The integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder [tex]z=y^{2}[/tex] and below the paraboloid [tex]z=8-2x^{2} -y^{2}[/tex] is 128/9.
The first step is to find the bounds of integration. The region in the first octant (x,y,z≥0) is bounded by the planes x=0, y=0, and z=0.
The parabolic cylinder z=y2 is bounded by the planes x=0 and [tex]z=y^{2}[/tex]. The paraboloid [tex]z=8-2x^{2} -y^{2}[/tex] is bounded by the planes x=0, y=0, and z=8.
The next step is to set up the integral. The integral is:
[tex]\int\limits {0^{1} } \int\limits {0^{\sqrt{x} } }\int\limits {y^{8}-2x^{2} -y^{2} 8xzdxdy[/tex]
We can evaluate the integral by integrating with respect to z first. The integral with respect to z is:
[tex]8x^{2} (8-2x^{2}-y^{2} )-8xy^{2} -y^{8} -2x^{2} -y^{2}[/tex]
Simplifying this expression, we get the equation:
[tex]8x^{2} (8-2x^{2}-y^{2} )-8xy^{2}[/tex]
We can now integrate with respect to x. The integral with respect to x is:
[tex]4(8-2x^{2}-y^{2} )^{2} -4xy^{2}-0^1[/tex]
Simplifying this expression, we get the equation:
[tex]4(8-2x^{2}-y^{2} )^{2} -4xy^{2}[/tex]
We can now integrate with respect to y. The integral with respect to y is:
[tex]4\frac{(8-2-y)^{3} }{3} -4y^{3} -0^1[/tex]
Simplifying this expression, we get the equation:
[tex]\frac{128}{9}[/tex]
Therefore, the integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder [tex]z=y^{2}[/tex] and below the paraboloid [tex]z=8-2x^{2} -y^{2}[/tex] is [tex]\frac{128}{9}[/tex].
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Solve the initial value problem below using the method of Laplace transforms. y" - 12y' + 72y = 40 e 4 y(0) = 1, y'(0) = 10
To solve the given initial value problem using the method of Laplace transforms, we need to perform the following steps:
Step 1: Take the Laplace transform of both sides of the given differential equation.
Step 2: Solve for the Laplace transform of y.
Step 3: Take the inverse Laplace transform to obtain y.
Step 4: Use the initial conditions to find the constants in the solution obtained in Step 3.1.
Taking the Laplace transform of both sides of the given differential equation: L{y" - 12y' + 72y} = L{40e⁴}L{y" - 12y' + 72y} = 40L{e⁴}.
Taking Laplace transform of y" term L{y"} - 12L{y'} + 72L{y} = 40L{e⁴}.
Using the Laplace transform property of derivatives,
we get:s²Y(s) - sy(0) - y'(0) - 12[sY(s) - y(0)] + 72Y(s) = 40/(s - 4)
Simplifying the above equation, we get: s²Y(s) - s - 10 - 12sY(s) + 12 + 72Y(s) = 40/(s - 4)⇒ s²Y(s) - 12sY(s) + 72Y(s) = 40/(s - 4) + s + 2
Using partial fraction decomposition, we can write the right-hand side of the above equation as:40/(s - 4) + s + 2 = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Now, the given equation becomes:
s²Y(s) - 12sY(s) + 72Y(s) = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Taking the Laplace transform of y(0) = 1 and y'(0) = 10, we get: Y(s) = (10s + 2 + 1)/[s² - 12s + 72]
Applying partial fraction decomposition to find Y(s),
we get: Y(s) = [3/(s - 6)] - [1/(s - 6)²] + [7/(s - 6)²] + [1/(s - 6)]
Taking the inverse Laplace transform of Y(s), we get: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Using the initial conditions y(0) = 1 and y'(0) = 10, we get: y(0) = 1 = 1 + 0 + 0 + 1, y'(0) = 10 = 18 - 3 + 7 + 1
Therefore, the solution to the given initial value problem is: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Answer: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
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What's the greatest common factor 25x^2 and 100x^4y^2
Answer:
I D K
Step-by-step explanation:
Max gets a weekly allowance of $17. He spends $3 each week on snacks. He splits the rest of his allowance into equal amounts for his college fund and spending money. How much money does Max keep for spending money each week? $
Answer:
$7
Step-by-step explanation:
The amount max keeps for spending = 1/2(total allowance - amount he spends on snacks)
total allowance = $17
amount he spends on snacks = $3
Amount he would have for his college fund and spending money. = $17 - $3 = $14
Since he splits the amount equally between his college fund and spending money, the amount he would have for spending can be determined by dividing 14 by 2
$14/2 = $7
Tell whether $x$ and $y$ are proportional. $x$ 0.25 0.5 0.75 $y$ 4 8 12
Answer:
x and y are proportional. Two quantities are proportional if there is a constant ratio between them. In this case, the ratio between y and x is always 16:
4/0.25=16
8/0.5=16
12/0.75=16
Since the ratio between y and x is always the same, x and y are proportional.
Step-by-step explanation:
Find the volume of the cylinder. Use 3.14 for T.
height of 1ft radius of 2ft
Answer:i don’t know yet give me a sec
Step-by-step explanation:
Answer:
12.56 cubic feet (ft^3)
Step-by-step explanation:
Area of the circular face of the cylinder = (pi)r^2, or (3.14)(2)^2.
This ends up being equal to 12.56. Multiply this by the height of the cylinder, 1, and you get 12.56, your final answer.
I would appreciate Brainliest, but no worries.
a) SST represents the _____sum of squares.
b) SSTr represents the _____sum of squares.
c) SSE represents the _____sum of squares.
d) Which of the following statements is TRUE?
SSE = SSTr + SST
SST = SST - SSE
MSE = MST + MST
MST = MST + MSE
SST = SSTr + SSE
e) Which of the following represents the average between group variation?
σ
MSE
s
MST
a) SST represents the total sum of squares.
b) SSTr represents the treatment sum of squares.
c) SSE represents the error sum of squares.
d) The true statement is: SST = SSTr + SSE.
e) The average between-group variation is represented by MST (mean square treatment).
How to explain the informationa) SST (Total Sum of Squares) represents the total variation in the data. It measures the total deviation of each data point from the overall mean.
b) SSTr (Treatment Sum of Squares) represents the variation attributed to the treatment or factor being studied. It measures the deviation of each group mean from the overall mean.
c) SSE (Error Sum of Squares) represents the residual or unexplained variation in the data. It measures the deviation of each individual data point from its respective group mean.
d) The true statement is: SST = SSTr + SSE. This equation states that the total variation (SST) is equal to the sum of the variation attributed to the treatment (SSTr) and the residual or unexplained variation (SSE).
e) The average between-group variation is represented by MST (mean square treatment). MST is calculated by dividing the treatment sum of squares (SSTr) by the degrees of freedom associated with the treatment. It represents the average variation between the group means and provides information about the treatment effect or the differences between groups.
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16. Max is sitting in the stands at the baseball stadium. He catches a
and decides to throw it back to a player standing on first base. If the
horizontal distance from Max to the player is 61 feet and the ball travels 76
feet, what is the angle of depression from Max to the player?
Gina Wilson (All Things Algebra), 2016
please help! no links please!
The value of x is: 75°
360° - 128° - 85° - 72° = 75°
18
A fruit salad was prepared containing 100 g of
acerola cherries, 100 g of kiwifruit, 300 g of
pineapple, and 200 g of strawberries. What is the
total amount of vitamin C, in grams, that is
contained in the listed fruits?
A)0.7g
B)2.069g
C)700g
D)2069g
20, 17, 14
Write donn
the
4 th
term
Answer:
11
Step-by-step explanation:
you subtract 3 every time, so 14-3 = 11
Nita is making pizza.
She needs 3/4 cup of cheese to make one whole pizza .
She has 3/8
Nita can make exactly one whole pizza or less than or more than
Answer:
Less than
Step-by-step explanation:
To see how 3/4 compares to 3/8, give em the same denominator. The simplest way is to multiply 3/4 by 2. Multiply each the numerator and denominator by 2. That gives you 6/8. She needs 6/8 but only has 3/8, so less than a pizza.
Is (2, 3) a solution to the equation y = x - 1?
yes or no
and pls explain for i can lead this already
Answer: No
Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal
A Food Marketing Institute found that 27% of households spend more than $125 a week on groceries. Assume the population proportion is 0.27 and a simple random sample of 467 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29? Answer =
Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.
In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.
The Population-proportion (p) is = 0.27
Sample-size (n) is = 467,
Sample-proportion (p') is = 0.29,
To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,
The formula to calculate the z-score is:
z = (p' - p)/√((p × (1 - p))/n),
Substituting the values,
We get,
z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),
z = 0.02/√((0.27 × 0.73) / 467),
z ≈ 0.97
We know that the probability associated with a z-score of 0.97 is 0.8340.
Therefore, the required probability is 0.8340.
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If 491 households were surveyed out of which 343 households have internet fiber cable, what is the sample proportion of households without fiber cable is
The sample proportion of households without fiber cable can be calculated by subtracting the proportion of households with fiber cable from 1.
In this case, out of the 491 households surveyed, 343 households have internet fiber cable. To find the proportion of households without fiber cable, we subtract the proportion of households with fiber cable (343/491) from 1. The proportion of households without fiber cable is 1 - (343/491). Simplifying this expression, we get (491 - 343)/491 = 148/491.
Therefore, the sample proportion of households without fiber cable is 148/491, which is approximately 0.3012 or 30.12%. This means that in the surveyed sample, around 30.12% of households do not have internet fiber cable. It's important to note that this proportion represents the sample and not the entire population, as it is based on the households surveyed.
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et k be a real number and A=[1 k 9 1 2 3 2 5 7]. Then determinant of A is ?
The determinant of A is -23 - k.
In case, we have a 3x3 submatrix starting at element (1,1) and ending at element (3,3). Therefore, we can calculate the determinant using cofactor expansion method:
| 1 k 9 |
| 1 2 3 |
| 2 5 7 |
= 1| 2 3 | - k| 1 3 | + 9| 1 2 |
| 5 7 | | 5 7 | | 5 7 |
= 1(2(7) - 3(5)) - k(1(7) - 3(2)) + 9(1(7) - 2(5))
= 1(4) - k(1) + 9(-3)
= -23 - k
Therefore, the determinant of A is -23 - k.
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A curve with the equation Sin(x) – y Cos(x) = y passes through two points A(nt, a) and B(a, b) (a
The equation of the curve as, (y - a) = (b - a) (x - nt) / (a - nt) which is a straight line passing through the two given points, A(nt, a) and B(a, b).
Given: Two points A (e.g., a) and B (a, b) are traversed by the curve whose equation is Sin(x) – y Cos(x) = y (a Solution: (sin x - y cos x) = y Taking y to the left, we get (sin x) = (y y cos x) Again, we can write y as (y) = (sin x) / (1 cos x) Simplifying this even further, we get (y) = (sin x / 2) / (cos x/2) Substituting the values of x = nt A( eg, a) and B( a, b), we get the condition in the structure, y - a = (b - a) (x - ex.)/( a-ex.)
Tackling the above condition, we get the condition bend which is a straight line going through two given focuses A (eg, a) and B(a, b). As a result, we obtain a curve in the form of an equation (y - a) = (b - a) (x - nt) / (a) - nt), which is a straight line that runs through the two points A(eg, a) and B(a, b) that have been given to us.
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Some pls help me I’ll give out brainliest please dont answer if you don’t know
Answer:
−
8
n
+
24
Step-by-step explanation:
A cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. What is the height of the cone?
A) 95 cm
B) 115 cm
C) 125 cm
D) 135 cm
Answer:
its d
Step-by-step explanation:
can someone help??!???!?!
Answer:
download discord
Answer:
im confused-
Step-by-step explanation:
Consider an upright cone that has a base radius of r and height h that has been obtained by revolving a triangular plane region (pictured below) about the y-axis. Apply the cylindrical shells method to con- Ty firm that the volume of the cone is V = arh. h + 0 r
By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
Given that,
Consider an upright cone that was generated by rotating the triangular plane region shown in the image about the y-axis. It has a base radius of r and a height of h.
We have to apply the cylindrical shells method to confirm that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h
We know that,
By using the disk method,
V = [tex]\int\limits^b_a {\pi [f(x)]^2} \, dx[/tex]
Differentiating on both the sides,
dV = π[f(x)]² dx
Integrating on both sides with the limits 0 to h
[tex]\int\limits^h_0 { dV }= \int\limits^h_0 {\pi[f(x)]^2 }dx[/tex]
V = [tex]\int\limits^h_0 {\pi \frac{r^2x^2}{h^2} } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}\int\limits^h_0 {x^2 } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{x^3}{3}]^h_0[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{h^3}{3}][/tex]
V = [tex]\frac{1}{3}[/tex]πr²h
Therefore, By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
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The areas of the squares adjacent to two sides of a right triangle are shown below. What is the area of the squares adjacent to the third side of the triangle
Answer:
11 square units
Step-by-step explanation:
Find the diagram attached
First we need to find the side length of the square with known areas.
Area of a square = L²
L is the side length of the square
For the green square
44 = L²
Lg = √44
For the purple square
Ap = Lp²
33 = Lp²
Lp = √33
Get the length (L) of the unknown square using pythagoras theorem;
Lg² = L²+Lp²
(√44)² = L²+(√33)²
44 = L²+33
L² = 44-33
L² = 11
Since Al = L²
Hence the area of the square adjacent to the third side of the triangle is 11 square units
If m3 is 52°, what is the measure of its vertical angle?
A.
128°
B.
38°
C.
52°
D.
142°
i need answer asap!
Answer:
C. 52 degrees
Step-by-step explanation:
Vertical angles share the same angle of measure.
Can you answer it right now pls
Answer:
4 times 10 to the negative seventh power
Step-by-step explanation:
We can see that the decimal has 6 zeros before it, and then it’s 4.
since there are 7 digits after the decimal point, we put 10 to the negative seventh power.
that gives us 0.0000001
to get 0.0000004, we need to multiply ten to the negative seventh power (0.0000001) by 4
The answer is a. which is 4 x 10‐⁷
Two cheeseburgers and one small order of fries contain a total of 1400 calories. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Find the caloric content of each item.
Let the calories of a cheeseburger be C, and the calories of a small order of fries be F. Using this notation: Two cheeseburgers and one small order of fries contain a total of 1400 calories. Calories in 2 cheeseburgers + Calories in 1 small order of fries = 14002C + F = 1400. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Calories in 3 cheeseburgers + Calories in 2 small orders of fries = 22603C + 2F = 2260. We can solve for C and F by solving these two equations for C and F using the method of elimination.
Let's double the first equation and subtract the second equation: 4C + 2F = 2800 -(3C + 2F = 2260). 1C = 540 C = 540. Calories in a cheeseburger = C = 540. Substituting this value of C into either of the two equations and solving for F gives us:2C + F = 14002(540) + F = 1400. F = 320. Calories in a small order of fries = F = 320. Therefore, two cheeseburgers contain 2C = 2(540) = 1080 calories, and one small order of fries contains F = 320 calories. Three cheeseburgers contain 3C = 3(540) = 1620 calories, and two small orders of fries contain 2F = 2(320) = 640 calories.
Answer: Calories in a cheeseburger = C = 540Calories in a small order of fries = F = 320. Calories in two cheeseburgers = 2C = 2(540) = 1080. Calories in three cheeseburgers = 3C = 3(540) = 1620. Calories in one small order of fries = F = 320Calories in two small orders of fries = 2F = 2(320) = 640.
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If difference scores begin to pile up away from a sample mean difference score of Mp= 0, which of the following statements is true? a. The critical region is small.
b. The null hypothesis will likely be rejected. c. The sample size is large. d. The null hypothesis will likely fail to be rejected.
If difference scores begin to pile up away from a sample mean difference score of Mp= 0, the null hypothesis will likely be rejected. So, correct option is B.
This suggests that there is a likely effect or relationship between the variables being compared.
Option b. The null hypothesis will likely be rejected is the correct statement in this scenario. When the observed differences are consistently far from zero, it implies that the null hypothesis, which assumes no significant difference or effect, is unlikely to be true.
Thus, based on the evidence provided by the data, we would reject the null hypothesis in favor of an alternative hypothesis that suggests the presence of a difference or effect.
The critical region refers to the region of extreme values that would lead to rejecting the null hypothesis. While the size of the critical region can vary depending on the chosen significance level, it does not directly indicate the likelihood of rejecting the null hypothesis in this context.
Similarly, the sample size (option c) does not provide information about the likelihood of rejecting the null hypothesis in this situation.
So, correct option is B.
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Solve for x , assume all segments that appear tangent are tangent.
Answer:
Step-by-step explanation:
x = 5
The value of x in the given angle is 5.
What is circle?A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.
Labelling the figure,
We have,
Measure of complete angle of circle = 360 degree
∠ABC = 360 - (81 + 74)
= 205 degree
Now from figure,
∠APE = (205 - 81 )/2
= 62 degree
Since we know that,
∠APE = 17x - 23
Therefore,
17x - 23 = 62
17x = 85
x = 5 degree,
Hence,
Required value is 5.
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Mrs. Hinojosa had 75 feet of ribbon. If each of the 18 students in her
class gets an equal length of ribbon, how long will each piece be?
Write your answer
2. Using a whole number of feet and a whole number of inches
Question is in picture
Answer: 1.7
Step-by-step explanation: We can use the pythagorean theorem!
A² + B² = C²
1² + B² = 2²
1 + B² = 4
4 - 1 = B²
3 = B²
√3 = B
1.7 = B
Hope this helps :)
-6x-27=6
give me the answer please .
Answer:
-5.5
Step-by-step explanation:
-6x - 27 = 6
+ 27 +27
-6x = 33
÷-6 ÷-6
x = - 5.5
I am pretty sure the awnser is -5.5 because -6 Multiplied by -5.5 Is 33. 33 minus 27 is 6
What is the area of the shaded region?
6 units
Answer:
Step-by-step explanation: