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Answer:

The volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]

Step-by-step explanation:

Let r be the radius of each sphere

We are given that distance between their centers is [tex]\frac{r}{2}[/tex]

Let [tex](\frac{-r}{4},0)[/tex] be the center of sphere 1 and [tex](\frac{r}{4},0)[/tex]be the center of sphere 2 .

Using the disk points

a=0 and b =[tex]\frac{3r}{4}[/tex]

[tex](x+(\frac{r}{4}))^2+y^2=r^2\\V=2 \int_{0}^{\frac{3r}{4}} \pi y^2 dx\\V=2 \int_{0}^{\frac{3r}{4}} \pi [r^2-(x+(\frac{r}{4}))^2]dx\\V=\frac{27 \pi r^3}{32}[/tex]

Hence the volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]

In attached diagram, we can see 2 circumferences with radius r, and separated centers by r/2.

The solution is:

V = (11/12)×π×r³

Let´s call circumferences  1 and 2, by symmetry, rotating area A will produce a volume V₁ identical a V₂, Obtained by rotating area B ( both around x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) ×r×x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) ×r×x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) ×r×(r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

Related Link : https://brainly.com/question/14301190

Answer:

-2^3= -8

8^2= 64

9^-1= 1/9

(-4)^-2= 1/16

Step-by-step explanation:

Wish this can help you.

The value of the expressions -2³, 8², 9⁻¹, and (-4)⁻² will be - 8, 64, 1/9, and - 1/16, respectively.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Simplify each expression, then we have

-2³ = - 8

8² = 64

9⁻¹ = 1/9

(-4)⁻² = 1 / (-4)² = - 1/16

The value of the expressions -2³, 8², 9⁻¹, and (-4)⁻² will be - 8, 64, 1/9, and - 1/16, respectively.

More about the value of the expression link is given below.

https://brainly.com/question/23671908

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Answer:

y= -x+8

Step-by-step explanation:

y=m+b Replaced M with -1 which will be -x.

y= -x+b Then replace the b with 8.

y= -x+8  

You do -x because its the same as -1.

Answer:

y = -x + 8

Step-by-step explanation:

Hi there!

We are given that the slope of a line is -1 and the y intercept of that same line is 8

We want to find the equation in slope-intercept form

Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept

As we are already given the values of the slope and the y intercept, we can simply substitute these values into the formula to find the equation.

First, substitute -1 as m in the equation:
y=-x+b (when 1 is the coefficient, you don't need to write '1' in front of a variable; when -1 is the coefficient, putting only a - sign will suffice)

Now substitute 8 as b in the equation

y = -x + 8

Hope this helps!

See more on this topic here: https://brainly.com/question/27187813

Answer:

Step-by-step explanation:

1. 120+21=141

2. 21-3=18

3. 7x-21

4. 20+x

5. 45+4x

6. 40+5c

7. 20+22r+26s

It will be nice if you give me brainliest

Good luck!

Answer:

b

Step-by-step explanation:

Answer:

Here's the parallel line: y = 5x - 4

Answer:

63

Step-by-step explanation:

Answer:

Maybe 55

Step-by-step explanation:

Answer:

3 and one third

Step-by-step explanation:

(3 1/3)

Answer: $49

Step-by-step explanation: if there are 7 days in a week and he is saving for 7 weeks, its 7 x 7= 49

Answer:

64$ if he doinles

Step-by-step explanation:

1,2,4,8,16,32,64

Answer:

4

Step-by-step explanation:

If there are 5 times as many the. terriers would make the 6th part.

So, 24÷6= 4

There are 4 terriers and 20 labs

Answer:

.001 or 1 thousandth

Step-by-step explanation:

.01/10=.001

Answer:

D. To provide a contrast to the actual enormity of the Biltmore

Step-by-step explanation:

Usually, when something is in "quotes", it's used to indicate sarcasm, emphasis, or a direct quote. This indicated emphasis.

Answer:

Year 7

Step-by-step explanation:

Hopefully this is helpful.

Answer:

ik im late and the other person was right but theres proof for the newcomers :)

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

9x−4=2x+3 Move all terms containing x to the left side of the equation.

7x−4=3 Move all terms not containing x to the right side of the equation.

7x=7 Divide each term by 7 and simplify. x = 1

Answer: 20/3 square inches

Step-by-step explanation:

Area = length*width

length = 5 in.

width = 4/3 in.

A = 5 * (4/3) = 20/3 in^2

Answer:

$316

Step-by-step explanation:

Since each cardigan costs $79 and there are 4 cardigans you would need to multyply 79×4. Which is $316. Kelly would be billed $316 for all four cardigans.

answer:

50

explanation:

Answer:

y=7x+4

Step-by-step explanation:

Answer:

- 14

Step-by-step explanation:

Step 1:

- 0.5x - 3 = 4      Equation

Step 2:

- 0.5x = 7        Add 3 on both sides

Step 3:

x = 7 ÷ - 0.5      Divide

Answer:

x = - 14

Hope This Helps :)

Answer:

(`1/4)^4

Step-by-step explanation:

Since the probability of landing on a head is theoretically the same as that of landing on tails, and since the four flips are entirely independent of one another, the desired probability is

(1/2)^4 or 1/16

Answer:

[tex]\displaystyle s=\frac{3\pi}{4}[/tex]

Step-by-step explanation:

Trigonometric Values

We need to find the angle s in the interval [π/2,π] where:

[tex]\displaystyle \sin s=\frac{\sqrt{2}}{2}[/tex]

There are two possible angles that have the same sine value in the first rotation of s. Any angle on the first quadrant has the same sine as its supplementary angle in the second quadrant.

The first angle s whose sine is [tex]\frac{\sqrt{2}}{2}[/tex] is:

[tex]\displaystyle s=\frac{\pi }{4}[/tex]

The other angle is its supplementary angle:

[tex]\displaystyle s=\pi-\frac{\pi }{4}=\frac{3\pi}{4}[/tex]

Only this last angle lies on the required interval, thus:

[tex]\boxed{\displaystyle s=\frac{3\pi}{4}}[/tex]

Answer:

Where are the answers to choose from?

Answer:

yes, Jenny has enough flour for both recipes

Step-by-step explanation:

First, find what Jody and Jenny need for both their recipes. For this, we need a common denominator, 8

1 5/8=13/8

3/4=6/8

13/8+6/8=19/8

Jody has 3 1/2 cups of flour, which is 7/2 cups or 28/8.

Now we need to make sure that 28/8 is greater than 19/8

28>9.... so she has enough flour!

Answer:

b

Step-by-step explanation: