The definition of the set E gives you a natural choice for the limits in the integral:
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]
Computing the integral, we get
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]
The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
What is triple integral?Triple integral integrates the integrand over three dimensions.
Given that:
E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
Evaluating the integral:
[tex]I = \int \int \int _E y \: dV[/tex]
[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]
Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
Learn more about triple integral here:
https://brainly.com/question/17206296
b) Are there any overall patterns in the data set? Striking deviations? Use
mathematical reasoning to justify your answer. (2 points)
Answer:
There is an outlier at 0, and a gap at 1,2, and 3. The peak is at 5, and the plot is more or less skewed left.
Step-by-step explanation:
a ladder 7.5m long rests against a wall . the botton of ladder is 2.1m from the wall . calculate how far the ladder reaches up the wall.
PLEASE SOLVE THIS QUESTION!!
Answer:
h = √(7.5² - 2.1²) = 7.2 m
Step-by-step explanation:
Pythagorean theorem
What's fish + nine?
I NEED HELP!?
Answer:
nine fish............
Answer: 9 Fish
Step-by-step explanation:
b
b. (2x) + +
)
(2x3/4)+1/4=
Answer:
Exact Form:
7/4
Decimal Form:
1.75
Mixed Number Form:
1 3/4
Step-by-step explanation:
To add fractions, find the LCD and then combine.
help help hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
E is correct
...............
which expression is equivalent to 15c + 20?
Answer: (3c+4)
Step-by-step explanation:
BIG IDEAS MATH
#6 i
pl
CRITICAL THINKING Seven out of every 8 students surveyed owns a bike. The difference between the number of students
who own a bike and those who do not is 72. How many students were surveyed?
A total of
students were surveyed.
I want the answer to be explained for a 6th grader
Answer:
9
Step-by-step explanation:
72 divided by 8 equals 9. So 9 students were surveyed.
May i please have the answer to this question?
Answer:
Well in order to solve these you can convert them into improper fractions.
So 11/5 + 11/6
Now to find the CM or someone multiple
So 5 and 6 have a common multiple of 30
So
66/30 + 55/30= 121/30
Now in mixed form
4 1/30
Answer:
4 1/30
Step-by-step explanation:
6/30+25/30 --> 6+25=31 --> 31/30
2+1=3
3+31/30=3 31/30= 4 1/30
Help !!
There’s Two Truths and One Lie
Below are three statements. 2 are true and one is not. Which one of the
statements is not true? Explain how you know this.
1) To solve x - 3 = 6, you could add 3 to both sides.
2) To solve x - 3 = 6, you could subtract 3 from both sides.
3) To solve x - 3 = 6, you could think of a number that when you subtract 3 would
give you 6.
Use the ( RACE )method to answer. Type your answer in the box below using complete
sentences. Your answer should have at least 2-3 sentences.
R: Restate the problem
A: Answer the question
C: (not used in math)
E: Explain
Answer:
1 & 3 correct, not sure how race method is used but it should be enough
Step-by-step explanation:
1 is correct since when you add 3 to -3 you get zero and leaves x on the left of the equal sign. then it's equally on both side so you add 3 to 6
2 isn't correct, -3-3 gives -6 and x-6=3 won't give much of an answer
3 is also correct. You basically think "a number that's 6 when you take away 3? could it be 9?" then you try and go 9-3? yes it's 6.
HELP!!!! ME PLSSSSSSSSSSSSSSSSSSSSS
Answer:
A for the Venn Diagram and B for the chart.
Step-by-step explanation:
1. Domain: (-2, -1, 0, 2)
Range: (-4, -2, 2)
2. Domain: (-4, 2, 1, 4)
Range: (-2, 1, 4, 4)
The domain represents the values of the independent variable (x) and the range represents the values of the dependent variable (y). The values of the independent variable are inputs that result in an output in a relation. The values in the range are outputs that correspond to inputs from the independent variable.
1
73
Lech bought 8 t-shirts al
for the same proe. After
using a coupon that took $4
off the pnce, her told
before tax was $36. What
was the cost of each shirts
Answer:
[tex]t=5[/tex] dollars per t-shirt
Step-by-step explanation:
Read the problem and write your equation while following along with it
We have 8 t-shirts
Lets 8 t-shirts be represented by 8t
So for our equation we will place and [tex]8[/tex]
Our equation: [tex]8t[/tex]Now it says we have a coupon that subtracts 4 dollars from our total
Our equation: [tex]8t-4[/tex]The final part to add to our equation says that our total before tax was 36 dollars
So here is our equation: [tex]8t-4=36[/tex]add [tex]$[/tex][tex]4[/tex] to both sides
[tex]8t=40[/tex]
Divide both sides by [tex]8[/tex]
[tex]t=5[/tex] dollars per t-shirt
-Side note, make sure to spell your question right. It was a tad bit confusing to read at the start.
-Brainliest please :)
43=8c-5 what is the value of c in this equation
Answer:
Move all terms that don't contain c to the right side and solve.
c = 6
Step-by-step explanation:
of the three lines in the graph one has slope m = 1 one has slope m = 2, and one has slope m = 1/5.
Put the lines in order from greatest to least slope.
Answer:
1/5 1 2
Step-by-step explanation:
Denise drew 8 stars with crayons. Then she drew 6 more stars. Trina drew 5 stars . How many fewer stars did trina draw then Denise?
Answer:
9
Step-by-step explanation:
Denise's stars altogether:8+6=14
Trina's stars:5
Answer:14-5=9
she drew 9 fewer stars
What are the zeros of the following function?
Answer:
Hence , (a,0) is a zeros of a function
ASAP
which of the following values of 'x' is the equation 4(x-2)-3x
= x +2 true?
A. -1
B. All Real Numbers
C. The equation has no solution
D. 3
E. 2
Answer: A
Step-by-step explanation:
What is 2 3/8 - 1 5/8 =
2 3/8 - 1 5/8
19/8 - 13/8
6/8
3/4
The answer is 3/4
Sub 2 Raging Sushi plz
Answer:
3/4
Step-by-step explanation:
estimation for 5.24 - 2.14
Answer:
3.1
Step-by-step explanation:
lemme know if you want the explanation
Marking as brainliest! Find the missing side
Answer:
The trick for these is finding out what makes the largest known value into the corresponding lower value. Then we use that number to find the missing side length based on the value we know.
1. The missing side length is 40.
We can find this by dividing 70 by 56 to get 1.25. We then multiply this by 32 to get our missing side length.
2. The missing side length is 91.
We can find this by dividing 130 by 30 to get 4.333(repeating decimal). We then multiply this by our known value (21) to get our answer of 91.
3. The missing side length is 21.
We can fid this by dividing 36 by 12 to get 3. Then we multiply this by 7 (our known value) to get our answer.
Step-by-step explanation:
hope this helps. . .<3
good luck! UwU
A company makes 110 bags. 30 of the bags have buttons but no zips. 23 of the bags have zips but no buttons. 23 of the bags have neither zips nor buttons. How many bags have zips on them?
Well, 30+23+23 = 76 which means there are only a total of 76 bags that are accounted for. 110-76 = 34 bags which we do not know if they have zips or not. If we assume they have zips, that would be 34+23 bags with zips which is 57 bags.
what is the height of h of the triangle?
Answer:
4.23 feet
Step-by-step explanation:
We need to use the inverse sine function to solve for h. Since sine = opposite / hypotenuse, we can set up the equation like this: sin(30) = h / 25.5. To solve for h, isolate the h by multiplying both sides: h = 25.5 * sin(30). So the height of the triangle is approximately 4.23 feet.
pleas help on the second ASAP it was due yesterday.. i dont even understand how to do any of it and i will give brainliest <3
Answer:
[tex]3x^{4}[/tex]
Step-by-step explanation:
I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.
Answer:
The answer is 3x^4
Step-by-step explanation:
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On which day would you expect that number to be reached?A) 8B) 9C) 10D) 11
Answer:
C
I hope it helps.
Divide the following polynomial, then place the answer in the proper location on the grid.
(a^2n - a^n - 6) (a^n + 8)
Answer:
Step-by-step explanation:
(a^2n/a^n+8) - (a^n/a^n+8) - (6/a^n+8)
I'm not sure if this is what you're looking for but I got this when dividing.
Solve for x. Round your answer to the nearest tenth.
Answer:
-x + 20
Step-by-step explanation:
13-x+3+4
13 - x + 3 - 3 = 4 + 3
13 - x = 7
= -x + 7 + 13
= -x + 20
#Carry on Learninghannah is making maffins. The recipe calls for 5/8 cup of milk to make 20 muffins. What is the unit rate for cups of milk per muffins? For muffins per cup of milk?
Answer:
32 muffins
Step-by-step explanation:
one cup of milk will make 32 muffins
you can set up a proportion of milk/muffins = milk/muffins
let 'x' = number of muffins made from one cup of milk
5/8 ÷ 20 = 1 ÷ x
cross-multiply to get 5x = 20(8)
5x = 160
x = 32
What is 8.981 times 1.981
Answer:
17.791361
Step-by-step explanation:
Hope this helps!
Can I get Braineist Pls?
Answer:
17.791361
You can cross multiply. I am almost sure this is the method. Put the first number over each other. Then multiply the numbers across. Hope this is helpful!
Use the image above for question ^^
A reflection over y = x, the coordinates reverse: (x,y) becomes (y,x)
Using point A which is located at (5,2) reflection y = x A' would become (2,5)
On the graph shown the location of A' is (2,5) so the answer is
4. a reflection over the line y = x
10% is what number is 28
Answer:
28 is 10% of 280
Steps to solve "28 is 10 percent of what number?"
We have, 10% × x = 28
or,
10
100
× x = 28
Multiplying both sides by 100 and dividing both sides by 10,
we have x = 28 ×
100
10
x = 280
If you are using a calculator, simply enter 28×100÷10, which will give you the answer.
Solve the equation: 3.017 + k = 5.134
Answer:
k=2.117
Step-by-step explanation:
Answer:
3.017 + k = 5.134
So, k = 5.134 - 3.017
So, k = 2.117