Answer:
[tex]\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]
Step-by-step explanation:
Given
[tex]x - y = 0[/tex]
[tex]x - y = 7[/tex]
[tex]x + y = 0[/tex]
[tex]x + y = 6[/tex]
Required
Evaluate [tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex]
Let:
[tex]u=x+y[/tex]
[tex]v =x - y[/tex]
Add both equations
[tex]2x = u + v[/tex]
[tex]x = \frac{u+v}{2}[/tex]
Subtract both equations
[tex]2y = u-v[/tex]
[tex]y = \frac{u-v}{2}[/tex]
So:
[tex]x = \frac{u+v}{2}[/tex]
[tex]y = \frac{u-v}{2}[/tex]
R is defined by the following boundaries:
[tex]0 \le u \le 6[/tex] , [tex]0 \le v \le 7[/tex]
[tex]u=x+y[/tex]
[tex]\frac{du}{dx} = 1[/tex]
[tex]\frac{du}{dy} = 1[/tex]
[tex]v =x - y[/tex]
[tex]\frac{dv}{dx} = 1[/tex]
[tex]\frac{dv}{dy} = -1[/tex]
So, we can not set up Jacobian
[tex]j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right][/tex]
This gives:
[tex]j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right][/tex]
Calculate the determinant
[tex]det\ j = 1 * -1 - 1 * -1[/tex]
[tex]det\ j = -1-1[/tex]
[tex]det\ j = -2[/tex]
Now the integral can be evaluated:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex] becomes:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du[/tex]
[tex]x^2 - y^2 = (x + y)(x-y)[/tex]
[tex]x^2 - y^2 = uv[/tex]
So:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du[/tex]
Remove constants
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du[/tex]
Integrate v
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du[/tex]
Integrate u
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0[/tex]
Expand
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}][/tex]
Open bracket
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}][/tex]
Expand
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]
Brainliest given to anyone who gets both answer
Helen draws a random circle,
She then measures its diameter and circumference,
She gets a circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm correct to 2 significant figures.
Helen wants to find the value of n using the formula n =
음
Calculate the lower bound and upper bound for Helen's value of .
Give your answers correct to 3 decimal places.
Answer:
3.115
Step-by-step explanation:
pi = 405 ÷ 130
= 3.1153846154
upper bound 3.116
lower bound 3.115
Edit : Incorrect Answer
Answer:
Lower Bound = 2.996
Upper bound = 3.244
Step-by-step explanation:
These two lines represent a system of equations.
What is the solution to that system?
Help ?
Answer: (-1,1)
Step-by-step explanation: Look at the intersection point of the lines
Please help :( The picutre is right below worth 20 pionts and will mark brainliest :)
oh and the question is right in the picture too also with the rest
Answer:
perpendicular
Step-by-step explanation:
peripenducular looks like a plus sign. HOPE THIS HELPS!
Branliest...
the length of a rectangle is 5 less than twice the width. if the perimeter of the rectangle is 14 centimeters, find the dimensions of the rectangle
Answer:
25cm and 15cm is what your looking for❤
What is the mean of the data set below 12, 15, 10, 11
Answer:
To find the mean, you add all the numbers given (12, 15, 10, and 11) and then divide by the number of values in the set (in this case, 4). This is the same as finding an average. To do this, you add 12 + 15 + 10 + 11 = 48. ... Therefore, the mean is 12.
Answer:
Your answer is given below:
Step-by-step explanation:
12+15+10+11/4
= 48/4
= 12
ㅡ TheExtraterestrial
A submarine is descending to examine the seafloor 2,100 feet below the surface. It takes the submarine 2 hours to make this descent. Write an equation to represent the relationship between the submarine's elevation and time
Answer:the sub goes down 32.81ft per min
Step-by-step explanation:
2100
2hours
1050ft
1hour
525ft
30min
262.5ft
15min
262.5 ft
7.5min
131.25
4min
65.625ft
2min
32.81ft
1mins
One of the legs of a right triangle measures 12 cm and the other leg measures 16 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer: 20 cm
Step-by-step explanation:
Given
For the right angle triangle, the length of the other two sides of triangle are 12 cm and 16 cm
Using the Pythagoras theorem, [tex](\text{Hypotenuse})^2=(\text{Perpendicular})^2+(\text{base})^2[/tex]
Insert the values
[tex]\Rightarrow H^2=12^2+16^2\\\Rightarrow H^2=144+256\\\Rightarrow H^2=400\\\Rightarrow H=\sqrt{400}\\\Rightarrow H=20\ cm[/tex]
When they arrived at the museum,Tyler's dad went to the ticket counter. For each of the 5 members of the family ,he purchased a general admission ticket for $8.75 and a ticket to see a special exhibit . He paid a total of $70?. How much did each of the ticket to the special exhibit cost
Answer:
5.25
Step-by-step explanation:
can you help me get the answer for this Q :)
Answer:
sorry need some points
Step-by-step explanation:
49 + 710 is 10390.49 + 710 is 10390.
What is the quotient of StartFraction 2 Superscript 4 Baseline Over 2 Superscript negative 4 Baseline EndFraction?
Answer:
256
Step-by-step explanation:
Given. :
2⁴ / 2^-4
2⁴ = 2 * 2 * 2 * 2 = 16
2^-4 = 1/2⁴ = 1 / (2 * 2 * 2 * 2) = 1 / 16
16 ÷ (1 /16)
16 * 16 /1
= 256
Answer:
Step-by-step explanation:
1/256 i believe
i’m so confused on how to do it
Answer:
785.4
Step-by-step explanation:
The formula to find the surface area of a cylinder is
2* pi* radius* height + 2* pi* 2radius.
2( 3.14) (5) (20)= 628
2 (3.14* 5*5)= 157
628+ 157= 785.
Topic - Solving Linear Inequalities.
Q - A vehicle with an empty fuel tank has a mass of 1050kg. One litre of petrol has a mass of 737g. What is the minimum amount of whole litres of petrol that would cause the total mass to exceed 1100kg?
Please help me.
Answer:
The minimum balance is 68 liters
Step-by-step explanation:
Let the number of liters of petrol required be x
Given that One litre of petrol has a mass of 737g, x liters will have a mass
= 0.737x kg
Recall that 1 kg = 1000g
Since the empty fuel tank has a mass of 1050kg
The total mass = 1050 + 0.737x IN kg
For the total mass to exceed 1100kg, then
1050 + 0.737x > 1100
0.737x > 1100 - 1050
0.737x > 50
Divide both sides by 0.737
x > 50/0.737
x > 67.84260516
help meee it's pythagorean theorem, just need answers plsssssss
Answer:
Hi, there your answer is C or D and the second page is C
Step-by-step explanation:
Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.
Answer:
128 if it wants the whole thing than 192
Step-by-step explanation:
HELP WILL GIVE BRAINLIEST SHOW WORK LOOK AT IMAGE
Solve the equation
1 . J + -2 = -22
J + -2 = -22
Adding a negative number changes the equation to subtract ruin:
J - 2 = -22
Now add 2 to both sides to get the answer:
J = -20
Collect like term
J= -22 - 2
J= - 20
if 6 = 68 degrees, find the measures of angles 4, 5 ,7
Answer:
4 = 68
5 = 112
7 = 112
Step-by-step explanation:
Hope it helps
I hope it's helpful .....
Help plz..And No links!! I repeat No links!!
Answer:
200 ft^3
Step-by-step explanation:
Volume of rectangular prism equation is
[tex]V=lwh[/tex]
steps in attachment
find the area of the irregular figure. 2in. 5in. 2in. 4in. 4in. 3in. 3in.
The shape can be split into 3 separate shapes:
On the left side a square 3 x 3 = 9 square inches.
The middle rectangle that is 2 x 5 = 10 square inches
The bottom rectangle which is 4 x 4 = 16 square inches
Total area = 9 + 10 + 16 = 35 square inches
Which of the following points IS not coplanar with points C. D and E?
R. It is not in the same plane as C, D and E
Johnny wants to buy a lottery ticket, so he decides on the ones that give him a 1 in 3 chance of winning! If Johnny buys 15 lottery tickets, how many times would you expect him to win?
Answer:
5 or less chances.
Step-by-step explanation:
well because if he buys 15, 1 in 3 chance tickets, the highest amount of times he would win would be 5 because 15 is the chances of winning multiplied by the tickets he could win.
James is 12 years old and his brother is 16. Which ratio represents James' age to his brother's age 4 years from now?
Answer:
16/20=1/4
Step-by-step explanation:
James is 1/4 younger then his brother
4:5 is the ratio which represents James' age to his brother's age 4 years from now.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that James is 12 years old
James brother is 16 years old.
We need to find the ratio which represents James' age to his brother's age 4 years from now.
After 4 years the James age is 12+4, 16 years
After 4 years the James brother age is 16+4, 20years
The ratio of James' age to his brother's age is 16/20
4/5
Hence, 4:5 is the ratio which represents James' age to his brother's age 4 years from now
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ5
Which graph represents the same relation as the table below?
Answer:
so Left hand side down that your answer
In the circle below, EG is a diameter and EF is tangent at E. Suppose mEF = 124°. Find the following. Does anyone know this?
Answer:
Step-by-step explanation:
If EG is a diameter, then arc EFG is a semicircle and its measure is 180. Arc FG then is 180 - 124 = 56. Since angle FEG is an inscribed angle and the arc it cuts off is arc FG, then the measure of the inscribed angle is half the measure of the arc it cuts off...so angle FEG is 28 degrees. Keep that in mind; we'll need it in a sec.
If HE is tangent to the circle at E, then angle HEG is a 90 degree angle. Adding that to angle FEG will give you angle FEH. Angle FEH = 90 + 28 = 118
As apart of her physical fitness training, Kaylee cycled at 30km/h and then jogged at 8 km/h. She spent 2 hours working out and covered a distance of 49 km. How long did Kaylee spend at each activity?
Answer:
for cycling, time is 1.5 hours
for hogging time is 0.5 hour.
Step-by-step explanation:
speed of cycling = 30 km/h
speed of jogging = 8 km/h
total time = 2 hrs
total distance, D = 49 km
Let the time for cycling is t, so that time time for jogging is 2 - t .
distance = speed x time
49 = 30 x t + 8 (2 - t)
49 = 30 t + 16 - 8 t
33 = 22 t
t = 1.5 hour
So, time for cycling is 1.5 hours and time for jogging s 0.5 hr.
The graph shows the function f(x).
Which equation represents f(x)?
Of(x) = -3
5
Of(x) = -3/x-1
3
2
Of(x) = 3-x-1
f(x)
Of(x) = -x
de
-10 -8 6 -4 -2,
2 4
6
8
10
L2
The
4
-5
1,99%
AI
[
Mark this and return
Save and Exit
Dlaxt
Submit
tiny
Answer:
C
Step-by-step explanation:
What we have to do here is to select a point from the graph
We can select the point (-8,1)
What this simply mean is that when x = -8, y = 1
Now, let us take a look at the second third option
f(-8) will be the cube root of -(-8) , with 1 subtracted from it
The cube root of 8 is simply 2, subtracting 1 from it will yield 1
so that makes the point (-8,1) valid
Answer:
C
Step-by-step explanation:
what is the slope of the line shown below?
Answer:
Up four over four = 4/2 = 2
Step-by-step explanation:
30,000,000 +40,000+6,000+20+2 in word form
Answer:
thirty million forty-six thousand twenty-two
hope this helps
have a good day :)
Step-by-step explanation:
can someone answer for me pls
x^2 + 10x + 24 ?
Answer: (x+4)(x+6)
Explaination:
x^2 + 10x + 24
x^2 + 6x + 4x + 24
x(x+6) + 4(x+6)
(x+4)(x+6)
Solution: (x+4)(x+6)
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student chosen randomly from the
class does not have a sister?
Has a brother Does not have a brother
Has a sister
3
12
Does not have a sister
2.
Answer:
Step-by-step explanation:
total students = 27
students do not have a brother probability = 13/27
students do not have a sister probability = 12/27
= 4/9
Hope this is correct :)
The probability that a student is chosen randomly from the class does not have a sister is 0.375.
The probability that a student is chosen randomly from the class Has a brother is 0.208.
The probability that a student is chosen randomly from the class does not have a brother is 0.7916.
The probability that a student is chosen randomly from the class Has a sister is 0.625.
What is the probability?Probability is the branch of mathematics, which discusses the occurrence of a random experiment.
First, we need to calculate how many total students there are.
Once we have the total we have to divide the number in the category that we want by the total number of students to calculate the probability of randomly getting a student in that category.
Total Students = 3 + 12 + 2 + 7 = 24 students
The probability that a student is chosen randomly from the class does not have a sister is;
[tex]= \dfrac{2+7}{24}\\\\=\dfrac{9}{24}\\\\=0.375[/tex]
The probability that a student is chosen randomly from the class Has a brother is;
[tex]= \dfrac{3+2}{24}\\\\=\dfrac{5}{24}\\\\= 0.208[/tex]
The probability that a student is chosen randomly from the class does not have a brother is;
[tex]= \dfrac{7+12}{24}\\\\=\dfrac{19}{24}\\\\= 0.7916[/tex]
The probability that a student is chosen randomly from the class Has a sister is;
[tex]= \dfrac{3+12}{24}\\\\=\dfrac{15}{24}\\\\= 0.625[/tex]
Learn more about proability here;
https://brainly.com/question/23959949
#SPJ2