Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along a diameter at an angle of π/6
Answers
Answer:
The answer is "[tex]\frac{\pi a^3}{9}[/tex]".
Step-by-step explanation:
please find the complete question in the attached file.
Let the sphere center be (0,0,0) and then let the intersection diameter lie all along the z-axis.
So one of the collision plans is the xz-plane the other is the path via an xz-plane angle.
[tex]\theta = \frac{\pi}{6}[/tex]
All appropriate region could then be indicated in spherical coordinates
[tex]E= {(\rho, \theta, \phi) : 0 \geq \rho \geq a, 0 \geq \theta \geq \frac{\pi}{6}, 0 \geq \phi \geq \pi }[/tex]
Calculating the volume:
[tex]\to v(E)=\int \int_{E} \int dV\\[/tex]
[tex]=\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}[/tex]
Related Questions
Question 1 of 5 Find the difference. (12m + 1) - (5m - 4) O A. 7m + 5 O B. 17m-3 O C. 17m+ 5 D. 7 m - 3
Answers
Answer: 7m + 5
Step-by-step explanation:
Distribute the Negative Sign:
=12m+1+−1(5m−4)
=12m+1+−1(5m)+(−1)(−4)
=12m+1+−5m+4
Combine Like Terms:
=12m+1+−5m+4
=(12m+−5m)+(1+4)
=7m+5
Three students attempt to define what it means for lines lll and mmm to be perpendicular.
Can you match the teacher's comments to the definitions?
Answers
Please find diagram attached
Answer and explanation:
Perpendicular lines are lines that meet at 90 degrees/ right angle.
The question seems to be incomplete but I will explain what perpendicular lines are in the context of lines lll and mmm, with some assumptions about the lines.
Assume that line III is 30mm long and line mmm is 25mm long, we say that line III is perpendicular to line mmm if line III meets line mmm at 90 degrees as we see in the diagram attached.
Find the missing side lengths leave your answerss as radicals
Answers
Answer:
n=7
m= 7[tex]\sqrt{3}[/tex]
Step-by-step explanation:
lmk if you need work
What's the axis of symmetry of y = 3x2 - 6x + 4
Answers
Answer: The axis of symmetry = 1
That's a vertical line passing through 1 on the x-axis
Step-by-step explanation: From standard form, ax² + bx + c
Use the values of a and b in the equation x = -b/2a to find s, the axis of symmetry.
x = -(-6)/2(3)
x = 6/6
x = 1
The required axis of the symmetry of the given parabola is x = 1.
Given that,
To determine the axis of symmetry of y = 3x² - 6x + 4.
A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The axis of symmetry of a parabola is given by -b/2a
Now. from the given parabolic equation y = 3x² - 6x + 4. we have a = 3 and b = 6.
Substitute the value in the symmetry equation
Axis of symmetry, x = -(-6)/2(2)
x = 1
Thus, the required axis of the symmetry of the given parabola is x = 1.
Learn more about parabola here:
brainly.com/question/4074088
#SPJ2
Find the value of θ from the following equation.(θ≤90°)
Answers
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
How should you improve sentence 1?
Where should you move sentence 4 to improve organization?
Answers
Answer:
by referencing the source
after sentence 2
Step-by-step explanation:
edge2020
CAN ANYONE HELP ME ASAP?!? PLEASEEE! I’ll give brainliest!
1-4
Answers
Answer:
35 degrees
42 degrees
x = 8 degrees
x = 7 degrees
Step-by-step explanation:
1)
m <1 = 70/2 = 35 degrees
2)
m <1 = 84/2 = 42 degrees
3)
6 + 4 x = (9 x + 4) / 2
12 + 8 x = 9 x + 4
12 - 4 = x
x = 8 degrees
4)
3 x - 1 = x + 13
2 x = 14
x = 7 degrees
write an equation of the line with a slope of -3/4 and y-intercept of -6
Answers
Answer:
y = -3/4x - 6
Step-by-step explanation:
To make Diane's special punch it take 4 cups of juice for every 7 cups of Lime soda. How much juice will be needed if we have 21 cups of soda? Using J for juice and S for soda, how will the equation look?
Answers
Answer:
Step-by-step explanation:
4 cups of J for every 7 cups of soda 4:7
21 cups of soda will take 12 cups of J
If you take the 7 and multiply by 3 you get the 21.
So you will need to multiply the 4 by the 3 to get the 12. You need to keep everything in proportion.
4:7 same as 12:21
What is the value of x in the diagram
Answers
Answer:
17
Step-by-step explanation:
Answer:
x = 23
Step-by-step explanation:
3x + 4x + 19 = 180
7x + 19 = 180
7x = 161
x = 23
What is the solution to the equation 23(y−6)=−(y+2)+1?
y=−35
y=15
y=95
y=275
Answers
Answer:
They all make the equation false?
Mr. Evans is paid $10.40 per hour for the first 40 hours he works in a week. He is paid 1.5 times that rate for each hour after that.
Last week, Mr. Evans worked 41.75 hours. He says he earned $434.20 last week. Do you agree? Complete the explanation that supports your answer.
Answers
Answer:
Step-by-step explanation: 16,888 this are the answer
How do you find the length of the side of a parallelogram?
A. slope formula
B. Midpoint formula
c.distance formula
Answers
9514 1404 393
Answer:
C. distance formula
Step-by-step explanation:
If you're starting from vertex coordinates, the distance formula is appropriate for finding the length of one side of a parallelogram. It will tell you the distance between two points:
d = √((x2-x1)² +(y2-y1)²)
Susie’s bakery is having a sale on all cookies.The bakery is offering a sale pack 4 cookies
Answers
giving brainliest it’s due asap pls help
Answers
Answer:
AB is parallel to CD - the reasoning looks right aswell although I don't know exactly what I'm answering here.. are you asking to check it?
15*PLEASE PLEASE PLEASE ANSWER VERY FAST AND CORRECT TYSM!
Answers
-2/15=13/15
Step-by-step explanation:
2/3-4/5=13/15
2/15=13/15
In how many ways can a chairman and a vice-chairman of a board of 6 members can occupy their seats.
Answers
Answer:
5
Step-by-step explanation:
Sent from my iPhone and it is the email address that you sent me
What is the answer to this geometry answer?
Answers
For what values of x∈[0,2π] does the graph of y=x+2cosx have a horizontal tangent?
Answers
Answer: x = pi/6 and x = pi/3.
Step-by-step explanation:
We have the function:
y = x + 2*cos(x)
It will have a horizontal tangent at the point where it's derivate is equal to zero.
Then first let's differentiate y.
y' = dy/dx = 1 - 2*sin(x).
Then we must find the value of x between 0 and 2*pi (or 0° and 360°)
y'(x) = 1 - 2*sin(x) = 0.
Let's solve that:
2*sin(x) = 1
sin(x) = 1/2.
We know that:
sin(30°) = 1/2.
and
Sin(120°) = 1/2
Then let's convert 30° into radians.
We know that:
pi = 180°.
Then:
pi/180° = 1.
30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6
120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.
Then the two values of x are: pi/6 and pi/3.
C is the midpoint of AB. D is the midpoint of AC. E is the midpoint of DC. If DE = x2 and CB = 3x2 + 3x, describe the relationship between DE and CB and find the length of AB. PLZ HELP!!
Answers
Please find illustration attached
Answer and explanation:
I have illustrated the bisection of the lines using a diagram so it's easier to solve length of AB
Comparing line DE and CB, we know that DE is half of line DC and DC is half of CB, because CB= AC
Therefore DE is a quarter of line CB because length of DE × 4 will be equal to CB
To find length of AB, we go from known to unknown
We know from what we are given that line AB has a midpoint C, CB in line AB = 3x²+3x
CB=AC because CB is half of line AB
Therefore line AB
=3x²+3x+3x²+3x
= 6x²+6x
(Ill give brainliest if u help!)
Which equation has a value less than 54,811?
A) 54,811 x 2 = ________
B) 54,811 x one and two fourths = ________
C) 54,811 x 1 = ________
D) 54,811 x two fourths = ________
Answers
Answer:
Answer is D
Step-by-step explanation:
Answer:
The answer would be D.
Step-by-step explanation:
Use the 3 trig ratios to find each unknown side length. Round all answers to 1 decimal
Note: Diagrams are not drawn to scale.
Answers
Note: You missed to add some of the details of the question.
Hence, I am solving your concept based on an assumed graph which I have attached. It would anyways clear your concept.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the right angled-triangle ABC as shown in the attached diagram
From the triangle:
Ф= ∠C = 30°
AB = 6 units
BC = y
tan Ф = opp ÷ adjacent
The opposite of ∠C = 30° is the length '6'.
The adjacent of ∠C = 30° is the length 'y'.
As Ф= ∠C = 30°
so
tan Ф = opp ÷ adjacent
tan 30 = 5 ÷ y
1 ÷ √3 = 5 ÷ y
y = 8.7 units
Therefore, the length of the unknown side length 'y' is 8.7 units.
(Giving brainliets to who ever helps me!!
Solve eight and three fifths minus two and four ninths.
A) six and seven forty fifths
B) six and seven fourteenths
C) seven and seven forty fifths
D) seven and seven fourteenths
Answers
Answer:
6.1555
Step-by-step explanation:
the 5 is infinite in 6.15 such as 6.155555555 it does not stop
Answer:
6 [tex]\frac{7}{45}[/tex]
Step-by-step explanation:
i have this question and this what i got its right
Graph the system of equations on your graph paper to answer the question. y = - x + 4, \qquad y = x - 2 What is the solution for the system of equations? Enter your answer by filling in the boxes.
Answers
Answer:
y=x+2
y=-x+8
Step-by-step explanation:
The ratio of books to magazines at Jessica’s house is 5:3. If there are 21 magazines at Jessica’s house, how many books are there?
Answers
Answer:
There are 35 books
Step-by-step explanation:
I hope this HELP! :)
A study found that a 95% confidence interval for the mean μ of a particular population was computed from a random sample of 1200 people and found it to be 10 ± 4. Therefore, we may conclude:_______
Answers
Answer:
95% confidence interval for the mean μ is (6,14)
The Population mean μ lies between ( 6, 14 )
Step-by-step explanation:
Explanation:-
Given random sample 'n' = 1200
95% confidence interval for the mean μ is determined by
[tex](x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} } )[/tex]
Level of significance = 95% 0r 0.05
Z₀.₀₅ = 1.96
[tex](x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} } )[/tex] = 10 ± 4
Mean of the small sample = 10
95% of confidence intervals are
( 10 ±4 )
( 10 -4 , 10+4)
( 6 , 14 )
95% confidence interval for the mean μ lies between ( 6, 14 )
0,2,3,5,8,10,15,17,24,26,?
Answers
Answer:
maybe 35 is the answer for the it
which value would make the statement true?
Statement- 2/?>4/12
Options- A.4
B. 6
C.12
D.24
Answers
Answer:
C and D.
Step-by-step explanation:
2/6 = 1/3 4/12 = 1/3
2/4 = 1/2
2/12 = 1/6
2/24 = 1/12
situation: the ratio of my friends that like basketball to the ratio of my friends that don’t like basketball is 41:30. This means that 41 out of my 71 friends like basketball. 57.74% of my friends like basketball and 42.26% of my class doesn’t like basketball.
question: if the ratio stayed constant for the whole school, what would your equivalent ratio be with a new total of 310 total people?
Answers
Answer:
17.9:13
Step-by-step explanation:
I know this because in order to find the percentage of 310, you must mutiply 310 by the percentage.
The number of students who like basketball:
310 x 0.05774 = 17.9
The number of students who don't like basketball:
310 x 0.04726 = 13
Hope this helps! :)
Answer:
17.9:13
Step-by-step explanation:
This is the answer
610 divided by 20 without a decimal
Answers
Answer:
30 remainder 1 or 30.5
Step-by-step explanation:
please make me brainliest