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
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what is 1,623 x 2,908? please help
Answer:
1,623 x 2,908 = 4,719,684
Answer:
4719684
Step-by-step explanation:
Tell me if you want one.
please help as fast as you can
Answer:
x= 32 i think
CD= 51
Step-by-step explanation:
Answer:
9x-15=7x-1. => 2x=14 x=7
CD= 7×7-1=48
Divide 2/3 by 1/5. Simplify your answer and write it as a mixed number.
Answer:
3.33
Step-by-step explanation:
3.33
mixed number= 3 1/3
Answer:
3 1/3
Step-by-step explanation:
[tex]\frac{\frac{2}{3}}{\frac{1}{5}}[/tex] =
[tex]\frac{2}{3} * \frac{5}{1} = \frac{10}{3}[/tex]
10/3 = 3 1/3
-Chetan K
The perimeter of the smallest square is 48 feet. What is the perimeter of the largest square?
Answer:
x > 48
Step-by-step explanation:
There’s nothing told to us or showed to us to answer It So I was only able to answer it with an inequality :(((
sorry if this didn’t help but once again… not enough information :(
Juan has x quarters and y dimes, having a minimum of 16 coins worth at most $3 combined. No less than 4 of the coins are quarters. Solve this system
of inequalities graphically and determine one possible solution.
Answer:
See belowStep-by-step explanation:
Quarter - 25¢, dime - 10¢, total - $3 = 300¢
Inequalities:
x + y ≥ 1625x + 10y ≤ 300x ≥ 4See attached for graphical solution. There are many solutions.
Possible one solution:
5 quarters and 17 dimesDoes the angle have to be
Answer:
Number 4
Step-by-step explanation:
Side-Angle-Side, it has to be between the two sides.
Gerald had scores of 83, 95, 92, and 98 on four exams in his algebra class. What score will he need on his fifth exam to have an overall average of 937 (All exams have a
maximum of 100 points.)
i literally can't figure out the answer to this, help would be very much appreciated.
(PICTURE INCLUDED BELOW)
Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?
A. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
B. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
C. Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
D. Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis
Answer:
B
Step-by-step explanation:
The figure is in quadrant 1. When you do a 180 degree rotation it will out the image diagonally across into quadrant 3. Next reflect across the y-axis to get it in quadrant 4.
A 180 rotation will always end up diagonally across regardless if it is counterclockwise or clockwise.
Answer:
A. Counterclockwise rotation around the origin by 180 degrees followed by reflection around the x-axis.
Step-by-step explanation:
180° would be turning it counterclockwise 2 times. Thus putting it on the points of figure P'Q'R'S'.
Reflecting it across the x-axis would be putting it in the same position as P'Q'R'S'.
This being said, either way you did it, as long as you did it one of the two ways it would become a copy of PQRS. The answer is A.
Hope this helped you. Let me know if I got it correct!
- Abigail (:
is 6y +2 - y + 3 and 3 - y + 2 + 6y the same
Answer:
Step-by-step explanation:
Yes.
All you have done is changed the order. They are exactly the same.
You can sort of verify this by using
-4 + 6 - 8 + 2 = - 4
2 + 6 - 4 - 8 =
8 - 12 = - 4
The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City D
Answer: 12% of people responded as City D
If 882 grams of FeS2 is allowed to react with 528 grams of O2 according to the following equation, how many grams of Fe2O3 are produced?
FeS2 + O2 → Fe2O3 + SO2
Balance the reaction:
a FeS₂ + b O₂ => c Fe₂O₃ + d SO₂
Matching up the atoms on either side gives the system of equations
• Fe: a = 2c
• S: 2a = d
• O: 2b = 3c + 2d
We have 3 equations with 4 unknowns. Suppose we fix one of the variables, say a = 2. Then
2 = 2c ===> c = 1
2•2 = d ===> d = 4
2b = 3•1 + 2•4 ===> b = 11/2
and so the balanced reaction is
2 FeS₂ + 11/2 O₂ => Fe₂O₃ + 4 SO₂
or
4 FeS₂ + 11 O₂ => 2 Fe₂O₃ + 8 SO₂
Look up the molar masses of each component element:
• Fe: 55.845 g/mol
• S: 32.06 g/mol
• O: 15.999 g/mol
Then the molar masses of the reactants are
• FeS₂: 119.965 g/mol
• O₂: 31.998 g/mol
Convert the given masses to moles:
• (882 g FeS₂) (1/119.965 mol/g) ≈ 7.35 mol FeS₂
• (528 g O₂) (1/31.998 mol/g) ≈ 16.5 mol O₂
In the balanced reaction, 4 moles of FeS₂ combine with 11 moles of O₂, or equivalently 1 mol FeS₂ is needed for every 11/4 = 2.75 mol O₂. Now,
(16.5 mol O₂) / (2.75 mol O₂) = 6
while
(7.35 mol FeS₂) / (1 mol FeS₂) = 7.35
which means the reaction consumes all of the available O₂ and we're left with 7.35 - 6 = 1.35 mol FeS₂.
For every 11 mol O₂ among the reactants, 2 mol Fe₂O₃ are produced. Then 16.5 mol O₂ makes for
(11 mol O₂) / (2 mol Fe₂O₃) = (16.5 mol O₂) / x
===> x = 3.00 mol Fe₂O₃
which has a mass of
(3.00 mol Fe₂O₃) (160. g/mol) ≈ 479 g Fe₂O₃
To find the mass of Fe2O3 produced, we convert the given masses of FeS2 and O2 into moles and use the molar ratio in the balanced chemical equation. The mass of Fe2O3 produced is 1170.68 grams.
To solve this problem, we need to convert the given masses of FeS2 and O2 into moles. From the balanced chemical equation, we can see that the molar ratio between FeS2 and Fe2O3 is 1:1.
This means that the number of moles of Fe2O3 produced will be equal to the number of moles of FeS2. We can use the molar mass of Fe2O3 to convert moles to grams.
First, we calculate the number of moles of FeS2 and O2:
Moles of FeS2 = 882 g / 120.17 g/mol = 7.34 mol
Moles of O2 = 528 g / 32 g/mol = 16.5 mol
Since the molar ratio between FeS2 and Fe2O3 is 1:1, we know that 7.34 moles of FeS2 will produce 7.34 moles of Fe2O3.
Now, we can calculate the mass of Fe2O3:
Mass of Fe2O3 = Moles of Fe2O3 x Molar mass of Fe2O3
Mass of Fe2O3 = 7.34 mol x 159.69 g/mol = 1170.68 g
Therefore, 1170.68 grams of Fe2O3 are produced.
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y=−3x+7x=−2y−16
(−6, 11)
(6, −11)
(11, −6)
(−11, 6)
Answer:
D. (−11, 6)
Step-by-step explanation:
C plus 3/8 equals 1 1/3 what does C equal
ASAP
Answer:
Exact Form:
C=23/24
Decimal Form:
C=0.9583
Step-by-step explanation:
Trey has bought 10 pounds of dog food. He feeds his dog
pounds for each meal. For how many meals will the food last?
Write your answer in simplest form
how many pounds does he feed his dogs for each meal?
Write the equation of the line graphed below in slope-intercept form.
a. y = 3x +12
b. y = 12x + 3
c. y = 2x + 3
d. y=12x
Answer:
C
Step-by-step explanation:
c. y = 2x + 3
first you need to find the y-intercept which is 3
and then the slope rise/run which is 2 so y = 2x + 3
The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?
Step-by-step explanation:
the numbers : x, y
x + y = 65
x = y + 5
we use the second equation in the first equation :
y + 5 + y = 65
2y + 5 = 65
2y = 60
y = 30
x = y + 5 = 30 + 5 = 35
Determine the total of each rectangle.Each number inside the rectangle represent the area of the smaller rectangle while each number along the side represents the length of the position on the side
Answer:
Hmmm, maybe this?
Step-by-step explanation:
i need a lot of help from the smartest people now right now
Answer:
K) I, II, and III
Step-by-step explanation:
Given the quadratic equation in standard form, h = -at² + bt + c, where h is the height or the projectile of a baseball that changes over time, t. In the given quadratic equation, c represents the constant term. Altering the constant term, c, affects the h-intercept, the maximum value of h, and the t-intercept of the quadratic equation.
I. The h-interceptThe h-intercept is the value of the height, h, when t = 0. This means that setting t = 0 will leave you with the value of the constant term. In other words:
Set t = 0:
h = -at² + bt + c
h = -a(0)² + b(0) + c
h = -a(0) + 0 + c
h = 0 + c
h = c
Therefore, the value of the h-intercept is the value of c.
Hence, altering the value of c will also change the value of the h-intercept.
II. The maximum value of hThe maximum value of h occurs at the vertex, (t, h ). Changing the value of c affects the equation, especially the maximum value of h. To find the value of the t-coordinate of the vertex, use the following formula:
t = -b/2a
The value of the t-coordinate will then be substituted into the equation to find its corresponding h-coordinate. Thus, changing the value of c affects the corresponding h-coordinate of the vertex because you'll have to add the constant term into the rest of the terms within the equation. Therefore, altering the value of c affects the maximum value of h.
III. The t-interceptThe t-intercept is the point on the graph where it crosses the t-axis, and is also the value of t when h = 0. The t-intercept is the zero or the solution to the given equation. To find the t-intercept, set h = 0, and solve for the value of t. Solving for the value of t includes the addition of the constant term, c, with the rest of the terms in the equation. Therefore, altering the value of c also affects the t-intercept.
Therefore, the correct answer is Option K: I, II, and III.
f(x) = 9x ^ 2 - 3 then what is f(3) ? Work must be shown for this problem or no credit will be earned.
Answer:
f ( 3 ) = 81
Step-by-step explanation:
→ Substitute in x = 3
9 × 3² - 3
→ Simplify
9 × 9 - 3
→ Simplify again
78
Determine f(4)+2×g (2)
Answer:
4f+4g
Step-by-step explanation:
5. Mohan and Sohan have the same storybook. Mohan has read 2/5 of the book and Sohan has read 2/7 of the book. Who has read more pages? 6. Sonali and Priya are classmates Sonali completed her homework in a of an hour and Priya in of an hour 3/4 . Who was faster?
#5
Mohan read =2/5Sohan read=2/7Compare
[tex]\\ \sf\longmapsto \dfrac{2}{5}>\dfrac{2}{7}[/tex]
Mohan read more pages.#6
Sonali completed in=1/2Priya completed in=3/4[tex]\\ \sf\longmapsto \dfrac{1}{2}=\dfrac{2}{4}[/tex]
Compare
[tex]\\ \sf\longmapsto \dfrac{2}{4}<\dfrac{3}{4}[/tex]
Sonali was faster
A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book
printed. The total production cost C (in dollars) is given by the function C-550 +15.95N, where N is the number of books,
The total revenue earned (in dollars) from selling the books is given by the function R=31.90N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.
Please answer me ASAP I need an answer.
Answer:
P = 15.95N - 550Step-by-step explanation:
The profit is the difference between the revenue and the total cost:
P = R - CSubstitute values:
P = 31.90N - (550 + 15.95N)P = 31.90N - 15.95N - 550P = 15.95N - 550The difference between cost and revenue is profit
P=R-CP=31.90N-(15.95N+550)P=31.90N-15.95N-550P=15.95N-550Pre college need help
Answer:
C
Step-by-step explanation:
plsss answer my questions in the picture
Answer:
8. B
9. B
10. B
thats my answer
Sally I went to the store and when is it by potato she noticed a sign that said six potatoes cost nine dollars
Answer:
Sally shouldn't be alone she has down syndrome.
Step-by-step explanation:
Which of the following correctly describes the graph?
Answer:
C is correct
Step-by-step explanation:
The x and y axes are linear, the plot is linear. The constant rate of change is assured with those conditions.
The set of all numbers less than or equal to -1
Answer:
-10,-100,-8,-7,-2,-4,-5,-20,-6,-3,-7
Out of the 25 students in Mrs. Green's class, 15 have a pet. What percent of the students in Mrs. Green's class have a pet?
if 9/24 equals 3/x , then x is ____
[tex]\\ \sf\longmapsto \dfrac{9}{24}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{8}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=24[/tex]
[tex]\\ \sf\longmapsto x=24/3[/tex]
[tex]\\ \sf\longmapsto x=8[/tex]
Answer the following questions.
(a) What percent of 80 is 44?
(b) What number is 45% of 40?
Answer:
a. 55%
b. 22
Step-by-step explanation:
Answer:
[tex]a)55[/tex]
b) 18
Step-by-step explanation:
→ Set up an for part a
[tex]\frac{80x}{100} =44[/tex]
→ Multiply both sides by 100
[tex]80x=4400[/tex]
→ Divide both sides by 80
[tex]x = 55[/tex]
→ Multiply both numbers together for part b
45 × 40 = 1800
→ Divide the answer by 100
1800 ÷ 100 = 18
