In Cartesian coordinates, the volume is
[tex]\displaystyle \iiint_R \mathrm dV[/tex]
where R is the set
[tex]R = \left\{(x,y,z) \, : \, -4\le x\le4 \text{ and } -\sqrt{16-x^2} \le y \le \sqrt{16-x^2} \text{ and }\right. \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~\left.-\sqrt{16-x^2-y^2} \le z \le \sqrt{16-x^2-y^2} \right\}[/tex]
Converting to spherical coordinates, we take
[tex]\begin{cases}x=\rho\cos(\theta)\sin(\phi) \\ y=\rho\sin(\theta)\sin(\phi) \\ z = \rho\cos(\phi)\end{cases}[/tex]
and we can compute the Jacobian to find
[tex]dV = dx\,dy\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
and the set R transforms to
[tex]R' = \left\{(\rho,\theta,\phi) \,:\, 0\le \rho\le4 \text{ and }0\le\theta\le2\pi \text{ and } 0\le\phi\le\pi\right\}[/tex]
The new integral and hence the volume is then
[tex]\displaystyle \iiint_R \mathrm dV = \iiint_{R'} \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi \\\\ = \boxed{\int_0^\pi \int_0^{2\pi} \int_0^4 \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi}[/tex]
what is 90x40+50-20x45=20-15(34)-(20)+
Answer:
2750=-510
Step-by-step explanation:
hope this helps ._.
A printer can print 32 pages in 80 sec.
The rate in lowest terms is______?
Answer:
0.4 pages per second
24 pages per minute
1 page can be printed every 2.5 seconds
Each answer is technically correct, use the one that's most appropiate
Step-by-step explanation:
32 pages in 80 seconds
32 / 80 = 0.4 pages per second
0.4 / 1
If they want it in minutes, multiply both sides by 60 seconds
0.4 * 60 / 1 * 60
24 pages per minute
A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
The answer would be two feet.
Step-by-step explanation:
Step 1. Do 10-6 (10 being the total space and 6 being the painting)
Step 2. Get the answer of 4.
Step 3. Divide four by 2 because it needs to be centered.
Step 4. Get the answer of two feet on each side.
I hope this helps! :)
Please solve this for me
What is 40% of 160?
OA 20
OB. 40
OC. 32
OD. 64
OE 75
The correct answer would be D. 64
The 40 percentage of 160 is 64, the correct option is D.
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We need to Write the percent as a fraction in simplest form
16.24%
So, we can rewrite it as;
16.24 / 100
16 and 24/100 or 16 6/25
So the percent as a fraction is 16 6/25
We are given that;
Total value= 160
Percentage= 40%
Now,
To find 40% of 160,
=40%=0.4
We can multiply 0.4 by 160.
=0.4*160
=64
Therefore, by the given percentage the answer will be 64.
Learn more about percent here:
https://brainly.com/question/11549320
#SPJ7
11. Reduce 48/72 to its lowest terms.
A. 6/9
B.2/3
c. 24/36
D. 30/54
Answer:
its A my friend because: 48/2=24. 72/2=36
24/2=12. 36/2=18
12/2=6. 18/2=9
i need the answer pls help pls
Answer:
B
Step-by-step explanation:
x² - 8x + 97 = 0
the general form to solve such quadratic equations is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -8
c = 97
so, we get
x = (8 ± sqrt((-8)² - 4×1×97))/(2×1) =
= (8 ± sqrt(64 - 388))/2 = (8 ± sqrt(-324))/2 =
= (8 ± sqrt(324×-1))/2 = (8 ± 18×i)/2 = 4 ± 9i
How did the structure of the Han dynasty reflect Confucianism? Increasing rebellions represented the emphasis on warfare. Crowning a new emperor reflected the importance of loyalty. The multiple levels of bureaucracy reflected the belief in social order. The need for new leaders highlighted the importance of self-promotion.
Answer:
the multiple levels of bureaucracy reflected the belief in social order
Step-by-step explanation:
fill in the missing values of the following number patterns
a) 24;12;0;__ ; __
b) -36; -25; -16; __; __
Answer:
A) 24;12;0;-12;-24 because the numbers are gradually going down and they go into the negatives which means they repeat the numbers in the beginning.
B)-36;-25;-16;-9;-4 i am uncertian on this one but i think im doing it right.
2 tan x - Sin 2x ÷ 2 Sin^2 x = tan x
Looks like the claim is
(2 tan(x) - sin(2x)) / (2 sin²(x)) = tan(x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
as well as the definition of tangent:
tan(x) = sin(x) / cos(x)
Then on the left side, we can cancel factors of 2 sin(x) to get
(2 sin(x) / cos(x) - 2 sin(x) cos(x)) / (2 sin²(x))
= (1/cos(x) - cos(x)) / sin(x)
Multiply this by cos(x)/cos(x) :
(1/cos(x) - cos(x)) / sin(x) = (1 - cos²(x)) / (sin(x) cos(x))
Recall that for all x,
sin²(x) + cos²(x) = 1
so that
(1 - cos²(x)) / (sin(x) cos(x)) = sin²(x) / (sin(x) cos(x))
= sin(x) / cos(x)
= tan(x)
as required.
In an experiment, the probability that event A occurs is 7/8, the probability that event B occurs is 7/9, and the probability that events A and B both occur is ¾ . What is the probability that A occurs given that B occurs?
Question 5 options:
0.829
0.125
0.762
0.964
Answer:
Here is answer
Step-by-step explanation:
sorry if it is wrong
I think 0.762 in the answer
Help please i need to finish or i will not pass
Answer:
its 12p bro...
Step-by-step explanation:
There are 12 cards a pack. Carter bought a unknown amount of packs, so this is represented by p.
Think of it this way.
12p = 12*p
This is because of the distributive property.
A video game allows players to design their own character using the following options.
Video Game Character
What is the probability of designing a female character with long, red hair?
A. 1/24
B. 1/12
C. 1/9
D. 1/4
Answer:
1/24
Step-by-step explanation:
Probability of making female character = 1/2
Probability of having long hair = 1/3
Probablity of having red hair = 1/4
Multiply all these probabilities ( 1/2 x 1/3 x 1/4) = 1/24
The probability of making a female character with long red hair in this video game is 1 in 24.
I hope this helps.
please help me please pleasr please
Answer:
which one's anwer you want
2. length= 65 ft width=24 m area=135 in2
The sets J and E are given below.
J= {2, 3, 4, 8)
E={0,1,3,7)
Find the intersection of J and E.
Find the union of J and E.
Answer:
See below
Step-by-step explanation:
Intersection is the elements that are in both sets : {3}
Union adds them together { 0 1 2 3 4 7 8 }
Which of the following algebraic expression represents 2 less than 3 lots of n? (A) - (B) (C) 3(n - 2) 2 – 3n 3 + n - 2 3n - 2 (D)
Answer:
D
2 less than means 2 to be subtracted3lots of n means 3 to be multiplied with n i.e 3nHence the expression is 3n-2
Mike earns $15 per hour and Sara earns $34 per hour. What is the relative change in wages from Mike to Sara?
Please help me thank you so much!
Answer: the third one
Step-by-step explanation: how i know by guessing
Go Q 7x12 7
what is it?
Answer:
7*12= 84
Step-by-step explanation:
Hope this helps.
In a parking lot there are only white cars, green cars, and red cars. If one car is selected at random from
the lot, the probability that the selected car would be a green car is 1/6, and the probability that it would
be a red car is 1/8. What is the probability that it would be a white car?
Answer:
17/24 chance for white car
Step-by-step explanation:
We know that there is a 1/6 chance that it will be green and 1/8 that it will be red so whatever's left has to be white. We can just add the fractions that we have and subtract them from one to get the probability of getting a white car.
1/6+1/8=?
Find the lowest common denominator (24)
4/24+3/24=7/24
Subtract it from 1
24/24-7/24=17/24
17/24 chance that it's white
i will give brainliest
Answer:
Below
Step-by-step explanation:
Population: 10,000
Sample: 250
HELP GIVING BRAINLIEST + STARS
Motion graphs! Oh yes, I remember those.
I will be using the example of a remote-control car.
For Section AB:
The car starts moving steadily in one direction.
For Section BC:
The car has stopped moving.
And finally, for section CD:
The car has turned around and returned to the starting point at a steady pace.
I hope this answers your question.
-Toremi
determine the elements of the relation A × A if -
A = { 1 , 2 , 3 }
thankyou ~
If X and Y are two sets, then X × Y is the Cartesian product of X and Y, which is the set of all pairs (x, y) such that x ∈ X and y ∈ Y.
This means
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5
Answer:
[tex]y=\frac{1}{4}x-5[/tex]
Step-by-step explanation:
Write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5
Slope-intercept form: y = mx + b
m = slope
b = y-intercept (when x = 0)
Ex:
y = 5x + 2
m = 5b = (0, 2)For our problem:
[tex]y=\frac{1}{4}x-5[/tex]
m = [tex]\frac{1}{4}[/tex]b = (0, -5)Hope this helps!
10. Cindy is wrapping a birthday present for her sister. The present is in a 10 points
box that has a length of 10 in, a width of 6 in and a height of 4 in. If the
wrapping paper costs $0.25 per square inch, how much would it cost to
wrap Cindy's present? *
Answer:
$648
First find the surface area, and then multiply that by 12 for the inches, then multiply that by the cost
Answer:
$62
Step-by-step explanation:
First find the surface area of the box: 2(lw+lh+wh) = 2(60 + 40 +24) = 124(2) = 248
Now create a ratio to find the total cost:
[tex]\frac{0.25}{1} = \frac{x}{248}[/tex]
Solve for x by cross multiplying -
x=62
HELP ASAP will get brainly user !!!
Answer:
46
Step-by-step explanation:
p=6,q=12.
Put the numbers where the letters are.
7x6+12/3
46
Hope this helps!
Answer:
[tex]beinggreat78~here~to~help~you~learn![/tex]
When doing short equations like this, you want to use P.E.M.D.A.S. That just means you want to use parentheses first, exponents second, multiply third, divide fourth, add fifth, and subtract last. In this case, since there are no parentheses, or subtraction, or exponents, we cross those three out, and make multiplication our top priority. But, what exactly does seven p mean? p is an assigned, substituted number. Sometimes people will use p instead of x as subs, but it really does not matter. So now that we have enough information, let's start.
[tex]7p=7 * number(In~this~case,~6)[/tex]
[tex]7 * 6 = 42[/tex]
The next step is to divide q(12) by three. Before adding, you want to divide, because it is your second-top-priority.
[tex]\frac{q}{3} = \frac{12}{3}~which~is~4[/tex]
Lastly, add the quotient and the product together.
[tex]7p(42) + \frac{q}{3} (4) = 46[/tex]
And we are done! The result is 46, so that means your answer is D! Yay!
What have we learned while doing this problem?
We have learned how to multiply and divide in order of operations while dealing with substitution.What is the area, in square feet, of the rectangle shown below
Answer:
Step-by-step explanation I can answer if you pin in the pic below
Matthew plays basketball for his high school. On average, he scores 33 points per game, with a standard deviation of 2 points. What percentage of basketball games will result in Matthew scoring less than 27 points?
Note: Assume that a Normal model is appropriate for the distribution of points.
Matthew will score less than 27 points in about 0.15% of his basketball games.
=======================================================
Explanation:
mu = 33 = population mean
sigma = 2 = population standard deviation
Let's find the z score when x = 27
z = (x - mu)/sigma
z = (27-33)/2
z = -6/2
z = -3
A score of 27 points is exactly three standard deviation units below the mean of 33 points.
Now refer to the Empirical Rule chart shown below. Notice that roughly 99.7% of the entire population is within 3 standard deviations of the mean. This is the span from z = -3 to z = 3.
That leaves about 100% - 99.7% = 0.3% left over for the two tails combined.
One tail has about (0.3%)/2 = 0.15% of the total area, and therefor about 0.15% of the total games will have Matthew scoring less than 27 points. This is an estimate of course.
To get a more accurate answer, you can use a Z table to find that
[tex]P(Z < -3) \approx 0.00135 \approx 0.135\%[/tex]
which isn't too far off from the 0.15%
Answer:
I believe is the correct answer
Step-by-step explanation:
a
.
Ben deposits $1,750 into each of two savings accounts.
Account I earns 2.75% annual simple interest
Account II earns 2.75% interest compounded annually
Ben does not make any additional deposits or withdrawals. Which amount is closest to the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years?
The difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years is $1.32.
What is the differnce in the interest?Simple interest is when only the amount deposited increases in value.
Simple interest = deposit x interest rate x time
1750 x 0.0275 x 2 = $96.25
Interest earned with compounding = future value - amount deposited.
The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate N = number of years1750 x (1/0275)^2 = $1847.57
$1847.57 - $1750 = $97.57
Difference in interest; $97.57 - $96.25 = $1.32
To learn more about future value, please check: https://brainly.com/question/18760477
The following points (-4, 3), (-2, -1), (3, 1) are vertices of a parallelogram, find the coordinates of the THREE POSSIBLE LOCATIONS, of the fourth vertex
Answer:
A’(5 , -3)
B’(1 , 5)
C’(-9 , 1)
Step-by-step explanation:
Let A be the point of coordinates (-4, 3)
Let B be the point of coordinates (-2, -1)
Let C be the point of coordinates (3, 1)
____
In this case we can form three parallelograms ABA’C, BAB’C , CAC’B
How to find the coordinates of the fourth point A’ of the parallelogram ABA’C
Since we know that the diagonals AA’ and BC of the parallelogram ABA’C intersect in their midpoint then we need to solve these two equations in order to get the coordinates of the point A’ :
[tex]\begin{aligned}\left\{\begin{array}{l}\frac{x_{A}+x_{A^{\prime}}}{2}=\frac{x_{B}+x_{C}}{2} \\\frac{y_{A}+y_{A^{\prime}}}{2}=\frac{y_{B}+y_{C}}{2}\end{array}\right.& \Leftrightarrow\left\{\begin{array}{l}-4+x_{A^{\prime}}=-2+3 \\3+y_{A^{\prime}}=-1+1\end{array}\right.\\\\& \Leftrightarrow\left\{\begin{array}{l}x_{A^{\prime}}=1+4=5 \\y_{A^{\prime}}=0-3=-3\end{array}\right.\\\\& \Leftrightarrow A^{\prime}(5,-3)\end{aligned}[/tex]
________________________
We can follow the same method for the other two parallelograms In order to get the coordinates of the points B’ and C’.
B’(1 , 5)
C’(-9 , 1)
