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:
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
Related Questions
$20,500 at 7% for 3 years,
Answers
Answer:
If it is simple interest then it is $24805
If it is a compound interest then it is $25113.38
Step-by-step explanation:
$8000 is compounded semiannually at a rate of 7% for 20 years.
Answers
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:
the other dude said it lol
Liam earns $7.00 an hour shoveling snow. What is the relationship between the number of hours and the amount he earns?
Answers
okay that's alll guess
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
HOW CAN WE SOLVE THIS 5-2+17=7 PLEASE HELP IAM CONFUSED
5X+17=7
Answers
Answer:
x = -2Step-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
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.
For more information, refer to the link given below:
https://brainly.com/question/22771970
Currently, Trevon is three times as old as Janice. In four years, the sum of their ages will be 48. If Janice's
current age is represented by n, which of the following equations could be used to correctly solve for n?
Answers
Answer:
n+3n+4=48
Step-by-step explanation:
At 2 P.M., the total snowfall is 23 inches. At 7 P.M., the total snowfall is 45 inches. What is the mean hourly snowfall? Write your answer in simplest form as a fraction or mixed number.
Answers
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?
Answers
Answer:56
Step-by-step explanation: jggjoohjmnj
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]
Using a calculator (in degree mode), we calculate the angle:
[tex]x=\tan^{-1}(0.6714)=33.9^\circ[/tex]
x=33.9°
{(0, -8), (5,3), (-4,3), (9, 2)}
Does the following relation represent a function?
A.Yes
B.No
Answers
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.
Your ship accidentally left an alien stranded at your starting location.
How does the slope of this line compare with the slope of the line from the origin to the point (1, 4)?
They are the same.
They are opposites of each other.
They are reciprocals of each other.
The second line has no slope.
Answers
Answer:
they are the same
Step-by-step explanation:
Answer:
They are the same got it right on edg
Step-by-step explanation:
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
Solve for x 10x+1=8x+25
Answers
Answer:
x=12
Step-by-step explanation:
(10(12)=8(12)+25)=(120+1=96+25)=(121=121)
10x-8x
2x=25-1
Subtract the other numbers
25-1=24
Divide both sides by 2
X=12
What is the capital of peru
Answers
Answer:
☆<《HOPE IT WILL HELP YOU 》>☆
Step-by-step explanation:
capital of Peru is Lima
Hey I have a question for y’all, what helps build preseverance in your opinion ?
Answers
Answer:ummm......
Step-by-step explanation:
what ur questions I don't get it
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
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
Answer:
5 tickets
Step-by-step explanation:
45.50t + 14.99 = 242.49
-14.99 -14.99
45.50t = 227.5
t = 5
Find the domain and the range of each relation. Use the vertical
Line test to determine whether each graph is the graph of a function.
Answers
Answer:
29) x> or equal to 0 and y= all real number
30) x= all real y> or equal to 0
0.01 is 1/10 of what? Pls help
Answers
Answer:
A thousand
Step-by-step explanation:
If correct please give brainliest <3
I’m not sure if this is true but lol
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
the average number of potholes per 10 miles of paved us roads is 130
Answers
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
Answers
Answer:
40.
Step-by-step explanation:
What is the slope of the line on the graph
ОА. 5/9
OB. 5/7
OC. 7/5
OD. 9/7
Answers
1. Jen went scuba diving. She makes the first stop on her descent at 45 meters below the
surface of the water. From that point she dives down further, stopping every 10 meters. If
she makes 3 additional stops, at what depth will she be?
Answers
If the equation were 6x + 2 = 5x + 17, would there be one unique solution? What is it, and what would it mean in terms of the situation?
Answers
Answer:
15
Step-by-step explanation:
6x +2 =5x +17
6x - 5x =17 - 2
x =15
unique solution
angle 1 and angle 3 are ??? angles will mark brainiest
Answers
Answer:
supplementaryStep-by-step explanation:
angles 1 and 3 = supplementary angles and equal to 180
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