(1 point) Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3,y=4x

Answers

Answer 1

Answer:

(1664π)/7

Step-by-step explanation:

We first need to know the points of intersection of the two functions, y = x³ and y = 4x.

To do this, we equate both functions

x³ = 4x

x³– 4x = 0

x(x² – 4) = 0

x(x – 2)(x + 2) = 0

x = 0, x = 2 and x = –2

Since we are looking for the volume formed by rotating the region inside the FIRST QUADRANT, then the needed points of x are 0 and 2. These are our limits of integration.

The formula for the area of the solid is

[tex] \int\limits^2_0 {\pi (4x)^3} \, dx -\int\limits^2_0 {\pi (x^3)^3} \, dx [/tex]

This gives:

[tex] \int\limits^2_0 {64\pi x^3} \, dx -\int\limits^2_0 {\pi x^6} \, dx [/tex]

On integration, we have

16π(2⁴) – π(2^7)/7

=

256π – 128π/7

= (1792π – 128π)/7

= (1664π)/7


Related Questions

makenzie earns 12.50 per hour being a lifeguard. how much will she earn in 5 days if she works 7 hours each day

Answers

5(12.50 x 7) = 437.5

Explanation: you take the amount she makes for one hour (12.50), times it with the hours she works in a day (7), and then times it with how many days she works (5).

1.) find the first four terms in ascending powers of X in the expansion (2+2X)¹² .show your working!!​

Answers

Answer:

15/8

Step-by-step explanation:

Please help me with this question!

Answers

Answer:

9 plates and mugs

He could buy 9.375

but you cant buy a portion of a plate so you buy 9

GIVING BRAINLIEST

Study the function below and then answer the
questions that follow.
f(x)=
-x-2 x<-2 -x^2 -2=0

Answers

Answer:

Step-by-step explanation:

Answer:

B then A

Step-by-step explanation:

Domain is B, range is A.

slope: -1 intercept: -7.9

what is the slope of each line that passes through the points?

what is the answer

Answers

Answer:

-1

Step-by-step explanation:

Since the question LITERALLY stated the slope is -1, the slope is literally -1

Need help math question worth 30 points help plzzzzzz

Answers

Answer:

c

Step-by-step explanation:

because the real awnser is 57/4 but simpfly

Answer:

C) [tex]14\frac{1}{4}[/tex]

explanation:

[tex]4\frac{5}{6} +4\frac{2}{3} +4\frac{3}{4} \\\\\frac{29}{6} +\frac{14}{3} +\frac{19}{4} \\\\\frac{58}{12} +\frac{56}{12} +\frac{57}{12} \\\\\frac{171}{12} \\\\14\frac{1}{4}[/tex]

Find the value of x.
Assume that segments that appear to be tangent are tangent.

Answers

Don't open it, it is a virus.

Solve for x in the picture below

Answers

Answer:

x = 16

Step-by-step explanation:

The sum of the exterior angles of a triangle = 360°

Sum the exterior angles and equate to 360

5x + 12 + 10x - 37 + 9x + 1 = 360 , that is

24x - 24 = 360 ( add 24 to both sides )

24x = 384 ( divide both sides by 24 )

x = 16

Answer:

x = 15

Step-by-step explanation:

The sum of angles in a triangle is 180deg.

Let's mark the measures of the internal angles as A, B and C.

We know that

A + B + C = 180deg

180deg - A + 180deg - B + 180deg - C = (9x + 1)deg + (5x + 12)deg + (10x - 37)deg

3*180deg - (A + B + C) = (24x - 24)deg

540deg - 180deg = (24x - 24)deg

360deg = (24x - 24)deg

360 = 24x - 24

384 = 24x

15 = x

Find the area of the largest square contained by a circle of radius r = 1cm. Explain your answer and justify that it is correct. Hint: Use the pythagorean theorem.

Answers

Answer:

2 square cm

Step-by-step explanation:

Given :

A square is inscribed in a circle whose radius is r = 1 cm

Therefore, the diameter of the circle is 2 r = 2 x 1

                                                                      = 2 cm.

So the diagonal of the square is 2r.

Using the Pythagoras theorem, we find each of the side of the triangle is [tex]$r \sqrt 2$[/tex].

Therefore, the area of the square is given by [tex]$\text{(side)}^2$[/tex]

                                                                         = [tex]$(r\sqrt 2)^2$[/tex]

                                                                         [tex]$= 2 r^2$[/tex]

                                                                         [tex]$= 2 (1)^2$[/tex]

                                                                         [tex]$=2 \ cm^2$[/tex]

Hence the area of the largest square that is contained by a circle of radius 1 cm is 2 cm square.

It costs $15,700 to build a particular car. This car sells for $24,322. What is the percent markup on the car to the nearest percent.

Answers

Answer: $15,700 - $24,322= 8622

Step-by-step explanation:

All you have to do is subtract

If the rectangular screen of a 40-inch monitor is 35 inches wide, what is the height of the monitor? Round to the nearest tenth.

Answers

Answer:

19.4

Step-by-step explanation:

We can solve this question using Pythagorean theorem

40^2 = h^2 + 35^2

1600= h^2+ 1225

1600-1225= h^2

375= h^2

h= √375

h = 19.4

Hence the height is 19.4

What is the equation of the line that passes through the point (4, 6) and is parallel to the line 2y - 4x = 1?
Select one:
O A. y = - 2x - 2
O B. y = 2x + 2
O C. y = x - 2
O D. y = 2x - 2

Answers

Answer:

D. y = 2x - 2

Step-by-step explanation:

1) First, find the slope of the given line. Place it in slope-intercept form to identify its slope easily. Isolate the y in the equation:

[tex]2y-4x = 1\\2y = 4x+1\\y = 2x+\frac{1}{2}[/tex]

A line placed in slope-intercept form is represented by the formula [tex]y = mx + b[/tex]. The [tex]m[/tex], or the coefficient of the x-term, represents the slope. Thus, the slope of this line is 2.

2) Lines that are parallel share the same slope. So, the slope of the parallel line will have 2 as its slope as well.

We now have enough information to write the equation of the line in point-slope form. From there, we can convert it to slope-intercept form and find out which option is correct.

Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex]. Since [tex]m[/tex] represents the slope of the line, substitute 2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (4,6) into the formula as well. Then, with the resulting equation, isolate y like before to find which option is correct:

[tex]y-6 = 2(x-4)\\y-6 = 2x-8\\y = 2x-2[/tex]

So, option D is correct.  

Supplementary angles always add up to 180 degrees. TRUE OR FALSE

Answers

Answer:

yes this is true.

Supplementary angles always add up to 180°.

Answer:

True

Supplementary angles always add up to 180°

Help with number 8 please :)) <3

Answers

the answer is D. when B = 1 or -1

Answer:

A

Step-by-step explanation:

a = integer/whole number

Any whole number divided by 0 is 0.

0 is an integer/whole number.

Luke and isabella make scale drawings.The scale from isabella's drawing is 6 m to 3 cm. The height of the fountain in isabella's drawing is 5 cm.The scale from the fountain to luke's drawing is 5m to 2cm. What is the height of the fountain in luke's drawing

Answers

Answer:

The answer is "[tex]2.5 \ cm[/tex]"

Step-by-step explanation:

While Luke is 5m to 2cm in size, it implies that every 2cm to Luke's drawing is 5m in real life. That real pond width must therefore be 5 m, given the fountain's width is 2 cm. As shown in the illustration, the step size for IsabelLa from the illustration to real life is [tex]\frac{6}{3} =2[/tex], which makes it simple to multiply any measure in the cm of her illustration by 2 to accomplish the exact size in m. So, in another direction around, they just have to divide the value by 2, instead of the divide from reality for drawing. So if the actual worth is 5m, it ought to be [tex]\frac{5}{2} = 2.5 \ cm[/tex] in its width.

Just the first four please 5th grade mathematics

Answers

I believe I have the answers :)

Question 1. <, >, >
Question 2. <, <, >
Question 3. >
Question 4. <

I hope this helps :)
If this is right please give me a like, if I’m wrong please tell me in the comments

PLEASE HELP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST

Answers

The answer is d i can explain if you want or need

Well there are 5 questions
Please help
Will give brainliest

Answers

Answer:

1. 30

2. x = 0

3. x = 10

4. 11.7

5. 60

Step-by-step explanation:

What is the range of possible values for x?

Answers

Answer:

Choice A) 0 < x < 18

Step-by-step explanation:

10x = 6x + 20

subtract

4x = 20

solve for x

x = 5

Write an expression showing the sum of a number H and a number W minus 11​

Answers

Answer:

h+w-11

Step-by-step explanation:

Answer:

H+W-11

Step-by-step explanation:

The two triangles below are similar. What is the similarity ratio of AABC to ADEF?

Answers

Answer:

2 : 1

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

AC : DF = 8 : 4 = 2 : 1

pls help me with this!

show this standard form equation in a graph

5x+y=-2​

Answers

Answer:

Step-by-step explanation:

One way to do this is to find the x- and y-intercepts and to plot these:

x-intercept:  Let y = 0:  5x = -2, or x = -2/5, so the x-intercept is (-2/5, 0).  Plot this point.

y -intercept:  Let x = 0:  y = -2, so the y-intercept is (0, -2).  Plot this point.

Finally, draw a line through these two points.

PLZS HELP THIS IS MY LAST QUESTION!!

Answers

Answer:

x = 30

Step-by-step explanation:

According to figure,

54° + 3x+36° = 180° [Linear pair]

=> 3x + 90 = 180

=> 3x = 180 - 90

=> 3x = 90

[tex] = > x = \frac{90}{3} [/tex]

=> x = 30 (Ans)

Answer:

x=30

Step-by-step explanation:

cuz that line is 180 degrees and using algebra you can subtract 54 from both sides and get 126 then u have to subtract the 36 from both side to geth 90 and then divide the 3x to get x by itself which would leave u with 30 so x=30

what is the volume of this pyramid?

the options are
A. 720
B. 1080
C. 1440
D. 2160

Answers

the answer is C grrrr

In circle P shown, the measure of angle P Q S is 20°.

Answers

Answer:

D 70

Step-by-step explanation:

Hello there!

A triangle formed inside of a circle using the diameter ( segment RQ ) is a right triangle

Meaning that the angle across from the hypotenuse ( diameter ) is a right angle ( = 90 degrees )

That being said we are given two angles (90 and 20 ) so we can easily calculate the measure of the missing angle

Remember the sum of the angles in a triangle is equal to 180 so we can find the missing angles by subtracting the given angles ( 90 and 20 in this case ) from 180

angle PRS = 180 - 90 - 20

180 - 90 = 90

90 - 20 = 70

Therefore your answer is D. 70

Hurry please! 30 points!

A ladder rests against the side of a barn. The tip of the ladder reaches 20 feet up the wall and the base of the ladder reaches a point on the ground 12 feet from the wall. About how tall is the ladder?

A. 23 ft
B. 16 ft
C. 12 ft
D. 9 ft

Answers

Answer:

A - 23ft

Step-by-step explanation:

Pythagorean theorem: 12^2 + 20^2 = X^2.

X^2 = 544. X = sqrt(544) which is around 23ft

Suppose 80 out of 400 cat owners surveyed said their cats have bad breath. What percent of the cat owners is this?

Answers

??? The link isn’t working for me :\

Subtracting fractions with unlike denominators

Answers

improper fraction - 37/15 or mixed fraction - 2 7/15

Please help me with this homework

Answers

Answer:

20

Step-by-step explanation:

use pythagorean theorem:

[tex]12^{2}[/tex] + [tex]16^{2}[/tex] = [tex]c^{2}[/tex]

144 + 256 = [tex]c^{2}[/tex]

400 = [tex]c^{2}[/tex]

[tex]\sqrt[ ]{400}[/tex] = c

20 = c

HELP OMG
I LOST MY AIRPODS AT SCHOOL

Answers

Answer:

how should we help?

Step-by-step explanation:

Answer:

dang that sucks..... try and play music at max vol and see if you hear any music coming from anywhere that's probably were the airpods are, if they are in the case then i dont know if u would hear anything. It all depends...

~ i hope this has helped ya out some how, hope ya find your airpods my friend!~

Step-by-step explanation:

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