evaluate the integral of f(x, y) = (x 2 y 2 ) −2 over the region given by x 2 y 2 ≤ 2, x ≥ 1 by changing to polar coordinates
Answers
To evaluate the integral of f(x, y) = (x² y²)⁻² over the region given by x²y² ≤ 2, x ≥ 1 by changing to polar coordinates, we first express x and y in terms of r and θ:
x = r cos(θ)
y = r sin(θ)
Then, we need to find the limits of integration in polar coordinates. The region x² y² ≤ 2 corresponds to the region r⁴ cos²(θ) sin²(θ) ≤ 2, which simplifies to r⁴ ≤ 2/(cos²(θ) sin²(θ)) = 2/(sin²(2θ)). So, the limits of integration for r are 1 ≤ r ≤ (2/sin(2θ))^(1/4), and the limits of integration for θ are 0 ≤ θ ≤ π/4.
Now, we can express the integral in polar coordinates:
∫∫(x² y²)⁻² dA = ∫∫(r⁴)⁻¹ r dr dθ
= ∫₀^(π/4) ∫₁^((2/sin(2θ))^(1/4)) r⁻³ dr dθ
= ∫₀^(π/4) [(-1/2) r^-2]₁^((2/sin(2θ))^(1/4)) dθ
= ∫₀^(π/4) [(1/2) - (1/2)(2/sin(2θ))^-2] dθ
= ∫₀^(π/4) [(1/2) - (1/8)sin^2(2θ)] dθ
= [(θ/2) - (1/16)sin(2θ)cos(2θ)]₀^(π/4)
= (π/8) - (1/16)
= 0.17157 (approx)
Therefore, the integral of f(x, y) = (x^2 y^2)^-2 over the region given by x^2 y^2 ≤ 2, x ≥ 1 by changing to polar coordinates is approximately 0.17157.
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Related Questions
Ball Mass Speed Kinetic energy
A 4.0 kg 0 m/s 0 J
B 4.0 kg 8.0 m/s 130 J
C 5.0 kg 8.0 m/s 160 J
Which correctly relates the kinetic energy of the balls above?
A = B
A > C
B = C
B < C
Answers
B = 130 J
C = 160 J
B < C
1 sack of flour contains 18 cups. It takes 3 cups of flour to make a batch of cookies. How many batches of cookies can you make with TWO sacks of flour? Identifiey the lead coefficient and the constant term of the following.
Answers
Answer:
12
Step-by-step explanation:
18x2=36
36/3=12
Write the inverse of the given conditional statement.
Conditional Statement: "If I live in Charleston, then I live in South Carolina."
Answers
Hope this helps
The inverse of the given conditional statement would be:
"If I do not live in Charleston, then I do not live in South Carolina."
Given that a conditional statement: "If I live in Charleston, then I live in South Carolina."
We need to find the inverse of this conditional statement.
To find the inverse of this conditional statement, we need to negate both the hypothesis (the "if" part) and the conclusion (the "then" part). The inverse will have the same logical structure but with the opposite meaning.
The hypothesis of the original statement is "I live in Charleston," and the conclusion is "I live in South Carolina."
To negate the hypothesis, we say "I do not live in Charleston," and to negate the conclusion, we say "I do not live in South Carolina."
Therefore, the inverse of the given conditional statement is: "If I do not live in Charleston, then I do not live in South Carolina."
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the___of the number -4 and 4 is 4
Answers
initial value on this table
Answers
Answer:correct me if I’m wrong but it’s 0.
Step-by-step explanation:
85-51=34. 34
—————=. —————=17
5-3. 2
And once 17 is the slope/rate of change,you can either go back 17 each time or….do an equation : f(x)=17(x-3)+51
Adam divides 32 divided by 8,032 In which place should he write the first digit of the quotient?
A.Ones
B. Tens
C. Hundreds
D. Thousands
Answers
Answer:
100
Step-by-step explanation:
8032\32
Answer:
251
Step-by-step explanation:
32 divided by 8032 =251
Consider the following statement:
"All right, isoceles triangles are special right triangles."
Do you agree or disagree with this statements? Provide a brief explanation
Answers
Answer:
"All right, isoceles triangles are special right triangles."
yes it agree this statement. as in right isosceles triangle always two angles are 45 and remaining 90.
How to make 2.5 a fraction
Answers
2 is a whole number and .5 multiplied by 10, then divided by 100, then simplify
Simplify 15.6 divided by negative 3..
Answers
Answer:
-5.2
Step-by-step explanation:
15.6 ÷ (-3) = -5.2
4. What is the solution to the system
of equations below?
8x + 3y = -6
7x + y = -12
Answers
Answer: x= −30/13 and y= 54/13
Step-by-step explanation: 8x + 3y= -6,7x + y= -12 7x+y+−7x= −12+−7x y=−7x−12 8x+3(−7x−12)=−6 −13x−36+36=−6+36 −13x/-13=30/-13 x= −30/13 y=−7x−12 y=−7(−30/13)−12 210/13−12/0 y=54/13 x= −30/13 and y= 54/13
It costs $96.60 for 6 adults and 1 child to see an exhibit on Egyptian mummies. Child tickets are $8.00. About how much does it cost one adult to see the exhibit?
Answers
Answer:
13.8 or 16.1
Step-by-step explanation:
u have to divide 96.60 by 7
When you listen to the sound of a bouncing ping-pong ball that has been dropped onto a cement floor, what mathematical pattern do you hear? Explain,
Answers
A drop of water is denser than a ping-pong ball.
Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.
The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.
The ping pong ball appears to oppose gravity and coast within the air.
Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.
In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.
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The sound which we hear when the pig pong ball is bounced on the floor
is 19.48 DB
The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.
a) \(\sum \ log(n)\)
by expanding the series for each value of n is
log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)
simplify the expanded form we get
0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982
=> 149.9963
b) \(\sum_{n=0}\) to infinity \(\sqrt{0.9^n}\)
formula for the sum of number in geometric progression
is a/1-r
to find the ratio of the successive terms
plugging into the formula
r = \(\frac{a_{n+1}}{a_n}\)
r = \(\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }\)
=> r = \(\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}\)
=> r = \(\frac{\sqrt{0.9} }{1}\)
=> r = \(\sqrt{0.9}\)
=> a = \(\sqrt{0.9^0}\)
=> a = \(\sqrt{1}\)
=> a= 1
by applying the formula having the value a =1 is
\(\frac{1}{1-\sqrt{0.9} }\)
rationalize the denominator by multiplying with \(1+\sqrt{0.9}\)
=> \(\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }\)
=> 19.4868
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what is the answer to −36= -12y -48
−12y−48
Answers
Answer:
-2.5
Step-by-step explanation:
-36= -12y+(-48)+(-12y)+(-48)
-36= (-24y)+(-96)
+96 +96
60= -24y
divide 60 by -24y and you get -2.5
A marathon runner travels 2/3 in 10 minutes. What is the runners rate in miles per hour ?
Answers
The runner's rate in miles per hour is D * 4/3 miles per hour.
Describe Distance?Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.
In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.
Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.
In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.
We can use the formula:
rate = distance / time
where distance is the distance traveled by the runner and time is the time taken to travel that distance.
Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:
total distance = distance traveled / (2/3) = distance traveled * 3/2
Let's denote the total distance of the marathon as D. Then:
D = distance traveled * 3/2
distance traveled = D * 2/3
We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:
10 minutes = 10/60 hours = 1/6 hours
Now we can calculate the runner's rate:
rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3
So the runner's rate in miles per hour is D * 4/3 miles per hour.
Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:
runner's rate = D * 4/3 miles per hour
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guys I need help in both please
Answers
Answer:
Graph 1 is not proportional
Graph 2 is proportional - y is 2 times x
Step-by-step explanation:
In graph 1, there is no x-y correlation
In graph 2, there is, when x=1, y=6
when x=2, y=12. Therefore, when x=3 y would equal 18.
the study of hypnosis and its relationship to hysteria was the starting point for
Answers
The study of hypnosis and its relationship to hysteria was the starting point for the development of psychoanalysis by Sigmund Freud.
The study of hypnosis and hysteria in the late 19th century by Sigmund Freud and his contemporaries led to the development of psychoanalysis, a form of psychotherapy that emphasizes the role of unconscious thoughts and feelings in shaping behavior. Through his work with patients suffering from hysteria, Freud became interested in the idea that psychological conflicts could be traced back to early childhood experiences, and that these conflicts could be resolved through the exploration of unconscious thoughts and feelings. This eventually led to the development of psychoanalysis as a theory and practice for the treatment of psychological disorders.
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Need help ASAP will give brainly if correct
Answers
Answer:
x < 7
Step-by-step explanation:
Let $a$, $b$, $c$, $d$, and $e$ be positive integers. The sum of the four numbers on each of the five segments connecting "points" of the star is 28. What is the value of the sum $a + b + c + d + e$?
Answers
Answer:
i dunno
Step-by-step explanation:
somebody help
Answer:
Step-by-step explanation:
\(a+c=23\\a+d=20\\e+c=21\\b+e=24\\d+b=22\\\)
...
If x:y = 3:5 and x + y = 3, then find the values of x and y.
Answers
Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answers
Answer:
Step-by-step explanation:
what is the surface area of the rectangular prism? length=12, height=6, and width=13
Answers
Jen buys 4 tires for $272.
What is the cost of 1 tire?
Answers
Divide the total cost by 4:
272 / 4 = 68
It cost $68 for 1 tire
Answer:
68
Step-by-step explanation:
272/4=68
Please do not answer questions with spamming keyboards or with "I don't know" to get points. people legitimately are looking for answers to school problems, and it doesn't help the use of this app by spamming nonsense or by answering their questions with nonsense instead of helping them. I understand you want points but it can be extremely rude.
Answers
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
I agree and also if you don't understand the problem or what exactly
it's asking don't put What do you mean as an answer but it in the comments of the question the persons asking.
Determine if the columns of the matrix form a linearly independent set. Justify your answer.
Answers
Without knowing the matrix in question, I cannot provide a specific answer to this question. However, the process for determining linear independence is as described above.
(a) consider the series 11−210 3100 ⋯ (−1)n−1n10n−1 ⋯. it converges to some value s. give an estimate e for s such that |s−e|<0.001.
Answers
The given series is 11 - 2/10 + 3/100 - ... (-1)^(n-1) * n/(10^(n-1)) + ... and it converges to a value 's'. We need to find an estimate 'e' for 's' such that the absolute difference between 's' and 'e' is less than 0.001. The estimation is - e| < 0.001 is 0.1101.
The given series can be rewritten as 1/10 + (1/100 - 2/10) + (1/1000 - 3/100) + ... + (-1)^(n-1) * (n/(10^(n-1))) + ...
To estimate 's' such that |s - e| < 0.001, we can start by calculating partial sums of the series. We add terms to the partial sum until the difference between two consecutive partial sums becomes less than 0.001.
Let's calculate the first few partial sums:
S_1 = 1/10
S_2 = 1/10 + 1/100 - 2/10
S_3 = 1/10 + 1/100 - 2/10 + 1/1000 - 3/100
...
We continue adding terms until the difference between S_n and S_(n-1) is less than 0.001. The value of S_n at this point will be our estimate 'e' for 's'.
By performing the calculations, we find that S_5 = 0.1101 and S_6 = 0.11001. The absolute difference between S_5 and S_6 is less than 0.001, satisfying the condition.
Therefore, an estimate 'e' for 's' such that |s - e| < 0.001 is 0.1101.
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PLS HELP ASAP PLS!!!
Answers
Answer:
Step-by-step explanation:
Use the distributive property:
\(2x^3 - 3x^2 - 7x + 2x^2 - 3x -7\)
Combine like terms:\(2x^3 -x^2 -10x-7\)
Alexi ha a rectangular piece of red paper that i 4 centimetre wide. It length i twice it width. He glue a rectangular piece of blue paper on top of the red piece meauring 3 centimetre by 7 centimetre. How many quare centimetre of red paper will be viible on top?
Answers
Red paper will be visible on top 11 \(cm^{2}\).
What is rectangle ?
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since,
What is area of rectangle ?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Area = length x breadth
Have given,
breadth of red rectangular paper is 4 cm,
length of red rectangular paper is 4 * 2 = 8 cm
Area of red rectangular paper will be
8 * 4 = 32 \(cm^{2}\).
breadth of blue rectangular paper is 3 cm,
length of blue rectangular paper is 7 cm
Area of red rectangular paper will be
3 * 7 = 21 \(cm^{2}\).
32 -21 = 11 \(cm^{2}\).
Red paper will be visible on top 11 \(cm^{2}\).
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The price of a ride pass at a fun park is $65. What is the
sale price after a 35% discount?
Answers
Answer:
What is 35% off 65 Dollars An item that costs $65, when discounted 35 percent, will cost $42.25 The easiest way of calculating discount is, in this case, to multiply the normal price $65 by 35 then divide it by one hundred. So, the discount is equal to $22.75.
Simplify the expression. \[ -2-(2-6 x) \] \[ -2-(2-6 x)= \]
Answers
The value of the investment at the end of 5 years for different compounding methods is as follows: (a) annually: $854,673.04, (b) semiannually: $857,081.36, (c) monthly: $857,994.34, (d) daily: $858,139.23, (e) continuously: $858,166.64.
To calculate the value of the investment at the end of 5 years for different compounding methods, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where A is the final amount, P is the principal investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Given that the principal investment (P) is $525,500 and the interest rate (r) is 9% (or 0.09), we can calculate the value of the investment for different compounding methods using the formula.
(a) Annually: Plugging in P = $525,500, r = 0.09, n = 1, and t = 5 into the formula, we get A = $525,500(1 + 0.09/1)^(1*5) = $854,673.04.
(b) Semiannually: Plugging in P = $525,500, r = 0.09, n = 2 (since it compounds semiannually), and t = 5, we get A = $525,500(1 + 0.09/2)^(2*5) = $857,081.36.
(c) Monthly: Plugging in P = $525,500, r = 0.09, n = 12 (since it compounds monthly), and t = 5, we get A = $525,500(1 + 0.09/12)^(12*5) = $857,994.34.
(d) Daily: Plugging in P = $525,500, r = 0.09, n = 365 (since it compounds daily), and t = 5, we get A = $525,500(1 + 0.09/365)^(365*5) = $858,139.23.
(e) Continuously: Plugging in P = $525,500, r = 0.09, n = infinity (continuous compounding), and t = 5, we get A = $525,500*e^(0.09*5) = $858,166.64, where e is the base of natural logarithm.
These values represent the approximate value of the investment at the end of 5 years for each compounding method, rounded to the nearest cent.
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A grocer wanted to mix 19 liters milk of $2.2 with 1 kg cacao to make a mixture of hot chocolate. What should be the cost of milk, if the total mixture costed 3 dollars?
Answers
Answer:
for this, I'm going to assume that the cacao powder costed $2.2. If the cacao costs $2.2 then the milk will cost $0.8.
Step-by-step explanation:
If you subtract 2.2 from 3 then you get 0.8. Also if you add 2.2 with 0.8 then you get 3. another way to simplify it is to add one zero on the end, like this 22+8=30.