Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=0, y= \cos(4 x), x = \frac{\pi}{8}, x = 0 about the axis y= -4f

Answers

Answer 1

The volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y= cos(4 x), x = π/8, x = 0 about the axis y= -4f

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have curves,

[tex]\rm y=0, y= \cos(4 x), x = \frac{\pi}{8}, x = 0[/tex]

Here the axis is y = -4f, but not mentioned the value of f.

We are assuming the f = 3/2

So the axis will be y = -4(3/2) = -6

Inner radius = 6

Outer radius = 6 + cos4x

[tex]\rm A(x) = \pi((6+cos4x)^2-6^2)[/tex]

[tex]\rm A(x) = \pi (cos^24x+12cos4x)[/tex]

[tex]\rm A(x) = \pi( \dfrac{1+cos8x}{2}+12cos4x)[/tex]

For the volume;

[tex]\rm Volume = \int\limits^\dfrac{\pi}{8}}_0 {A(x)} \, dx[/tex]

Put the function A(x) in the above integration and solve we will get:

[tex]\rm Volume = 3\pi + \dfrac{\pi^2}{16}[/tex]

Thus, the volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=0, y= \cos(4 x), x = π/8, x = 0 about the axis y= -4f

Learn more about integration here:

brainly.com/question/18125359

#SPJ4

Find The Volume Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified

Related Questions

The volumes of two similar figures are given. The surface area of the smaller figure is given. find the surface area of the larger figure
V=2875 m^3
V = 1472 m^3
S.A. = 928 m^2
The surface area of the larger figure is [blank] m^2

Answers

Step-by-step explanation:

the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).

and the volume of 3 dimensions (side lengths).

"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).

so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.

in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.

let's call the scaling factor f.

1472 × f³ = 2875

and then

928 × f² = large S.A.

let's use the first to get f :

1472 × f³ = 2875

f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64

f = 5/4

f² = (5/4)² = 5²/4² = 25/16

large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²

A town has a population of 2.33 x 104 and grows at a rate of 7% every year. Which a equation represents the town's population after 6 years?

Answers

Answer:

[tex]p = (2.33 \times {10}^{4})( {1.07}^{6} )[/tex]

Which equals 4 quarts?

6 cups
16 pints
16 cups
O
12 pints

Answers

16 is equal to 4 quarts

Answer:

16 cups

Step-by-step explanation:

1 quart = 4 cups

a professor teaches four different science classes. he wants to try out a new style of exam, so during finals, he gives the new exam to 15
randomly selected students in each class. the other students take the regular exam.
what is the sample in this situation?

Answers

The sample in this situation where professor wants to try out a new style of exam, thus, during finals, is 15.

What is random sample?

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

Sample is the particular group which is gathered from a data. A professor teaches four types of science classes. Professor wants to try out a new style of exam, thus, during finals,

The gives the new exam to 15 randomly selected students in each class and remaining other students take the regular exam. Thus, the sample is 15.

Hence, the sample in this situation where professor wants to try out a new style of exam, thus, during finals, is 15.

Learn more about the random sample here;

https://brainly.com/question/17831271

#SPJ1

Which is the equation of the line passing through (0, 4) and (8, 0)?

A. Y= - 1/2+ 8
B. Y= - 1/2+4
C. Y= -2x+4
D. Y= -2x+8

Answers

Answer:

B: y = -(1/2)x + 4

Step-by-step explanation:

I'll assume the x term is missing from options A and B:

IThey should read:

A. Y= - (1/2)x+ 8

B. Y= - (1/2)x+4

Use the two given points to calculate the slope of the line of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

(0,4) and (8,0)

Rise = (0 - 4) = -4

Run = (8 - 0) = 8

Slope, m, = -4/8 or -(1/2)

The perpendicular line has the form y = -(1/2)x + b. There are options that have a -(1/2) slope: A and B.

To narrow it down, we need to calculate a value of b.

Use y = -(1/2)x + b and solve for b using either of the two given points [(0,4) or (8,0)]. I'll use (0,4).

y = -(1/2)x + b

4 = -(1/2)(0) + b

b = 4

The equation is thus y = -(1/2)x + 4, option B

Lines m and n are parallel on a coordinate plane. Lines m and n are transformed by the same rotation, resulting in image lines s and t. Which statement describes the relationship between lines s and t?

Answers

The statement that best describes the relationship between lines s and t is: Lines s and t are parallel.

What are parallel lines?

Parallel lines are as those lines that does not intersect one another despite being equal to each other.

Lines s and t are said to be parallel lines because they are cut by transversal which in turn means that transversal intersect lines s and t to make it parallel lines.

Therefore the statement that best describes the relationship is :Lines s and t are parallel.

Learn more about parallel lines here:brainly.com/question/24607467

#SPJ1

The perimeter, p, of a square is a function of its side length, s. The perimeter of the square is 28 inches or less. What is the domain of the function for this situation

Answers

The domain of the function for this situation is; s<= 7.

What is the domain of the function?

It follows from the task content that the perimeter , p, of a square is a function of its side length, s. The perimeter of the square is 28 inches or less.

On this note it follows that;

P = 4s <= 28

Hence, it follows that; s<=7.

Read more on domain of a function;

https://brainly.com/question/1942755

#SPJ1

If 3n + 2 = 8, find the value of n.

Answers

Answer:

Step-by-step explanation:

3n+2=8

Collect like terms

3n=8-2

3n=6

Divide both sides by 3

3n÷3=6÷3

n=2

How many possible phone numbers can we make out of XXX – XXXX, where X can be any number 0-9? Show your work and leave your answer in either exponential or factorial form.

Answers

There are 10⁷ possible phone numbers from the digit 0 to 9.

What is Permutations?

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set.

Here, there are total 10 possible digits (0 to 9) we can use to create 7 digit phone numbers.

For first place there are 10 possible digits.

similarly for second place again 10 possibilities and so on.

So total number of phone number = 10 X 10 X 10 X 10 X 10 X 10 X 10

= 10⁷

Thus, there are 10⁷ possible phone numbers from the digit 0 to 9.

Learn more about Permutations from:

https://brainly.com/question/14767366

#SPJ1

Possible phone numbers can be 10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!.

10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex]. (with repetition)

What is number system?

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

There are 7 digit phone number represented with a XXX-XXXX .

So the first x can be 10 different numbers

let us take

10 ___ ___ ____ ____ ____ ____, but which ever number you use, it is then used up.

So then you only have 9 numbers left

10 x 9 x ___ x ___ x ___ x ___ x ___ .

Then, once that number is used it can't be used again, so on

10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!

If the repetition takes place then,

the first place have possibilities of 10 digits

10 __ __ - __ __ ___ __

Now, again repetition is allowed again there are possibilities of 10 digits.

10 10 __- __ __ __ __

and carrying the same way,

10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex].

Learn more about this concept here:

https://brainly.com/question/17283970

#SPJ1

Ingrid and Reed want to choose a tool that will allow them to measure the volume of a box. Which tool is most useful for Ingrid and Reed to measure the volume of a box?

Answers

A tape measure will give LxWxH of the box giving you volume

How is the graph of the parent quadratic function transformed to produce the graph of y=-(2x+6)²+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up
3 units.
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up
3 units.
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3
units.
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3
units.

Answers

Answer:

the final option

Step-by-step explanation:

the negative sign causes a reflection, the +6 in the parentheses cases a 6 unit shift left and the +3 causes a 3 unit shift up

pls help. due at 11:59

Answers

Answer:

see the attachment!

i hope this can help you.

How can l use models to find part of a number?

Answers

Answer:

In math, number blocks are commonly used as models, where a small square equals 1, a long rectangle equals 10, and a large square equals 100. As models, blocks can be used for addition, subtraction, multiplication, and division. You can represent a problem given by using the correct models.

The square root of 8+3 times the square root of 2 + the square root of 32

Answers

Answer:

[tex]9 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \sqrt{8} + 3 \sqrt{2} + \sqrt{32} \\ \\ = \sqrt{ {2}^{2} \times 2} + 3 \sqrt{2} + \sqrt{ {2}^{4} \times 2 } \\ \\ = 2 \sqrt{2} + 3 \sqrt{2} + {2}^{2} \sqrt{2} \\ \\ = 2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} \\ \\ = 9 \sqrt{2} [/tex]

What is the center of a circle with equation (x-4)2 + y2 = 5?

Answers

Answer:

(4,0)

Step-by-step explanation:

standard equation for a circle is (x−h)^2 +(y−k)^2 =r^2

circle center: h, k with radius: r

(x-(+4)^2 + (y-0)^2 = 5

the center is (4, 0)

Find the values of x and y in parallelogram PQRS. PTy, TR 4x1, QT 2y, TS 5x+8

Answers

Answer:

Step-by-step explanation:

Work out length of AB

Answers

AB is 2√137 in simplest form

or 23.4 rounded to the nearest tenth.

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\:Note }}}[/tex]

★ 1st let's know what is the given figure is and it's related concepts for solving !

➣ Given Triangle is a right angled triangle

➣ It is having 3sides let's know what are the name of these sides

➣ 1st AB is know as hypotenuse

➣ 2nd AC and is called Base of the triangle

➣ 3rd BC whích is know as perpendicular of the triangle

➣ Hypotenuse(H):-The side of a right triangle opposite the right angle.

➣ Perpendicular(P):- Exactly upright; extending in a straight line.

➣ Base(B):- it also known as the side opposite to hypotenuse

➣Perpendicular and base are know as the leg of right angled triangle

➣ We can easily find length of one missing side by using a theorem name as "Pythagorean theorem"

➣ Pythagorean theorem :- A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides

★ Note :- The Pythagorean theorem only applies to right triangles.