beef required to make each sandwiches is [tex]\frac{3}{8}[/tex], and not [tex]\frac{8}{8}[/tex] as erroneously typed in the question.

Given that each deli sandwiches made, uses [tex]\frac{3}{8}[/tex] pounds of roast beef.

Marisa started with 5 pounds, and had 2[tex]\frac{3}{4}[/tex] pounds left.

Thus,

pounds of roast beef used = 5 - 2[tex]\frac{3}{4}[/tex]

                                             = 5 - [tex]\frac{11}{4}[/tex]

                                             = [tex]\frac{20 - 11}{4}[/tex]

                                             = [tex]\frac{9}{4}[/tex]

                                             = 2[tex]\frac{1}{4}[/tex]

Marisa had used 2[tex]\frac{1}{4}[/tex] pounds of roast beef. So that;

the number of del sandwiches made = 2[tex]\frac{1}{4}[/tex] ÷ [tex]\frac{3}{8}[/tex]

                                                    = [tex]\frac{9}{4}[/tex] ÷ [tex]\frac{3}{8}[/tex]

                                                    = 6

Therefore, the number of sandwiches made by Marisa is 6.

Answer: 11,700,000

Step-by-step explanation:

Number of people in Pennsylvania =13,000,000

Fraction of people that will show Christmas spirit for Santa's sleigh to deliver all packages = 9/10

The number of people that would have to show Christmas spirit for packages to be delivered in PA will be:

= 9/10 × 13,000,000

= 11,700,000

9514 1404 393

Answer:

  14

Step-by-step explanation:

Assuming the grade is proportional to the number of problems answered, we have ...

  a/20 = 70/100

  a = 20(0.70) = 14 . . . . multiply by 20

The student answered 14 problems correctly.

Answer: The answer is –0.6, wait a second, did you duplicate your question?

Step-by-step explanation:

Answer:

x = - 15

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180, that is

35 - 5 - 8x - 2x = 180 ( simplify left side )

30 - 10x = 180 ( subtract 30 from both sides )

- 10x = 150 ( divide both sides by - 10 )

x = - 15

Answer:

First Step of solving this expression: Multiply

Answer for the expression: 40

Step-by-step explanation:

To find the first step you need to follow the order of operation

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

Since there are not Parenthesis or Exponents then you may skip that step but there is a multiplication sign so the first step is Multiplication

To solve multiply 6 and 3

Which is 18

Now the expression looks like this:

28-11+18+5

Now simplify from left to right:

28-11=17

17+18=35

35+5=40

Hope this helps!

Answer: Multiply 6*3, then add 18+5, then subtract 28-11, then add them:

17 + 23 = 40!

Step-by-step explanation: PEMDAS:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

The distance is 10.5 miles

Step-by-step explanation:

Mathematically; we want to calculate the distance between the two towns in the question

Distance = speed * time

15 minutes to hours is 15/60 = 1/4 hours

So the distance would be;

Distance = 42 mph * 1/4 = 10.5 miles

Answer:

7

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

−3x + 6 > 12

Move all terms not containing x to the right side of the inequality.

Subtract 6 from both sides of the inequality.

−3x > 12 − 6

Subtract 6 from 12.

−3x > 6

Divide each term by −3 and simplify.

Divide each term in −3x > 6 by −3. When multiplying or dividing both sides of an i nequality by a negative value, flip the direction of the inequality sign.

(-3x/-3)<(6 /-3)

Cancel the common factor of −3.

Divide 6 by −3.

x < −2

( − ∞ , − 2 )

Answer:

8porque9x8da72

Step-by-step explanation:

     a

Answer:

Step-by-step explanation:

To find the number of volleyballs she can buy all you have to do is divide 75 by 9 which gives you 8.3333333 So she can buy approximately 8 volleyballs with 3 dollars to spare. You could also just multiply 9 by 8 to check your answer wich gives you 72 dollars

Answer:

9

Step-by-step explanation: 6+3=9

The rent is $9

Answer:

3x+2=3x+2 because, you have to combine your like terms, so here is an example..

                 3x + 2

there are no like terms to combine here so the problem stays how it was, so there saying 3x+2 = 3x+2 because they're stating the problem then saying that the answer is the same because there is no like terms her to combine.

Hope this helps,

Answer:

a. 3 : 2

b. 2 : 15

c. 3 : 2

Step-by-step explanation:

Red fish = 3

Yellow fish = 6

White fish = 4

Black fish = 2

Total number of fishes = 15

a) Ratio of the Number of yellow fish to the number of white fish.

Yellow fish : White fish

6 : 4

= 6 /4

= 3/2

= 3 : 2

Ratio of the Number of yellow fish to the number of white fish = 3 : 2

b) Ratio of the Number of black fish to the total number of fish

Black fish : Total fish

2 : 15

= 2 / 15

= 2 : 15

Ratio of the Number of black fish to the total number of fish = 2 : 15

c) Ratio of the Number of red fish to the number of black fish

Red fish : black fish

= 3 : 2

= 3/2

= 3 : 2

Ratio of the Number of red fish to the number of black fish = 3 : 2

x=12, y=[tex]6\sqrt{2}[/tex]

This triangle is a special right triangle, a 45-45-90 triangle. In this format, the the hypotenuse will be [tex]x\sqrt{2}[/tex], while the side lengths would be x. With this in mind we can already figure out y is [tex]6\sqrt{2}[/tex]. The hypotenuse would be [tex](6\sqrt{2} )(\sqrt{2} )=12[/tex]