Help pls show with work

The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.

Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is

π (radius) (height) = π (1/y)² ∆y = π/y² ∆y

and the volume of a stack of n such disks is

[tex]\displaystyle V_n = \sum_{i=1}^n \pi {y_i}^2 \Delta y[/tex]

where [tex]y_i[/tex] is a point sampled from the interval [1, 5].

As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,

[tex]\displaystyle V = \lim_{n\to\infty} V_n = \int_1^5 \frac{\pi}{y^2} \, dy[/tex]

[tex]V = -\dfrac\pi y\bigg|_{y=1}^{y=5} = \boxed{\dfrac{4\pi}5}[/tex]

Answer:

yeah they are equivalent

Step-by-step explanation:

[tex]\\ \tt\longmapsto (-1)(-x)[/tex]

[tex]\\ \tt\longmapsto x[/tex]

Yes equal

Note that

Answer:

Midpoint (1/2, -5/2)

Step-by-step explanation:

To find a midpoint, add the x's of the endpoints and divide by 2. Then add the y's and divide by 2.

C(-3, -4)

D(4, -1)

Midpoint:

( x+x /2 , y+y /2 )

( -3+4 /2 , -4+-1 /2 )

( 1/2, -5/2)

There are 1.5 revolution in one second.

What is relation between minute and seconds?

The relation between minute and seconds is;

1 minute = 60 seconds

A windmill makes 90 revolutions in one minute.

Now, In one minutes number of revolution = 90

Since, 1 minute = 60 seconds

Hence, In 60 second number of revolution = 90

In 1 second number of revolution = 90/60 = 1.5

So, There are 1.5 revolution in one second.

Therefore, There are 1.5 revolution in one second.

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Answer:

(p-3)(p+14)

Step-by-step explanation:

factors of 42:

1 x 42

2 x 21

3 x 14

6 x 7

The only pair that would work are -3 and 14

Answer:

chicken= $10.20

beef= $12.90

the difference between them is $2.70

Step-by-step explanation:

so you do 3.40 *3 and get 10.20.

then 4.30*3 and get 12.90

then 12.90- 10.20= $2.70

Answer:

1 pound of chicken costs=$3.40

3 pounds of chicken costs=3×3.40

=$10.2

1 pound of beef costs=4.30

3 pounds of beef costs=3×4.30

=$12.9

Now,

How much more does the beef cost?

=12.9--10.2

=$2.70

hope it helps you :)

Answer:

I think it could be 88-?

Answer:

it's 88

Step-by-step explanation:

u multiply 11*8 and u get 88 in. squared

pls mark as brainliest ;)

Answer:

After the reflection:

U: (5,2)

V: (3,1)

W: (3,-3)

Z: (5,-6)

Step-by-step explanation:

To reflect over the x axis, you need to move the point left or right across the x axis (in this case, right) an equal amount of times. Ex: -5, you would move 10 to the right, or 5 to get to 0, then another 5 to equal it out

x= 5/3

go on chrome it'll show you

It would take 220 minutes for Angela's and Benjamin's monthly bills be the same

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the cost after x minutes, hence:

For angela:

y = 0.15x + 49

The y intercept is $49 and the rate of change is $0.15 per minute

For Benjamin:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-60=\frac{80-60}{200-0} (x-0)\\\\y=0.1x+60[/tex]

The y intercept is $60 and the rate of change is $0.10 per minute

For 200 minutes:

Angela: y = 0.15(200) + 49 = $79

Benjamin: y = 0.10(200) + 60 = $80

To be the same:

0.15x + 49 = 0.1x + 60

x = 220 minutes

It would take 220 minutes for Angela's and Benjamin's monthly bills be the same

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In the elimination method, one variable is eliminated from the system of equations to find the value of the other.

To create the opposite terms of the x-variable-

To solve the system of equations and find the value of the variables, the elimination method is used.

In this method, one variable is eliminated from the system of equations to find the value of the other.

Given information-

The system of the equation given in the problem is,

[tex]\rm 3x-\dfrac{1}{4}y=15[/tex]

The second equation given in the problem is;

[tex]\rm \dfrac{2}{3}x-\dfrac{1}{6}y=6[/tex]

To eliminate the x term, make the coefficient of x of both equations equal.

It can be done by multiplying the coefficient of x term of the first equation to the second equation and the coefficient of x term of the second equation to the first equation.

The first equation is multiplied by;

[tex]\rm 4\times 3x-4\times \dfrac{1}{4}y=15\times 4\\\\12x-y=50[/tex]

The second equation is multiplied by;

[tex]\rm -6 \times \dfrac{2}{3}x- -6 \times\dfrac{1}{6}y= -6 \times6\\\\-4x-y=-36\\\\4x+y=36[/tex]

Hence, to create the opposite terms of the x-variable-

The first equation is multiplied by the number 4.

The second equation is multiplied by the number -6.

Learn more about the elimination method here;

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Answer:

4, -6

Step-by-step explanation:

Answer:

Draw the top and bottom line segments equal length and parallel. The perpendicular bisector of the lines are gonna be one line of symmetry. Next, draw the horizontal line of symmetry halfway between those. Pick two points on the horizontal line of symmetry that are symmetrical about the vertical line of symmetry. Connect those points to the ends of the top and bottom segments.

Step-by-step explanation:

(Images for more context)

15/4 divided by 5/8 = 6/1 = 6

Answer:

B

Step-by-step explanation:

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the temperature of the metal bar after x seconds, hence:

Since the metal bar has an initial temperature of 30°C, hence:

b = 30, also m = 1°C (increase), The equation becomes:

y = 1(x) + 30 = x + 30

To reach 70°C:

70 = x + 30

x = 40 seconds

To reach 74°C:

74 = x + 30

x = 44 seconds

It would take about 40 seconds for the temperature to reach 70°C and 44 second to reach 74°C.

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Answer:

true

The height of Mount Everest is times the height of a waterfall.

Answer:

The answer would be D. 5

Step-by-step explanation:

Answer: D. 5

Step-by-step explanation: i did the test

Answers:

==================================================

Explanation for problem 1

Divide each term over its previous term.

We can stop here. The two results 0.8 and 0.75 do not match up, so we don't have a common ratio. Therefore, this sequence is not geometric. A geometric sequence must have each ratio of adjacent terms to be the same value throughout the list of numbers.

Side note: This sequence is arithmetic because we are subtracting the same amount each time (12) to generate each new term.

--------------------------------------

Explanation for problem 2

Like before, we'll divide each term by its previous term.

Each ratio found was 2. This is the common ratio and it shows we have a geometric sequence. It indicates that each term is twice that of its previous term. Eg: the jump from 12 to 24 is "times 2".

Answer:

B. 20x^4-39x^3+26x^2-6x

Step-by-step explanation:

(5x^2-6x+2)*(4x^2-3x)

20x^4 -15x^3 -24x^3 + 18 x^2 +8x^2 - 6x

20x^4 -39x^3 + 26x^2  - 6x

Answer:

-2 -7

0   -1

1     2

3    8

Step-by-step explanation:

Answer:

25 , 17

Step-by-step explanation:

Let the unknown two numbers be x & y.

According to the question,

Sum of 2 numbers is 42.

x + y = 42  ⇒ ( 1 )

Their difference is 8.

x - y = 8 ⇒ ( 2 )

First let us find the value of x.

( 1 ) + ( 2 )

x + y + x - y = 42 + 8

2x = 50

Divide both sides by 2.

x = 25

And now let us find the value of y.

x + y = 42

25 + y = 42

y = 42 - 25

y = 17

Therefore, the two numbers are 25 , 17

Hope this helps you :-)

Let me know if you have any other questions :-)

Answer:

[tex]let \: the \: numbers \: be \: x \: and \: y \\ x + y = 42....(1) \\ x - y = 8....(2) \\ now \\ x + y = 42 \\ x = 42 - y \\ again \\ x - y = 8 \\ x = 8 + y \\ putting \: the \: value \: of(x) \\ \\ 42 - y = 8 + y \\ 2y = 42 - 8 \\ 2y = 34 \\ y = 34 \div 2 \\ y = 17 \\ putting \: the \: value \: in \: equation \: (1) \\ x + y = 42 \\ x = 42 - 17 \\ x = 25[/tex]

x=25 and y=17

hope it helps.

stay safe healthy and happy.

Answer:

15 pencils

Step-by-step explanation:

total pencils=225x3=675 pencils

boxes=675÷20=33r15

therefore the answer is 15 pencils

Answer:

2/21+6/7 = 20/21

Step-by-step explanation:

2/21+6/7

=2/21+(6*3/7*3)

=2/21+18/21

=20/21

Hope this helps! Comment any questions <3

Answer:

20/21

Step-by-step explanation:

2/21 + 6/7

Get a common denominator of 21

2/21  + 6/7 *3/3

2/21 + 18/21

20/21

Answer:

5000+500+10+3=5500+13=5513

Step-by-step explanation:

Answer:

5.515x10³

Step-by-step explanation:

first we abb them together and we get 5513

Answer:

3

Step-by-step explanation: