Given that R is the region enclosed by y = x² and y = 9. The value of the double integral over the region is I =81.
We are given the region R that is enclosed by y = x² and y = 9.
The x values range from -3 to 3.
The y values range from x² to 9.
We thus evaluate the double integral as follows:
I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dA
I= [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
We integrate the integral with respect to y from x² to 9, and then integrate that expression with respect to x from -3 to 3.
We get: I = [tex]\int_{(-3)}^ {(3)} \int_{(x^2)}^{( 9)[/tex] dydx
I= [tex]\int_{(-3)}^ {(3)[/tex] (9 - x²) dx
= [tex]\int_{(-3)}^ {(3)} 9 dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[tex]\int_{(0)}^ {(3)} x dx - \int_{(-3)}^ {(3)[/tex] x² dx
= 18[(3²/2) - (0²/2)] - [(3³/3) - (-3³/3)]
= 18(9/2) - 54
= 81
Answer: I = 81.
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8
p varies directly as the square root of q.
p = 8 when q = 25.
Find p when q = 100.
Answer:
16
Step-by-step explanation:
p=k√q
8=k√25
8=k5
k=8/5
p when q=100
p=8/5*√100
p=8/5*10
p=16
hey guys pls help
explain answer pls
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evaluate the iterated integral by changing to cylindrical coordinates. 0 −1 √1 − x2 −√1 − x2 1 xy2 dz dy dx 0
To evaluate the iterated integral ∫∫∫ R x[tex]y^{2}[/tex] dz dy dx over the given region R in cylindrical coordinates, we first convert the limits of integration and the integrand to the cylindrical form. Then we evaluate the integral using the appropriate transformations and calculations.
In cylindrical coordinates, we express points in three-dimensional space using the variables (ρ, θ, z), where ρ represents the distance from the origin to a point projected onto the xy-plane, θ denotes the angle measured counterclockwise from the positive x-axis to the projection of the point onto the xy-plane, and z represents the height of the point above or below the xy-plane.
To evaluate the given iterated integral, we begin by transforming the limits of integration. The outermost integral corresponds to the variable ρ, which ranges from 0 to 1. The next integral corresponds to θ and remains unchanged since the region R does not involve any angular restrictions. The innermost integral corresponds to z and ranges from the lower limit of √(1 - [tex]x^{2}[/tex]) to the upper limit of √(1 - [tex]x^{2}[/tex]), as determined by the given limits of integration.
Next, we convert the integrand, [tex]xy^2[/tex], to cylindrical coordinates. The variable x is replaced by ρcosθ, and y is replaced by ρsinθ, giving us [tex]ρ^3cosθsin^2θ[/tex].
With the limits of integration and the integrand expressed in cylindrical coordinates, we proceed to evaluate the iterated integral. Following the order of integration, we integrate ρ from 0 to 1, θ from 0 to 2π, and z from √(1 - [tex]x^{2}[/tex]) to -√(1 -[tex]x^{2}[/tex]). The integration of ρ yields [tex]ρ^4[/tex]/4, the integration of θ results in 2π, and the integration of z simplifies to 0.
Finally, we substitute the limits of integration and perform the calculations: (∫(0 to 1) [tex]ρ^4[/tex]/4 dρ) * (2π) * (0). Evaluating the integral of[tex]ρ^4[/tex]/4 yields 1/20, and multiplying this by 2π and 0 gives us the final result of 0.
Therefore, the evaluated iterated integral in cylindrical coordinates is 0.
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determine if the described set is a subspace. assume a, b, and c are real numbers. the subset of r3 consisting of vectors of the form a b c , where a=b=c
The subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].
To determine if the described set is a subspace, we need to check if it satisfies three conditions: closure under addition, closure under scalar multiplication, and contains the zero vector.
Let's consider the subset of [tex]R^{3}[/tex] consisting of vectors of the form (a, b, c), where a = b = c.
Closure under addition: Let (a₁, b₁, c₁) and (a₂, b₂, c₂) be two vectors in the subset.
Their sum is (a₁ + a₂, b₁ + b₂, c₁ + c₂).
Since a₁ = b₁ = c₁ and a₂ = b₂ = c₂, we have (a₁ + a₂, b₁ + b₂, c₁ + c₂) = (a₁ + a₁, b₁ + b₁, c₁ + c₁) = (2a₁, 2b₁, 2c₁).
Since 2a₁ = 2b₁ = 2c₁, the sum is also in the subset.
Closure under scalar multiplication: Let (a, b, c) be a vector in the subset and let k be a real number.
The scalar multiple k(a, b, c) is (ka, kb, kc). Since ka = kb = kc, the scalar multiple is also in the subset.
Contains the zero vector: The zero vector is (0, 0, 0). Since 0 = 0 = 0, it is in the subset.
Therefore, the subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].
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Consider a binomial distribution. About 47% of Salinas residents bank entirely online. A random sample of 62 residents is selected. Find the probability that less than 21 bank entirely online. 0.0229 0.0339 None of these 0.0251 0.228
Given information: Consider a binomial distribution. About 47% of Salinas residents bank entirely online.
A random sample of 62 residents is selected. Find the probability that less than 21 bank entirely online. The given data follows binomial distribution with n = 62 and p = 0.47
Let X be the random variable representing the number of residents bank entirely online. Then X ~ B(62, 0.47) We need to find the probability that less than 21 bank entirely online. P(X < 21) = P(X ≤ 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20Using binomial probability distribution, P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)
Now, we can use a calculator or software to find this sum. Using software or calculator, P(X ≤ 20) = 0.0251Therefore, the probability that less than 21 bank entirely online is 0.0251. Hence, the correct option is 0.0251.
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PLS HELP IM STRUGGLING!!!!!!
Answer:
i think ist D correct me if im wrong
Step-by-step explanation:
Answer:
22.7
Step-by-step explanation:
if ∡M is 90° then you can do:
sin 65 = h/25
h = 25(sin 65°)
h = 22.65
The radius of a circle is 1 inch. What is the area?
r=1 in
Give the exact answer in simplest form.
Answer:
3.14 square inches or π square inches
Step-by-step explanation:
The radius of a circle is 1 inch. What is the area?
r=1 in
The formula for the area of a circle is given as:
πr²
The radius (r) = 1 inch
Hence,
Area of the circle = π × 1²
= 3.1415926536 square inches
Approximately = 3.14 square inches or we can say that the Area of the circle = π square inches
Help with number one only,no bad answers or links please.
Answer: 180 ft^3
Step-by-step explanation:
Answer: 180 ft is the answer
Step-by-step explanation:
Use the given prompt to answer question # to question #. The Angels baseball team contracted researcher Melanie to summarize information regarding pitcher Shohei Ohtani's batting average. Her goal is to compare the number of times he was at bat to the number of times he actually hit the ball in 2018 versus 2019. She specifically samples the Angels home games from each of those years and summarizes the information in the chart below. 2018 2019 Total 103 54 49 Ohtani hit the ball Ohtani didn't hit the ball 141 130 271 Total times at bat 195 179 Has Ohtani's proportion of hitting the ball (his batting average) decreased from 2018 to 2019? Use a 1% significance level, and assume the Central Limit Theorem conditions hold. Note/in case you wanted more information: A baseball player's batting average is the proportion of times the player hits the ball compared to the number of times they were at bat (Example, if a player was at bat 10 times but only hit the ball 2 times, their batting average is § = 0.2).
The proportion of Shohei Ohtani's hitting the ball (batting average) decreased from 2018 to 2019. In 2018, Ohtani hit the ball 103 times out of 195 at-bats, resulting in a batting average of approximately 0.528.
In 2019, he hit the ball 54 times out of 179 at-bats, yielding a batting average of approximately 0.302. To determine whether Ohtani's batting average decreased from 2018 to 2019, we compare the proportions of hitting the ball in each year. Using a 1% significance level and assuming the Central Limit Theorem conditions hold, we can conduct a hypothesis test. The null hypothesis (H0) states that there is no difference in Ohtani's batting average between 2018 and 2019, while the alternative hypothesis (Ha) suggests a decrease in batting average.
To test the hypotheses, we can use a two-sample z-test for proportions. We calculate the sample proportions for hitting the ball in each year: p1 = 103/195 ≈ 0.528 in 2018 and p2 = 54/179 ≈ 0.302 in 2019. The standard error for the difference in proportions is given by the formula sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)), where n1 and n2 are the sample sizes.
Next, we calculate the test statistic z using the formula z = (p1 - p2) / sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)). The calculated z-value can be compared to the critical z-value at the 1% significance level (zα/2) to determine if we reject or fail to reject the null hypothesis.
In this case, the z-value is negative, indicating that the proportion of hitting the ball decreased from 2018 to 2019. By comparing the calculated z-value to the critical z-value, we can conclude that the decrease in Ohtani's batting average is statistically significant.
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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
3 ∫ 2 √x^3 – 8dx
The function [tex]√(x^3 - 8)[/tex] at each x value is 0.25 * [-1.902 - 1.609]. The interval [2, 3] into subintervals and apply the respective formulas.
To approximate the integral ∫[2 to 3] √(x^3 – 8) dx using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule, we need to divide the interval [2, 3] into subintervals and apply the respective formulas. Let's compute the approximations for each rule.
Step 1: Determine the subinterval width, h.
We can calculate h using the formula:
h = (b - a) / n
Given:
a = 2
b = 3
Let's use different values of n for each rule.
For Trapezoidal Rule, let's set n = 4.
For Midpoint Rule, let's set n = 4.
For Simpson's Rule, let's set n = 2.
Step 2: Compute the approximations for each rule.
Using the Trapezoidal Rule:
Approximation = (h / 2) * [f(a) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(b)]
For n = 4:
h = (3 - 2) / 4 = 0.25
Approximation = (0.25 / 2) * [f(2) + 2f(2.25) + 2f(2.5) + 2f(2.75) + f(3)]
Evaluate the function √(x^3 - 8) at each x value:
f(2) ≈ √(2^3 - 8) ≈ -2
f(2.25) ≈ √(2.25^3 - 8) ≈ -1.726
f(2.5) ≈ √(2.5^3 - 8) ≈ -1.414
f(2.75) ≈ √(2.75^3 - 8) ≈ -1.125
f(3) ≈ √(3^3 - 8) ≈ -0.464
Approximation = (0.25 / 2) * [-2 + 2(-1.726) + 2(-1.414) + 2(-1.125) + (-0.464)]
≈ (0.125) * [-2 - 3.452 - 2.828 - 2.25 - 0.464]
≈ (0.125) * [-11.994]
≈ -1.49925
Using the Midpoint Rule:
Approximation = h * [f(x1) + f(x2) + ... + f(xn)]
For n = 4:
h = (3 - 2) / 4 = 0.25
Approximation = 0.25 * [f(2.125) + f(2.375) + f(2.625) + f(2.875)]
Evaluate the function √(x^3 - 8) at each x value:
f(2.125) ≈ √(2.125^3 - 8) ≈ -1.902
f(2.375) ≈ √(2.375^3 - 8) ≈ -1.609
f(2.625) ≈ √(2.625^3 - 8) ≈ -1.335
f(2.875) ≈ √(2.875^3 - 8) ≈ -1.073
Approximation = 0.25 * [-1.902 - 1.609]
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Find the value of the variable. If the answer is not an integer, leave it in simplest radical form,
15
A. 16^2
B16
C 17
D. 17^2
A pro-athlete is offered an eight-year
contract with a starting salary of
$400,000. She will receive an increase
of so each year.
The athlete's salary each year forms a geometric
sequence
What is a1, in thousands?
What is r?
Answer:
400
1.05
Step-by-step explanation:
The athlete should take the second offer.
It is given by the formula,
A = P(1+r)ⁿ
where A is the value after n period of time, P is the initial amount, and,
r is the rate of increment or decrement.
Now, Total amount = $400,000(1+5%)⁷
= $400,000(1+0.05)⁷
= $400,000(1.4071)
= $562840.17
Now, the total amount that the pro-athlete will get in 8 years is,
Total amount = $425,000(1+4%)⁷
= $425,000(1+0.04)⁷
= $425,000(1.3159)
= $559,271
Since the total amount that the athlete will get in the next 8 years is more for the second offer, the athlete should take the second offer.
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By looking at your graph, how can you tell that () = 2
has an inverse (function)?
Part b: The length of the hypotenuse is?
Answer:
B
Step-by-step explanation:
cus thats the formula
Express 0.09 as a fraction.
Answer:
9/100 is the answer i believe
Answer:
the answer is 9/100
Step-by-step explanation:
9 ÷ 100= 0.09
Joe, Josie and Bob has $35 when they put their money together. Joe has half as much as Josie. Bob has four times as much money as Joe. How much money does Josie have?
Answer: $10
Step-by-step explanation:
Let Josie's money be x
Since Joe has half as much as Josie. Joe's money will be: x/2 = 0.5x
Bob has four times as much money as Joe. Bob's money will be = (4 × 0.5x) = 2x
Therefore, we add all the amount together and equate to $35. This will be:
x + 0.5x + 2x = 35
3.5x = 35
x = 35/3.5
x = 10
Josie has $10
12!!! POINTS “what is the mode” question!
Answer:
The mode is 23
Step-by-step explanation:
A university department installed a spam filter on its computer system. During a 21-day period, 6693 messages were tagged as spam. How much spam you get depends on what your online habits are. Here are the counts for some students and faculty in this department (with log-in IDs changed, of course): ID Count ID Count ID Count ID Count AA 1818 BB 1358 CC 442 DD 416 EE 399 FF 389 GG 304 HH 251 || 251 JJ 178 KK 158 LL 103 All other department members received fewer than 100 spam messages. How many did the others receive in total? Make a graph and comment on what you learn from these data. .
The number of people who received fewer than 100 spam messages in the university department is calculated below:
Total number of messages tagged as spam = 6693
Total number of people = 12
Total number of people who received more than 100 spam messages = 11
Number of people who received fewer than 100 spam messages = 1
The number of people who received fewer than 100 spam messages can be calculated by subtracting the total number of people who received more than 100 spam messages from the total number of people in the department.
Thus, the other 1 person received a total of: 6693 - (1818 + 1358 + 442 + 416 + 399 + 389 + 304 + 251 + 251 + 178 + 158 + 103) = 474
Graph illustrating the data collected from students and faculty in the department. it is clear that the majority of students and faculty members in the department received more than 100 spam messages. One person received fewer than 100 spam messages. The number of spam messages received seems to decrease with time, which may indicate that the spam filter is effective.
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find the value of each variable 13-17
Answer:
Step-by-step explanation:
Question 13.
By applying cosine rule,
cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{10}{y}[/tex]
y = 10√2
By applying sine rule,
sin(45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{x}{y}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{x}{10\sqrt{2} }[/tex]
x = 10
Question 15.
By applying sine rule,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{y}{32}[/tex]
y = 16√3
By applying cosine rule,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{32}[/tex]
x = 16
Question 17.
By applying sine rule,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{11\sqrt{3} }{y}[/tex]
y = 22
By applying cosine rule,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{y}[/tex]
[tex]\frac{1}{2}=\frac{x}{22}[/tex]
x = 11
Which is the cosine ratio of ∠A?
ACB is right angle triangle. The length of AC is 28, the length of CB is 195, and the length of AB is 197.
A. 195197
B. 28197
C. 28195
D. 19528
Answer:
d . 19528
Step-by-step explanation:
maaf jika salah
Please help! Will give Brainliest! SHOW ALL WORK
Factor by grouping:
3x^(3)-6x^(2)+15x-30
the answer would be b on scholar
Answer:
3 (x² + 5) (x - 2)
Step-by-step explanation:
3x³- 6x² + 15x - 30
=> 3 (x³ - 2x² + 5x - 10)
=> 3 [x²(x - 2) + 5 (x - 2)]
=> 3 (x² + 5) (x - 2)
6 1⁄6 - 3 5⁄12 =
plz help me with it
Answer:
33/12 or 2.75
Step-by-step explanation:
6 1⁄6 - 3 5⁄12
37/6 - 41/12
74/12 - 41/12
33/12 or 2.75
I WILL GIVE BRAINLIEST!!!
Answer:
*Pew Pew*
Step-by-step explanation:
There are a total of 105 students in a drama club and a yearbook club. The drama club has 15 more students than the yearbook club. How many students are in the drama club? the yearbook club?
HELP ME PLZZ
A cone has a volume of 686 cubic centimeters. If the cone is 14cm high, what is its diameter?
Answer:
3.9mm
Step-by-step explanation:
Write an equation of the line that passes through a pair of points:
a. y = x + 3
b. y = x - 3
c. y = -x + 2
d. y = -x-2
Answer:
C. y = -x + 2
Step-by-step explanation:
Sana nakatulong
help ASAP please! ill mark brainliest!
Answer:
8!
Step-by-step explanation:
Answer) 8!
Explanation) i dont have one :')
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
A is the answer.
Step-by-step explanation: It would go up about 2.2 i hope i helped! <3
Answer: A is your answer
Step-by-step explanation:
put this is y-intercept form 5x + 4y = -4
Answer:
slope-intercept form: y= -5/4x-1
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
Paul uses a coordinate plane to design his model town layout. Paul moves the market 2 units left and 3 units down. He says the ordered pair for the new location of the market is (0, 6). Explain Paul's mistake and write the correct ordered pair for the new location of the market.
Answer:
(1,5) because, before it was at (3,8) and
3 – 2 = 1
8 – 3 = 5
For further explanation:
(3,8) / (2,3) = (1,5)
2 for 2 units left and 3 for 3 units down