Find the volume common to two spheres, each with radius r, if the distance between their centers is r/2. [Hint: It may be helpful to look at the previous question and see how it relates to this one. ] intersectingspheres

Answers

Answer 1

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]

Answer 2

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

Find The Volume Common To Two Spheres, Each With Radius R, If The Distance Between Their Centers Is R/2.

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If a mother is 20 years old when her baby is born how old will she be when she is twice as old as her child

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Answer:

40.

Step-by-step explanation:


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i calculated 31674.08 may i please get brainliest for my work

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

Sally is making lemonade. The ratio of cups of water to teaspoons of lemonade mix is 2 to 5. If Sally wants to make a larger batch, how many cups of water does she need is she used 25 teaspoons of lemonade mix?

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Step-by-step explanation: jggjoohjmnj

{(0, -8), (5,3), (-4,3), (9, 2)}
Does the following relation represent a function?
A.Yes
B.No

Answers

yes, x values don’t repeat

Answer:

Yes

Step-by-step explanation:

If you look at all of the x values: 0,5,-4,9

You can see that none of them repeat. This makes it a function.

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Answer:

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Step-by-step explanation:

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Currently, Trevon is three times as old as Janice. In four years, the sum of their ages will be 48. If Janice's
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Answers

Answer:

n+3n+4=48

Step-by-step explanation:

In triangle QRS the measure of right angle S is SQ=90 degrees Sq=47 feet and Rs=70 feet. Find the measure of angle R to the nearest tenth of a degree

Answers

Answer:

x=33.9°

Step-by-step explanation:

Trigonometric Ratios

In a right triangle, i.e. the triangles that have an internal angle of 90°, the so-called trigonometric ratios are valid.

There are six trigonometric ratios that can be used in right triangles, depending on the data available for each problem.

The current question gives us two sides in a right triangle and requires us to calculate the angle x.

The angle x 'looks' at the sides of the triangle in this way: RS=70 is the adjacent leg, SQ=47 is the opposite leg, and RQ is the hypotenuse.

We should use the trigonometric ratio that relates both the adjacent and the opposite led. There are two possibilities: The tangent and the cotangent. We'll use the tangent for no particular reason.

The tangent of an angle is defined as:

[tex]\displaystyle \tan\x=\frac{\text{opposite leg}}{\text{adjacent leg}}\\[/tex]

Use the given values:

[tex]\displaystyle \tan x=\frac{47}{70}=0.6714[/tex]

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[tex]x=\tan^{-1}(0.6714)=33.9^\circ[/tex]

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Answer:

29) x> or equal to 0 and y= all real number

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What is the capital of peru

Answers

Answer:

☆<《HOPE IT WILL HELP YOU 》>☆

Step-by-step explanation:

capital of Peru is Lima

Jody decides to ride her bike from her house to the park. The distance she travels on her bike, in kilometers, is equal to the function f(t), where t represents the number of hours she has been riding her bike. Jody rides her bike from her house to the park. Before Jody leaves her house f(0) = 0, and when Jody reaches the park f(2) = 30. From the information given, determine whether each statement is a correct interpretation that can be made about Jody's bike ride. Select Correct or Incorrect for each statement. Correct Incorrect It takes Jody 2 hours to bike to the park. The park is located 2 kilometers from Jody's house. When Jody is at her house she has biked for 0 hours.

Answers

Answer:

A)It takes Jody 2 hours to bike to the park.- Correct

B)The park is located 2 kilometers from Jody's house.- Incorrect

C) When Jody is at her house she has biked for 0 hours.- Correct

Step-by-step explanation:

We are given that The distance she travels on her bike, in kilometers, is equal to the function f(t), where t represents the number of hours she has been riding her bike.

f(t)= Distance covered in t hours

t = time in hours

Jody rides her bike from her house to the park. Before Jody leaves her house f(0) = 0

So, Distance covered in 0 hours is 0 km

So, When Jody is at her house she has biked for 0 hours

Jody reaches the park f(2) = 30.

So, Distance traveled in 2 hours is 30 km

So, It takes 2 hours to reach park

A)It takes Jody 2 hours to bike to the park.- Correct

B)The park is located 2 kilometers from Jody's house.- Incorrect

C) When Jody is at her house she has biked for 0 hours.- Correct

Answer:

1. Correct

2. Incorrect

3. Correct

Step-by-step explanation:

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5X+17=7

Answers

Answer:

x = -2

Step-by-step explanation:

5X + 17 = 7

subtract 17 each side

5x + 17 - 17 = 7 - 17

divide 5 both sides

5x = -10  

simplify

5x/5 = -10/5

x = -2

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Answers

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Answers

Answer:

15

Step-by-step explanation:

6x +2 =5x +17

6x - 5x =17 - 2

x =15

unique solution

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Answers

Answer:

x=12

Step-by-step explanation:

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10x-8x
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Subtract the other numbers
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If a room has 28 people in it, how many people Are in a room 14 times it’s size?

Answers

Answer:

392

Step-by-step explanation:

times 28 by 14 and youll get 392 - may i get brainliest :)

Answer:

392 people would be in the room

Step-by-step explanation:

you do 8 times 4 which is 32 then you multiply 8 times 10= 80 add them together  112, then multiply 20 times 4= 80, finally 10 time 20=200 add all together it equals 392

Find the measure of angle b

Answers

Answer:

40 degrees

Step-by-step explanation:

180-140=40

Answer:

40° that's the answer hope I helped

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Step-by-step explanation:

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The Stanford-Binet Intelligence Scale is an intelligence test, which, like many other IQ tests, is standardized in order to have a normal distribution with a mean of 100 and a standard deviation of 15 points.

As an early intervention effort, a school psychologist wants to estimate the average score on the Stanford-Binet Intelligence Scale for all students with a specific type of learning disorder using a simple random sample of 36 students with the disorder.

Determine the margin of error,
, of a 90% confidence interval for the mean IQ score of all students with the disorder. Assume that the standard deviation IQ score among the population of all students with the disorder is the same as the standard deviation of IQ score for the general population, =15

points.

Give your answer precise to at least two decimal places.

Answers

Answer:

4.11

Step-by-step explanation:

Margin of error equals critical value times standard error.

MoE = CV × SE

For 90% confidence and n > 30, the critical value is z = 1.645.

The standard error is SE = σ/√n = 15/√36 = 2.5.

Therefore, the margin of error is:

MoE = (1.645) (2.5)

MoE = 4.11

The margin of error of a 90% confidence interval for the mean IQ score of all students with the disorder is 4.1125 and this can be determined by using the formula of margin of error.

Given :

Standardized in order to have a normal distribution with a mean of 100 and a standard deviation of 15 points.A school psychologist wants to estimate the average score on the Stanford-Binet Intelligence Scale for all students with a specific type of learning disorder using a simple random sample of 36 students with the disorder.90% confidence interval.

According to the given data, the confidence is 90% and n > 30, so the critical value is z = 1.645.

Now, to determine the standard error using the below formula:

[tex]\rm SE = \dfrac{\sigma}{\sqrt{n} }[/tex]

[tex]\rm SE = \dfrac{15}{\sqrt{36} }=\dfrac{15}{6}[/tex]

SE = 2.5

Now, the formula of margin of error is given by:

[tex]\rm MOE = z\times SE[/tex]

MOE = (1.645) [tex]\times[/tex] (2.5)

MOE = 4.1125

So, the margin of error is 4.1125.

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Answer:

supplementary

Step-by-step explanation:

angles 1 and 3 = supplementary angles and equal to 180

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Answers

Answer:

If it is simple interest then it is $24805

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Step-by-step explanation:

Bethany uses the equation d=3.75h to find the distance, d, she travels while walking for h number of hours. what is the constant of proportionality between d and h? show your work

Answers

Answer:

The constant of proportionality between d and h is 3.75

Step-by-step explanation:

The direct proportionality function is called any function in which the dependent variable (y) is obtained by multiplying the independent (x) by a constant value. This type of function is more commonly called a linear function and has an expression of the form:

y=m*x

The value m is a constant called the constant of proportionality or the slope of the line and represents the inclination of the line with respect to the abscissa axis, that is, the x axis. Graphically this linear function is a line with slope m that passes through the origin of coordinates, that is, the point 0 in x and 0 in y, which is the point (0,0).

You know that Bethany uses the equation d=3.75*h to find the distance, d, she travels while walking for h number of hours.  Comparing with the direct proportionality function y = m * x, then y is represented by the distance d, x is represented by the number of hours h and the constant of proportionality or slope m is the number 3.75.

So, the constant of proportionality between d and h is 3.75

HELP!!!!!
answer asap! this is due in two hours!!

Answers

Answer:

it is 56

Step-by-step explanation:

there are 4 sides and they are all 10 and if you add them they are 40 and if you do the bottom it is 16 and 40 + 16 is 56  hope it helps

Online concerts tickets cost 37$ each, plus a service charge of 8.50$ per ticket. The web site also charges a transaction fee of 14.99$ for the purchase. You paid 242.49$. How many tickets did you buy?

Answers

5 tickets I’m pretty sure

Answer:

5 tickets

Step-by-step explanation:

45.50t + 14.99 = 242.49

          -14.99      -14.99

           45.50t = 227.5

                    t  = 5

Add.

0.125 + 0.25 + 0.33

Answers

Answer:

0.705

Step-by-step explanation:

Answer: the answer is .705

Step-by-step explanation:

the numbers 0.25 and 0.33 are technically 0.250 and 0.330

so just line them up and add. 0.250+0.125+0.330=0.705

Titus took 30 minutes to walk 2 miles at a constant rate. Let d represent the distance Titus walks in miles after t minutes. What are two different constants of proportionality for the relationship between distance, in miles, and time, in minutes?

Answers

Answer:

15 and 1/15

Step-by-step explanation:

Given

Time (t) = 30 minutes

distance (d) = 2 miles

To determine the first constant of proportionality

Let time be directly proportional to distance.

t = kd

Where k is the constant of proportionality

Make k the subject

k = t/d

Substitute values for t and d

k = 30/2

k = 15

To determine the second,

Let distance be directly proportional to time.

d = kt

Make k the subject

k = d/t

Substitute values for d and t

k = 2/30

k = 1/15

Hence, the constant of proportionality are

15 and 1/15

What is the slope of the line on the graph
ОА. 5/9
OB. 5/7
OC. 7/5
OD. 9/7

Answers

B I think 5/7 should be


1. Jen went scuba diving. She makes the first stop on her descent at 45 meters below the
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she makes 3 additional stops, at what depth will she be?

Answers

15 meters because 45 - (10 +10 + 10)
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