Find the midpoint of the segment that has endpoints at
(a+b, a-b) and (a, b).

Answer:

a) 8π

b) 8/3 π

c) 32/5 π

d) 176/15 π

Step-by-step explanation:

Given lines :  y = √x, y = 2, x = 0.

a) The x-axis

using the shell method

y = √x = , x = y^2

h = y^2 , p = y

vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]

     = [tex]( 2\pi ) \int\limits^2_0 {y.y^2} \, dy[/tex]  

∴ Vol = 8π

b) The line y = 2  ( using the shell method )

p = 2 - y

h = y^2

vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]

     = [tex]( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy[/tex]

     = ( 2π ) * [ 2/3 * y^3  - y^4 / 4 ] ²₀

∴ Vol  = 8/3 π

c) The y-axis  ( using shell method )

h = 2-y  = h = 2 - √x

p = x

vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]

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

     = ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

d) The line x = -1    (using shell method )

p = 1 + x

h = 2√x

vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]

Hence   vol = 176/15 π

attached below is the graphical representation of P and h

Answer:

False

Step-by-step explanation:

If you see closely, Angle 3 is slightly smaller than Angle 6''

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Q1 =46

Step-by-step explanation:

Q1=(N+1)/4  (N means no of data)

=8+1/4

=9/4

=2.25

=2 nd term + (3 rd term - 2 nd term)

=44 +(46 - 44)

=44 + 2

=46

Answer:

1. f(x) = x² - 1 is an even function.

It has two-to-one relationship since f(-x) = f(x)

The answer is no

2. f(x) = x², same as above, the answer is no

3. The function f(x) = x³ is an odd function and its inverse is:

Both have one-to-one and onto relationship

The answer is yes

Answer:

d=23.43

Step-by-step explanation:

Given data

A(-6,8)

X1=-6

Y1=8

B(12, - 7)

X2=12

Y2=-7

The expression for the distance between two points is

d=√((x_2-x_1)²+(y_2-y_1)²

Substitute

d=√((12+6)²+(-7-8)²

d=√((18)²+(-15)²

d=√324+225

d=√549

d=23.43

Answer:

[tex]116^o[/tex]

Step-by-step explanation:

All triangles equal [tex]180^o[/tex]. Therefore, in order to find the value of [tex]x^o[/tex], all you will have to do is subtract [tex]64^o[/tex] from [tex]180^o[/tex].

[tex]180^o-64^o=116^o[/tex]

[tex]x^o=116^o[/tex]

Answer:

120 [tex]{ft}^{3}[/tex]

Step-by-step explanation:

To find the volume of a rectangular prism, multiply the lengths of all of the sides

3 x 5 x 8 = Ans --> 3 x 40 = Ans -->120 = Ans

Therefore, the volume of the rectangular prism is 120 [tex]{ft}^{3}[/tex]

Answer:

[tex]base = \sqrt{ {4}^{2} + {3}^{2} } \\ = \sqrt{25} = 5 \\ x = \sqrt{ {6}^{2} - {5}^{2} } \\ x = \sqrt{11} \\ x = 3.3[/tex]

Answer:

Terry has 1500 sweets.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the number of sweets Terry has.

y is the number of sweets Alex has.

If Terry gives 30% of his sweets to Alex,they will have the same number of sweets.

This means that:

[tex](1 - 0.3)x = y + 0.3x[/tex]

[tex]0.7x = y + 0.3x[/tex]

[tex]y = 0.4x[/tex]

If Terry gives 750 of his sweets to Alex,then Alex will have 80% more sweets than Terry.

This means that:

[tex]y + 750 = 1.8(x-750)[/tex]

We want to find x, and since [tex]y = 0.4x[/tex]

[tex]y + 750 = 1.8x - 1350[/tex]

[tex]0.4x + 750 = 1.8x - 1350[/tex]

[tex]1.4x = 2100[/tex]

[tex]x = \frac{2100}{1.4}[/tex]

[tex]x = 1500[/tex]

Terry has 1500 sweets.

Answer:

[tex]95 - \frac{3}{4} [/tex]

[tex] = \frac{95}{1} - \frac{3}{4} [/tex]

[tex] = \frac{380}{4} - \frac{3}{4} [/tex]

[tex] = \frac{380 - 3}{4} [/tex]

[tex] = \frac{377}{4} [/tex]

[tex] = 376\frac{1}{4} [/tex]

Answer:

1003.4375

Step-by-step explanation:

16055/16 is 1003.4375

I.)

1.) 7N = 50

2.) 35 - 16 = N

3.) 2P + 8 = 24

4.) R/5 = 9

5.) 30 - 10 = 20

II.)

1.) Twinity increased by eight times N

2.) D decreased by eleven

3.) The quotient of X and nine is K

4.) Five times X

5.) Three times a decreased by 5 is thirteen

6.) Nothing

7N = 50

35 - 16 = N

2P + 8 = 24

R/5 = 9

30 - 10 = 20

Twenty increased by eight times N

D decreased by eleven

The quotient of X and nine is K

Five times X

Three times a decreased by 5 is thirteen

I can help you in the comments section. Can you rephrase this question?

Answer:B

Step-by-step explanation:

Answer: 4/5

Step-by-step explanation:

Answer:

[tex]21 + x[/tex] packs

Step-by-step explanation:

Given

[tex]Washable \to 21[/tex]

[tex]Non \to x[/tex]

Required

The total packs bought

This is calculated as:

[tex]Total = Washable + Non[/tex]

[tex]Total = 21 +x[/tex]

Answer:

The answer would be E, the tire makes 700 revolutions in 2 minutes.

Step-by-step explanation:

One revolution is equal to the circumference of the tire :

[tex]C = 2\pi r = 2(1)(\frac{22}{7} ) = \frac{44}{7}[/tex]

The car travels at 2,200 feet per minute. To calculate the number of revolutions, divide the speed by the circumference.

[tex]2,200[/tex] ÷ [tex]\frac{44}{7}[/tex] = 350

This means that in 1 minute the tire makes 350 revolutions. To find out how many revolutions the tire would make for 2 minutes you simply multiply by 2.

350*2 = 700

So the answer would be E, the tire makes 700 revolutions in 2 minutes. Hope this helps, please mark brainliest!

Answer:

[tex]h = 7.69cm[/tex]

Step-by-step explanation:

Given

[tex]Volume = 455cm^3[/tex]

[tex]l = h[/tex]

Where:

[tex]h \to height[/tex]

[tex]l \to base\ length[/tex]

Required

The height

The volume is calculated as:

[tex]Volume = l^2 * h[/tex]

This gives:

[tex]Volume = h^2 * h[/tex]

[tex]Volume = h^3[/tex]

Rewrite as:

[tex]h^3 =Volume[/tex]

So, we have:

[tex]h^3 = 455cm^3[/tex]

Take cube roots

[tex]h = \sqrt[3]{455cm^3}[/tex]

[tex]h = 7.69cm[/tex] --- approximated

Answer:

c.) The absolute change is 35 students and the relative change indicates an increase of 23.3%

Step-by-step explanation:

the participants increasing = 185-150=35

the percentage = 35/150 × 100% = 23.3%

Option (C) The absolute change is 35 students and the relative change indicates an increase of 23.3% is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

In 2011, there were 150 participants in a quiz competition. In 2012, there were 185 participants in this quiz competition.

c) The absolute change is 35 students and the relative change indicates an increase of 23.3%

The change in participent = 185 - 150 = 35

Percentage change = (35/150)×100 = 23.3%

Thus, option (C) The absolute change is 35 students and the relative change indicates an increase of 23.3% is correct.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ2

Answer:

5.291 * 10^4

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Answer:

I'll setup the problem and you can compute the answer

Step-by-step explanation:

The formula for simple:

I = P*r*t

I = interest

P = loan amount

r = interest rate per period (period = days)

n = number of periods

P = 10,170

r = .0764/365

t = 272