Find the volume between the cone
X= sqrt(y^2 + z^2) and the sphere
x^2 + y^2 + z^2 = 16.
Answers
The volume between the cone and the sphere is approximately 23.55 cubic units.
We are given that;
[tex]X= sqrt(y^2 + z^2)[/tex]
[tex]x^2 + y^2 + z^2 = 16.[/tex]
Now,
To find the volume between the cone and the sphere, we can use a triple integral in spherical coordinates.
The cone corresponds to the equation [tex]$\rho = 2\cos(\phi)$[/tex], where [tex]$\rho$[/tex] is the radial distance, [tex]$\phi$[/tex]is the polar angle, and [tex]$\theta$[/tex] is the azimuthal angle. The sphere corresponds to the equation [tex]$\rho = 4$[/tex]. The limits of integration are:
[tex]$0 \leq \theta \leq 2\pi$$0 \leq \phi \leq \frac{\pi}{4}$$2\cos(\phi) \leq \rho \leq 4$[/tex]
The volume element in spherical coordinates is [tex]$\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Therefore, the volume is:
[tex]$V = \int_{0}^{2\pi}\int_{0}^{\frac{\pi}{4}}\int_{2\cos(\phi)}^{4}\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Evaluating this integral, we get:
[tex]$V = \frac{32}{3}\pi - 8\sqrt{2}\pi + 16\pi$[/tex]
Therefore, by volume of cone the answer will be 23.55 cubic units.
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Related Questions
Greatest common factor for 3,27, and 33
Answers
Answer:
it's 3.
Step-by-step explanation:
Here's why........3 only has 2 factors 1 and it's self and 3 times 9 is 27 and 3 times 11 is 33 they all have 3 as a factor.
CHECK MY ANSWERS PLEASE!!
1. If OQ and RT are parallel lines which statement is true?
A) OPS is congruent to RSU
B) OPS is congruent to RSP (my answer)
C) OPS is congruent to OPN
D) OPS is congruent to TSU
-----------------------------------------
2. If OQ and RT are parallel lines which statement is true?
A) RSP is congruent to RSU
B) RSP is congruent to PST
C) RSP is congruent to TSU
D) RSP is congruent to OPS (my answer)
Answers
Answer:
1. A) OPS is congruent to RSU
2. C) RSP is congruent to TSU
Step-by-step explanation:
1. Since OQ and RT are parallel lines that are cut across by the transversal line, NU, therefore, angle OPS and angle RSU are corresponding angles formed. Corresponding angles are congruent.
✅Therefore: A) OPS is congruent to RSU. OPTION A IS TRUE.
❌OPS and RSP are consecutive interior angles. They are not congruent. They are supplementary. So, option B is NOT TRUE.
❌OPS and OPN are linear pair angles. Linear pair angles are not congruent. They are supplementary. Therefore, OPTION B IS NOT TRUE.
OPS and TSU are also not congruent.
2. Angle RSP and angle RSU are vertical angles. Vertical angles are congruent. Therefore, the statement that IS TRUE is:
C) RSP is congruent to TSU
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Answers
Answer:
the value of y is 3 more than twice x
Step-by-step explanation:
we find the slope is 2 because 4/2=2
y=2x+b
we put in the first point (1,5)
5=2+b
b=3
y=2x+3
Answer:
i think its c
Step-by-step explanation:
because 4 times 1 is 4 and if u add 1 than u get 5 which is y
im not sure if this is right lmk
I need help plz help
Answers
If f(x) = 4x2 – 3x + 7, what is f(-2)?
Answers
Answer:
29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
Assuming that you meant the first term to be 4x² then you just plug in -2 to all of the x-values in the function
Use fives fact to help you solve 7 x 6. Show your work using
Answers
/ \ = 7 x 2 = 14
4 2 + __
42
Using the "fives fact" (5 x 6 = 30) as a starting point, we added one more group of 6 to reach the final result of 36.
To use the "fives fact" to solve 7 x 6, we can break it down into simpler calculations using the fact that 5 x 6 = 30.
Here's the step-by-step calculation:
1. Start with the "fives fact": 5 x 6 = 30.
2. Since we need to find 7 x 6, we can add another 6 to the result of 5 x 6:
30 + 6 = 36
Therefore, 7 x 6 equals 36.
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Find the slope
How can I find the slope
Answers
Answer:
You should use the y2 - y1 /x2 - x1
To find the answer you should be able to plug in the x and the y in the equation with the coordinates that you have but I'm not sure if you don't have what you'll do
(3,1) and (-2,-1) are the two point.
You could do the y2-y1/x2-x1. Which is (-1) - 1 = -2 and (-2) - 3 = -5. Two negatives make a positive so the answer would be 2/5.
Read the description of f below, and then use the drop-down menus to complete an
explanation of why f is or is not a function,
f relates each student in Mr. Well's history class to their score on a final exam.
Answers
Answer:
because a function always gives a determined answer from what was placed into the domain, this is not a function. what is put into the domain (students) may not get the same result through f.
Answer: 1. the students 2. the final exams 3. is- domain- one- range brainliest plzz??
Cody's Aunt pays him $30 to walk her dogs 6 times at this rate how many times must he walk the dog in order to earn $100
Answers
$5 = 1 walk
Divide 100 by 5 and you get 20
Which equation justifies why 9 1/3 = ∛9?
(9 1/3)³ = 9(1/3·3) = 9
(9 1/3)³ = 9(1/3+3) = 9
(9 1/3)³ = 9(1/3-3) = 9
(9 1/3)³ = 9(3-1/3) = 9
Answers
Answer:
(91/3)3=9(1/3-3)=9
Step-by-step explanation:
Answer:
hows your day
Step-by-step explanation:
How many integers are between - 6,01 and 7.75?
13
14
15
16
Answers
Answer:
14 integers
Step-by-step explanation:
Given
[tex]Range: -6.01\ to\ 7.75[/tex]
Required
Determine the number of integers
Integers implies numbers without decimals; it could be positive or negative or 0.
So, within the range: the integers are:
[tex]-6, -5, -4,-3,-2,-1,0,1,2,3,4,5,6,7[/tex]
Notice that the above numbers are integers within the given range.
By counting them, we get the required number of integers.
[tex]Numbers = 14[/tex]
Hence, there are 14 integers
A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an
approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. What
percentage of filled boxes of rice have a weight between 28 and 29 ounces?
Find the z-table here.
O 33.1%
O 36.7%
O 63.3%
66.9%
Answers
Answer:
D
Step-by-step explanation:
I got it right
Using the normal distribution, it is found that 66.9% of filled boxes of rice have a weight between 28 and 29 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by: [tex]\mu = 28.2, \sigma = 0.4[/tex].
The proportion of filled boxes of rice have a weight between 28 and 29 ounces is the p-value of Z when X = 29 subtracted by the p-value of Z when X = 28, hence:
X = 29:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29 - 28.2}{0.4}[/tex]
Z = 2
Z = 2 has a p-value of 0.977.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 28.2}{0.4}[/tex]
Z = -0.5
Z = -0.5 has a p-value of 0.308.
0.977 - 0.308 = 0.669 = 66.9%.
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Which is a correct frost step for solving this equation
Answers
Answer:
you have to post the equation
Step-by-step explanation:
2. Paula learned to play a total of 10 pieces over the course of 5 weeks of piano lessons. In all, how
many weeks of piano lessons will Paula need before she will be able to play a total of 18 pieces?
Answers
Find the QUOTIENT of 0.4452 and 0.06.
Answers
Answer:
7.42
Step-by-step explanation:
When you divide by something smaller than 1, the answer becomes bigger because you are trying to see how many times 0.06 can fit in 0.4452. Hope this helps
PLEASE HELP I WILL MARK BRAINLIEST
Find the area of a square with side length x when x is equal to the given value. Is the area of a square and the length of its side directly proportional? Justify your answer.
1. x=15 ft.
2. x=10 in.
3. x=3 in
so can you figure out the correct answers for 1,2 and 3? You have to figure out what the area of the square is for each value and you need to figure out if the area of the square and the length of its side is or is not directly proportional to quantities.
Answers
Answer:
1. 15*15
2. 10*10
3. 3*3
Step-by-step explanation:
Answer:
Square the given value
Step-by-step explanation:
1. 15^2=225
10^2=100
3^2=9
A square has sides of EQUAL length. area is length times width. So, if each side is the same, square the given value.
In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Write an equation to represent this scenario using the variable b to represent Team B’s total points.
Translate the scenario.
Team A =
Team B =
Team C =
The equation representing this scenario is
.
Answers
Answer:
Team A = 449
Team B = 227
Team C = 307
Equation is
(2b-5) + b + (b+80) = 983
simplyfying
4b+75 = 983
Step-by-step explanation:
Take 4b+75 = 983
b = (983 - 75)/4 = 227
now
Team A = 5 less than twice as many as team B = 2b - 5 = 2 *227-5 = 454-5= = 449
Team B = b = 227
Team C = 80 more than team B = b+80 = 227+80 = 307
or you can just subtract 983 - (Team A +Team B)
Answer:
Team A = 449
Team B = 227
Team C = 307
Equation is
(2b-5) + b + (b+80) = 983
simplyfying
4b+75 = 983
Step-by-step explanation:
the other persons answer
Simplify the followingexpression (-5)(-3)(4)
Answers
A negative times a negative equals a positive. This means that -5 x -3 = 15.
Then you multiply that by four and get 60.
Hope this helps and have a nice day!!
Someone help me please
Express the cosine of < W as a ratio of the given side lengths.
Answers
Please help
Multiple choice
Will appreciate it if u help!
Answers
Answer:
Linear
Step-by-step explanation:
It's constant. Each X is going up 1 while each Y is going up 80
In 2015, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. At this rate, what would be the population in 2040? Round to the nearest whole number. Enter your answer in the box.
Answers
Answer:
320904
Step-by-step explanation:
7 years 5months plus 10 months equal?
Answers
Answer:
8.25 years
Step-by-step explanation:
hope this helps :)
If alice earns 56% more than wallaceAlice's salary is how many times Wally's salary?
Answers
Answer:
Alice's salary is 1.56 times Wally's salary
Step-by-step explanation:
Let Wally's salary = x
Alice's salary = x + 56% of x
= x + 0.56x
= 1.56x
= 1.56 * Wally's salary
Answer:b
Step-by-step explanation:
How do you find
the rate of change of a function?
Answers
Answer:
xfghzfgfrxeshixeah
Step-by-step explanation:
LG's SSL looks sl lid
What is 7/5 into a mixed number?
Answers
Answer:
improper fraction: 7/5
mixed number: 1 2/5
Answer:
1 and 2/5 or 1 2/5
Step-by-step explanation:
7/5 is a mixed number
7 - 5 = 2
The mixed number for the fraction 7/5 is 1 and 2/5
I Hope That This Helps! :)
You move right 7 units. You end at (8, 7). Where did you start?
Answers
Answer:
y=mx+b 58
Step-by-step explanation:
helppp me please will give brainliest
Answers
Answer:
y=-2x+11
Step-by-step explanation:
PLS SOLVE!!!!! THANK YOU!!!!!
Answers
• The height of a particular species of tree, in feet, r years after it is planted can be modeled by the
linear function h(x) = 5.27 +3.12x. Which of the following best interprets the y-intercept of the
linear model?
a. The average height of the species when planted is 5.27 feet.
b. The average height of the species when planted is 3.12 feet.
c. The species of tree grows by an average height of 5.27 feet per year.
d. The species of tree grows by an average height of 3.12 feet per year.
Answers
can you please help me with this question .
Answers
Answer:
The answer is 4
Explanation:
5 divided by 20 is 4 right?