Answers
The integrand and given boundary for R suggests we should use
u = x - 4y
v = 5x - y
with 0 ≤ u ≤ 3 and 6 ≤ v ≤ 9.
Then
x = (4v - u)/19
y = (v - 5u)/19
and the Jacobian for this transformation is
[tex]J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac1{19}\begin{bmatrix}-1&4\\-5&1\end{bmatrix}\implies|\det J|=\left|\dfrac1{19}\right|=\dfrac1{19}[/tex]
The integral is then
[tex]\displaystyle\iint_R 2\frac{x-4y}{5x-y}\,\mathrm dA = \frac1{19} \int_6^9 \int_0^3 \frac{2u}v\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle \frac2{19} \int_6^9 \frac{3^2-0^2}{2v}\,\mathrm dv[/tex]
[tex]=\displaystyle \frac9{19} \int_6^9 \frac{\mathrm dv}v[/tex]
[tex]=\dfrac9{19}(\ln9-\ln6)=\dfrac9{19}\ln\dfrac96=\boxed{\dfrac9{19}\ln\dfrac32}[/tex]
Related Questions
HELP 6th GRADE MATH
To find the the area of a triangle, you can use the expression b x h divided by 2
where b is the base of the triangle and h is its height. What is the area of a triangle with a base of 2 and a height of 4?
Answers
Answer: What is the formula for finding the area of a triangle?
Not technically, but sometimes you may have to find the height using the Pythagorean Theorem, so if you have the hypotenuse and the base of a right triangle, the height, h = √(c^2 - b^2), so the area of the triangle could be found by A = 1/2 b √(c^2 - b^2), but it is the same principle as A = 1/2 b h.
Step-by-step explanation:
im in 6th grade to so thats easy
What is the answer to 34.50r+78.50(810-r)
Answers
Answer:
-44r+63585
Step-by-step explanation:
Answer:29045 is the answer
Step-by-step explanation:
Evaluate -3- (-4) - (-2) + 1.
Answers
Answer:
4
Step-by-step explanation:
-3+4+2+1=4
What is the blank answer?
Answers
Answer:
you.. need to provide a picture
Step-by-step explanation:
An experimenter flips a coin 100 times and gets 58 heads. Find the 90% confidence interval for the probability of flipping a head with this coin.
a. [0.483, 0.677]
b. [0.383, 0.627]
c. [0.533, 0.538]
d. [0.483, 0.477]
e. [0.403, 0.677]
f. None of the above
Answers
Answer:
The correct option is f.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
It is provided that an experimenter flips a coin 100 times and gets 58 heads.
That is the sample proportion of heads is, [tex]\hat p=0.58[/tex].
The critical value of z for 90% confidence level is, z = 1.645.
*Use a z-table.
Compute the 90% confidence interval for the probability of flipping a head with this coin as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.58\pm 1.645\cdot\sqrt{\frac{0.58\times(1-0.58)}{100}}\\\\=0.58\pm 0.0812\\\\=(0.4988, 0.6612)\\\\\approx (0.499, 0.661)[/tex]
Thus, the 90% confidence interval for the probability of flipping a head with this coin is (0.499, 0.661).
The correct option is f.
If point S is located at (0, 0), point T is located at (0, 6), point U is located at (12, 0), and point V is located at (0, 10), what are the coordinates of point W that makes
Answers
Answer:
(20,0)
Step-by-step explanation:
Trust me :)
Answer:
(20,0)
Step-by-step explanation: trust the guy ^
A local zoo has two large snakes. The anaconda is currently 5.23 meters long and grows
1.27 meters every month. The python is 4.76 meters long and grows 2.04 meters per month.
How many months ( ) m does the zookeeper need to wait for the two snakes to be the
same length?
i really need to know this. my nine weeks ends tomorrow and im behind in math. plzzzzzzzzzzzzz answer this plz, i beg of you
Answers
for the anaconda 5.23 + 1.27 m where m is the number of months, and the total length is in meters
The anaconda starts at 5.23 meters and grows 1.27 meters each month for m months
for the python 4.76 + 2.04m where m is the number of months, l is the length of the python in meters
The python starts at 4.76 meters and grows 2.04 meters each month for m months
5.23 + 1.27 m = 4.76 + 2.04m m is the number of months Each side is
Michael’s $1200 car insurance is paid bi-yearly. The second payment is three times the first payment. Find the amount of the first and second payment.
Answers
300x 3 =900 second year
Question 1 (1 point)
Mr. Whittaker had 24 bags of marbles. If 1/4 were red and 3/8 were yellow. How many were neither red or yellow
6
15
10
9
Answers
Answer:
the answer is 9
Step-by-step explanation:
3/8 = 9
1/4=6
9+6=15
24-15=9
so 9 is your answer
DONT FORGET TO MARK BRAINLIEST
1
Which equation has a constant of proportionality equal to1/2
Choose 1 answer:
Answers
Answer:
C
Step-by-step explanation:
3/6 = 1/2 when simplified.
I have alot of questions
Answers
Answer:
The coordinates of the vertex D. are (2, -5)
The coordinates of the vertex E. are (3, -2)
The coordinates of the vertex F. are (6, -4)
Step-by-step explanation:
The point D of the graph is located +2 on the x-axis and -5 on the y-axis
The point E of the graph is located +3 on the x-axis and -2 on the y-axis
The point F of the graph is located +6 on the x-axis and -4 on the y-axis
I hope that this helps! :)
intersecting lines r s and t are shown below. what is the value of x
Answers
Answer:
15
Step-by-step explanation:
Anyone know the answer?
Answers
Answer:
kira put the points in the wrong places
A city planner wants to construct a new road south of Town Hall and north of the Community Center. The city planner currently has the road plotted as a set of parallel lines as shown on the map. However, the current plan for the road would cover a historical marker. ( please help )
Which transformation should the city planner apply to this road so that it preserves the historical marker and still passes south of Town Hall and north of the Community Center?
translate the road up 2 units
translate the road up 4 units
translate the road down 2 units
translate the road down 4 units
Answers
Answer:
translate the road down 4 units
Hope this helps
3.55. Постройте график линейной функции:
1) у = 2/3х – 4;
2) y = 2x + 6;
3) у = -1,5х – 3;
4) y = -1/2x + 1;
5) y = 5/3x - 2;
6) y = -4/3x + 2;
Answers
Answer:
4) y = -1/2x + 1;
Step-by-step explanation:
maybe
or maybe not
Example of a balance point
Answers
a home's loss of heat is equal to heat created in the home or when both sides of a seesaw are at an equal level.
definitonss for math really easy
Answers
Answer:The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. Two lines in the x y xy xy -plane can intersect once, never intersect, or completely overlap.
A system of linear equations is usually a set of two linear equations with two variables. x + y = 5 x+y=5 x+y=5x, plus, y, equals, 5 and 2 x − y = 1 2x-y=1 2x−y=12, x, minus, y, equals, 1 are both linear equations with two variables. When considered together, they form a system of linear equations.
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial the 3 is a constant term.
Step-by-step explanation:
A botanical garden contains several cube-shaped planters. One planter
holds a tree and has a volume of 2 to the power of 7 cubic feet. Another planter holds a
small shrub and has a volume of 2 to the power of 4 cubic feet. How many times larger is the
volume of planter with the tree than the volume of planter with the shrub?
Answers
Answer:
hmmmmmmmmmmmmmmmmmmmm
Which of the following numbers of identical kits can Ms. Tyson make?
Answers
Answer:
answer is 1, 2, 6
Step-by-step explanation:
Answer:
1,2, and 6
Step-by-step explanation:
What is the prime factorization of 5? Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17
Answers
Answer:
The prime factorization of 5 is 5 x 1
Step-by-step explanation:
5 is a prime number but the only factors that make up 5 are 5 and 1
Hope this helps!
Can someone help me? Please i need this done
Answers
I WILL MARK BRAINIEST
It showstopper answers I got wrong so please answer correctly and don’t give me answers I already put thanks
Answers
B) Side length of B to side length of C is 4:5.
Perimeter of C is 280, so let's put that into the side length of C's place:
4:280
But the 4 also would have to change so let's figure out how much we multiplied 5 by to get 280:
280 / 5 = 56
So let's do 4 x 56 = 224
Our new ratio is 224:280
Therefore the perimeter of mirror B is 224cm.
C) Side length of A to side length of B is 3:4.
We know the perimeter of B from the previous part (224) so let's put that in the 4s place:
3:224
But we also have to change 3, so let's figure out how much we multiplied 4 by to get 224:
224 / 4 = 56
Therefore to determine A's perimeter we do 3 x 56 = 168.
Mirror A's perimeter is 168cm.
D) The side length of mirror A is the perimeter divided by 4 (as they are squares).
168 / 4 = 42. Side length of mirror A is 42cm.
E) Area of a square is side length squared, so the area of mirror A is 42².
42² = 1,764cm².
Multiply 16.852 × 0.86 = _____
Answers
Answer:
14.49272
Step-by-step explanation:
16.852 × 0.86 = 14.49272
For what value of b, would the equation 34(12x−9)+b4=5−3(2−3x) have infinitely many solutions?
Answers
Answer:
23
Step-by-step explanation:
Which is the coefficient in the expression 7 + 14?
Answers
Andrew sold 45 tickets to the school play and Sara sold 60 tickets. Which of the following is equivalent to the ratio of the number of tickets Andrew sold to the number of tickets Sara sold?
a. 6:8
b. 8:10
c. 6:10
d. 10:12
Answers
Answer:
a
Step-by-step explanation:
definitely not d
Answer:
A
Step-by-step explanation:
can anyone help me with this one...
A package of cookies includes 54 chocolate chip cookies. Peter is going to split these cookies with 4 of his friends. Write an expression to represent the situation.
Please help!!!...
Answers
Answer:
13 and a half
Step-by-step explanation:
54 / 4 simple math honey, let me know if you need more help my door is always open!
An expression to represent the situation is 54/4.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, a package of cookies includes 54 chocolate chip cookies.
Peter is going to split these cookies with 4 of his friends.
So, the expression is Total number of cookies/Number of friends
= 54/4
= 13.5
Therefore, an expression to represent the situation is 54/4.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ3
Caleb runs laps at the local track. The circular track measures 70 feet across its diameter. How many feet will Caleb run if he stays on the outer edge of the track? (Round to the nearest whole number.)
Answers
Answer:
Caleb will run 237 ft
Step-by-step explanation:
Answer:
Caleb will run 220 ft.
Step-by-step explanation:
70 * pi = 220 ft
Which expression is equivalent to y^3-2y^2+y
Answers
Answer:
the first one i did it yesterday
I need help solving this
Answers
Answer:
It's D.
Step-by-step explanation:
31-4 = 27 , 63 + 27 = 90 :) so the answer's D. 31
Answer:
D) 31
Step-by-step explanation:.
It is a right angle. All right angles equal 90°. So the two angles add up to 90
90= 63 + x - 4
Add 4 to each side
94 = 63 + x
Subtract 63 to each side
31 = x