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
pls help i need it.
You are the Parish Youth Ministry treasurer Every year your organization conducts a fundraising activity to help the poor school-children in your parish. This year, your organization aimed to help 500 school-children by providing them school supplies. You have been tasked by the Parish Priest to lead this year's fundraising activity. Together with your co-officers, you go to Divisoria which is known to be the place where the cheapest prices for school supplies can be found. Here is the list of the items that you need and their prices. what is the total amount of this price per item? make a clear and accurate computation of the trial amount needed to buy all the school supplies that you need. present it to the praish priest who will approve budget. guide questions:
1. how much money does your organization need for this project?
2. if you already have a an existing fund of php 1,200.00, do you still need to raise a fund or not? why?
3. are you also a member/officer of an organization in your parish? if yes, write one among your remarkable experience for being a member of the organization.
Step-by-step explanation:
each child gets a certain amount of items costing the specified price by item.
so, we need to multiply the number of children with the number of items with the price per item to get the total cost.
500×3×3.5 for pencils = 5,250
500×5×7.5 for notebooks = 18,750
500×1×21.75 for crayons = 10,875
500×2×9.26 for pad paper = 9,260
total 44,135
since we have only 1,200 available in the existing fund, we need a new one to cover the remaining
44,135 - 1,200 = 42,935
wich of the of the following is correct setup to find: a 12% bonus is $ 30.72 of what amout
Triangle ABC is isosceles. What is the measure of angle C?
A. 25°
B. 30°
C. 60°
D. 75°
The answer is D, 75°.
All the interior angles of a triangle add up to 180°. With this information, we can set up this equation:
(x + 5) + (3x) + (3x) = 180
Combine like terms.
(x + 5) + (3x) + (3x) = 180
7x + 5 = 180
-5 -5
7x = 175
/7 /7
x = 25
Now, since this is an isosceles triangle, we can easily substitute the value of x into 3x. 3 • 25 = 75 which is 75°.
e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.
Answer:
Step-by-step explanation:
4/50 = 0.08
0.08(100) = 8%
From a club with 12 members, how many ways could you choose a committee of 5?
Step-by-step explanation:
that is 12 over 5
12! / (5! × (12-5)!) = 12×11×10×9×8/5×4×3×2 =
= 11×9×8 = 792
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:
pls help i’ll mark brainliest!!
Interpret the slope of the function in the terms of the problem.
25 ml of water are lost every hour
5 ml of water are lost every hour
10 ml wat are lost every hour
2mL of water are lost
In a scale drawing of a painting. 1 centimeter represents 5 inches.
scale 1 cm :5 in
Answer the following
(A) The height of the real painting is 25 inches. What is the height of the painting in the scale drawing?
______ cm
(B) In the scale drawing, the lenght of the painting is 6 cm. What is the lenght of the real painting?
____ inches
Please no links just answers :)
Answer:
a(5
b)30
Step-by-step explanation:
in the first one you divide 25 by 5
in the second one you multiply 6 times 5
Beth had k dollars. She spent 8 dollars on a bag and the rest of the money on 4 notepads. Find the cost of each notepad in terms of k.
Answer:
Price of a notepad in terms of k ⇒ (k - 8)/4
Step-by-step explanation:
Let the price of a notepad be n.
8 + 4n = k
In order to get the answer, we've to make n as the subject of the above equation.
8 + 4n = k
4n = k - 8
n = (k - 8) / 4
Solve x
2/x -2 = 3/2x+3
Answer:
since we don't have to go back in and you can come over you
Write slope intercept form of th equation of each line
Answer:
y = 8/5x + (-4) or y = 8/5x -4
Step-by-step explanation:
Slope-intercept form is written like this:
y = mx + b
The variable m, represents slope and b, represents the y-intercept.
To find slope, you have to find the rise/run or in other words, change of y over change of x.
From the look of the line, the slope has to be positive because the line is going up.
To go from the bottom point to the top, we have to go up 8 points and go to the right 5 points. Thus the slope is 8/5.
Now for the y-intercept. This part is easy. Just ask yourself this...
"Which of the two points is on the y-axis?"
In this case, it is the bottom point which is -4.
So your equation should look like this:
y = 8/5x + (-4)
or y = 8/5x - 4 because when you have a plus sign and a minus sign, the result is negative.
hope this helps :)
(HELP ASAP PLEAE!!)Expression A: 3x + 2
Expression B: 1 + 3x + 1
Which statement can be used to show that these expressions are equivalent?
A. 3x + 2 can be rewritten as 1 + 3x + 1 using the distributive
property
B. Both expressions involve addition.
C. Each expression includes the term 3x.
D. The expressions name the same number regardless of the value
of x.
Answer:
its c
Step-by-step explanation:
Find X for brainiest
Answer:
136°
Step-by-step explanation:
Look at the attached paper for the steps.
Answer:
136°
Step-by-step explanation:
In quadrilateral ABCD,
[tex]m\angle A = 180\degree - 107\degree = 73\degree[/tex](Angles in linear pair)
[tex]m\angle B = 61\degree [/tex](Vertical Angles)
[tex]m\angle C= 90\degree [/tex](Given)
[tex]m\angle A +m\angle B+m\angle C+m\angle D= 360\degree[/tex](Interior angle sum postulate of a quadrilateral)
[tex]73\degree +61\degree+90\degree+x= 360\degree[/tex]
[tex]224\degree+x= 360\degree[/tex]
[tex]x= 360\degree-224\degree[/tex]
[tex]x= 136\degree[/tex]
Encuentra las coordenadas del punto P(x,y) que divide al segmento P1P2 con coordenadas
de sus extremos P1(x1,y1) y P2(x2,y2) dada la razón r.
P1(-1,6) P2(3,-3) r = ¾
Usando segmentos de línea, se encuentra que el punto es [tex]P\left(2, -\frac{3}{4}\right)[/tex]
El punto P1 es dado por (-1,6).El punto P2 es dado por (3, -3).El punto P divide el segmento en la razón [tex]r = \frac{3}{4}[/tex], o sea:
[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]
La coordenada x de P1 es -1.La coordenada x de P2 es 3.La coordenada x de P es x.[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]
[tex]x + 1 = 3[/tex]
[tex]x = 2[/tex]
La coordenada y de P1 es 6.La coordenada y de P2 es -3.La coordenada y de P es y.[tex]P - P_1 = \frac{3}{4}(P_2 - P_1)[/tex]
[tex]y - 6 = -\frac{27}{4}[/tex]
[tex]y = -\frac{27}{4} + \frac{24}{4}[/tex]
[tex]y = -\frac{3}{4}[/tex]
El punto es [tex]P\left(2, -\frac{3}{4}\right)[/tex]
Un problema similar es dado por https://brainly.com/question/4854238
Which comparison is incorrect?
-3> -7
-9> 4
-4>-6
7>5
Answer:
-9> 4
Step-by-step explanation:
-9> 4
Positive numbers are greater than negative numbers and knowing that makes this comparison incorrect.
Hope this helps :)
Separate 846 into 3 parts so that the second part is twice the first part and the third part
is triple the second part.
x=1st
2x= and
32x)= 3(2x)
Answer:
it is 1 ok have fun babby and enjoy your Christmas ok baby bye bye
Answer:
1) 94, 2) 188, 3) 564
Step-by-step explanation:
This is pretty simple. The first thing you want to do is come up with an algebraic equation to solve this. It will be x + 2x + 6x=846 . The first x represents the smallest part, or the first part. The second part is represented by 2x because it is twice the first, and 6x is 3 times the second part which is 6 times the first part. Combine like terms to get 9x = 846. Now isolate the variable by dividing 9 from both sides. This will give you x = 94. Now just plug in the x to find the second and third part.
Hope this helped :)
Grace wants to collect data on the weight of her puppy as it grows. She decides to construct a table with age in weeks and weight in kilograms as variables. Will the ordered pairs from Grace’s data represent a function, a relation or a neither?
There are 550 calories in 100 g of bacon. There are 196 calories in a fried egg. Philip has 60 g of bacon and two fried eggs for breakfast. Work out the total number of calories in this breakfast.
Answer:
509.6 calories
Step-by-step explanation:
196+196=392 calories
10g of bacon=19.6 calories
60g of bacon=19.6×6=117.6 calories
392+117.6=509.6 calories
Please look at picture for question.
Answer:
[tex]\frac{-1}{5}m -\frac{4}{5}[/tex]
Step-by-step explanation:
Combine the like terms (2/5) and (-3/5) m
This will give you -1/5
place the remainder of the equation.
if you like my answer, please mark me brainliest !! thanks !! <3
Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10
Answer:
-369
Step-by-step explanation:
Replace r with 10.
9(-3(10)-10))
9(-30-11)
9*-30+9*-11
-270+ -99
-369
Hope this helped. :)
(1/2)power 5=?? please help
[tex] \frac{1}{2} \: to \: the \: power \: of \: 5 \: is \: \frac{1}{32} or \: 0.03125 [/tex]
Answer:
[tex] \ {\boxed{ \tt ( \frac{1}{2}) ^{5} = \frac{1}{32} }}[/tex]
Step-by-step explanation:
[tex] \\ \tt( \frac{1}{2} )^{5} [/tex]
[tex] \\ \tt= \frac{ {1}^{5} }{ {2}^{5} } [/tex]
[tex] \\ \tt = \frac{1 \times 1 \times 1 \times 1 \times 1}{2 \times 2 \times 2 \times 2 \times 2} [/tex]
[tex] \\ \tt = \frac{1}{32} [/tex]
2950 divided by 67 in partial quotints
Answer:
Math answers to fraction 2950 divided by 67 can be calculated as follows.
2950/67 math problems division = 44.0298507463. Therefore 44.0298507463 to 2 decimal places= 44.03
2950/67 divided by 2 » (2950/67) ÷ 2 » 44.0298507463 ÷ 2 = 22.0149253731 . Check 2950/67 long division below
Step-by-step explanation:
Slope = -7 and passing through (-4,34)
if it is asking for point slope form the answer is : y-34=-7(x+4)
if it is asking it in slope intercept form the answer is: y=-7x-62
Phil uses the model below to help him with multiple decimals. write a multiplication equation to represent the decimal model.
Multiplication equations can be modeled using decimal models.
The multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
From Phil model, we have the following highlights
50 boxes are shaded vertically90 boxes are shaded horizontallySo, the multiplication expression is:
[tex]\mathbf{\frac{50}{100} \times \frac{90}{100}}[/tex]
Express as decimals
[tex]\mathbf{0.50 \times 0.90}[/tex]
Multiply
[tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
Hence, the multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
Read more about decimal models at:
https://brainly.com/question/19979966
Rationalize the denominator.
9-10/2
V2+1
Answer:
d. 19√2 -29
Step-by-step explanation:
Multiply numerator and denominator by the conjugate of the denominator.
[tex]\dfrac{9-10\sqrt{2}}{\sqrt{2}+1}=\dfrac{(9-10\sqrt{2})(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}\\\\=\dfrac{9\sqrt{2}-9-10\cdot2+10\sqrt{2}}{2-1}=\boxed{19\sqrt{2}-29}[/tex]
Answer:
Step-by-step explanation:
if in a game of glass stepping stones. there are 18 tiles of glass. two in each row. one is tempered and will be fine if you jump on it. and the other will break. if 1 player was to play what are his/her chances of getting across?
(NO links)
Answer:
10
Step-by-step explanation:
Help help help help help help
Answer:
70.2
Step-by-step explanation:
28.08 / 0.4 = 70.2
when 8 is subtracted from a certain number and the result is multiplied by 3 and the answer is 21 what is the original number
Step-by-step explanation:
The Real Answer Is 63
Maybe Positive Or Negative
If your heart rate is 155 beats per minute during strenuous exercise, what is the time per beat in units of seconds
Answer:
5 beats per second
Step-by-step explanation:
statistic operation depends
31,807 = 81 =
Remainder:
Answer:
Answer: (31807/81) ÷ 2 = 196.339506173
Step-by-step explanation:
Math answers to division of fraction 31807/81
31807 81 = 392.679012346
392.679012346 = 3926.79012346 to the nearest tenth
392.679012346 = 392.68 to the nearest hundredth
392.679012346 = 392.679 to the nearest thousandth
= 0 to the nearest tenth
= 0 to the nearest hundredth
= 0 to the nearest thousandth
Other Divisions Math homework are
31807 divide by half plus 20
Homework answers: (31807/2) + 20 = 15923.5
31807 divide by half plus 40
Homework answers: (31807/2) + 40 = 15943.5
31807/81 divided by 2
Answer: (31807/81) ÷ 2 = 196.339506173
