The value of the double integral is 13 times ∬S (x + y) dA = 13(15) = 195.
We can first find the region R in the uv-plane that corresponds to the square S in the xy-plane using the transformation:
x = 2u + 3v
y = 3u - 2v
Solving for u and v in terms of x and y, we get:
u = (2x - 3y)/13
v = (3x + 2y)/13
The vertices of the square S in the xy-plane correspond to the following points in the uv-plane:
(0, 0) -> (0, 0)
(2, 3) -> (1, 1)
(5, 1) -> (2, -1)
(3, -2) -> (1, -2)
Therefore, the region R in the uv-plane is the square with vertices (0, 0), (1, 1), (2, -1), and (1, -2).
Using the transformation, we have:
x + y = (2u + 3v) + (3u - 2v) = 5u + v
The double integral becomes:
∬S (x + y) dA = ∬R (5u + v) |J| dA
where |J| is the determinant of the Jacobian matrix:
|J| = |∂x/∂u ∂x/∂v|
|∂y/∂u ∂y/∂v|
= |-2 3|
|3 2|
= -13
So, we have:
∬S (x + y) dA = ∬R (5u + v) |-13| dudv
= 13 ∬R (5u + v) dudv
Integrating with respect to u first, we get:
∬R (5u + v) dudv = ∫[v=-2 to 0] ∫[u=0 to 1] (5u + v) dudv + ∫[v=0 to 1] ∫[u=1 to 2] (5u + v) dudv
= [(5/2)(1 - 0)(0 + 2) + (1/2)(1 - 0)(2 + 2)] + [(5/2)(2 - 1)(0 + 2) + (1/2)(2 - 1)(2 + 1)]
= 15
Therefore, the value of the double integral is 13 times this, or:
∬S (x + y) dA = 13(15) = 195
So, the answer is (E) none of the above.
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Does the point (6, 0) satisfy the equation y = x + 6?
yes or no
Answer:
No.
Step-by-step explanation:
You have to replace the (6,0) with the equation at hand. So, since 6 is in the X spot and 0 is in the Y spot, the equation would then look like 0=6+6. The equation is false as you can see.
No, this point does not lie on the line y = x + 6.
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the equation of line as -
y = x + 6
For point (6, 0), we can write -
0 = 6 + 6
0 ≠ 12
Therefore, no, this point does not lie on the line -
y = x + 6
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What kind of solution does the equation have? - 13 = 5(1 + 4m) - 2m
Answer: = − 1
Step-by-step explanation:
please simplfy 7x + 6 + 3x – 2 – 5x
Answer:
5x+4
Step-by-step explanation:
Answer:
5x + 4
Step-by-step explanation:
7 + 3 - 5 = 10 - 5 = 5x
6 - 2 = 4
5x + 4
Which of the following statements is NOT a property of parallelograms?
Opposite angles are congruent.
Opposite sides are parallel.
Parallelograms have 4 straight sides.
All sides are parallel.
Answer:its that all sides are parallell
Step-by-step explanation:
because it has two sets of parrallel sides all of them are not paralell
Answer:
All sides are parallel.
Step-by-step explanation:
shapes can't even be made if all the sides are parallel. The angles need to be added up to 360 degrees. There won't even be angles if all the lines are parallel. The opposite sides have to be parallel.
Ben is standing 8 feet from
the base of a telephone pole.
The angle of elevation from the
point on the ground where he is
standing to the top of the pole
is 62°. Find the height of the
telephone pole. Round to
the nearest tenth.
Answer:
Approximately 15.05 ft
Step-by-step explanation:
You need to use tangent for this question.
Since tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
to find the Opposite, we need to rearrange the equation to:
Adjacent × tan θ = Opposite.
So if you insert 62 for θ and 8 feet for Adjacent, you will get:
8 × tan(62) = Opposite.
and you will get approximately 15.05 feet for your Opposite side
1. simplify the following fractions: 12/36
Answer:
1/3
Step-by-step explanation:
12/36 = 6/18 = 3/9 = 1/3
I REALLY NEED HELP!!!!
Answer:
1 2/8 inches
Step-by-step explanation:
smallest = 2/8
largest = 1 4/8
difference = 1 2/8
solve for x
103.5
4.7
55.0
Answer:
It will be the first one
Step-by-step explanation:
Hope this Helped
Solve. Then, rewrite the complete number sentence in decimal form
Step-by-step explanation:
a)
6.9+1.1= 8
b)
9.9+2.45=12.35
[tex]12 \frac{35}{100} [/tex]
c)
2.4+8.9=11.3
[tex]11 \frac{3}{10} [/tex]
d)
6.37+7.7=14.07
[tex]14 \frac{7}{100} [/tex]
What is the y-intercept
Answer:
-2
Step-by-step explanation:
hope this helps!!!!!!!?
Which number makes the equation true?
blank divided by eighteen equals one third
Question 13 options:
32
24
12
6
Answer:
6
Step-by-step explanation:
x/18 = 1/3
3x = 18
x = 6
a rectangular garden measures 22.7 m by 16.6 m how many meters of fencing materials are needed to enclose it the fencing materials cost 12.50 per meter
Answer:
78.6m of fencing
That would cost $982.50
Step-by-step explanation:
Perimeter: 2(22.7)+2(16.6)=P
P = 78.6
Cost: 78.6*12.50
C = 982.50
The expression 2x^2+5x-12 is equivalent to which of the following?
a
(2x-3)(x+4)
b
(x+3)(2x-4)
c
(2x-3)(2x+2)
d
(2x+3)(x-4)
Answer:
letter D
Step-by-step explanation:
2
x
2
−
5
x
−
12
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
2
⋅
−
12
=
−
24
and,
N
1
+
N
2
=
b
=
−
5
After trying out a few numbers we get:
N
1
=
−
8
and
N
2
=
3
3
⋅
(
−
8
)
=
−
24
, and
3
+
(
−
8
)
=
−
5
2
x
2
−
5
x
−
12
=
2
x
2
−
8
x
+
3
x
−
12
=
2
x
(
x
−
4
)
+
3
(
x
−
4
)
(
x
−
4
)
is a common factor to each of the terms
=
(
2
x
+
3
)
(
x
−
4
)
Answer:
a see below for explanation
Step-by-step explanation:
2x^2 + 8x - 3x - 12
2x^2 +5x - 12
What is the equation for a line with a slope of 5 and a y-intercept of 11?
Answer:
y=5x+11
Step-by-step explanation:
-2x^3+15x^2-22x-15; (x-3) polynomial function
Answer: Down Below
Step-by-step explanation: Solving for -2x^3 + 15x^2 - 22x - 15(x - 3) = 0
Standard form:
−2x3 + 15x2 − 37x + 45 = 0
Factorization:
−(2x − 9)(x2 − 3x + 5) = 0
What are the intercepts of the graphed function?
x-intercept = (0, –1) y-intercept = (0, –3)
x-intercept = (0, –1) y-intercept = (–3, 0)
x-intercept = (–1, 0) y-intercept = (0, –3)
x-intercept = (–1, 0) y-intercept = (–3, 0) Oops! The y-intercept was incorrect!
Answer:
The first option.
Step-by-step explanation:
Write an algebraic expression for three times the quantity q minus eleven
I need help this question is due in 20 minutes
Answer:
20,067.68
All I did was 23,200 and minus $195.77 15 times! Your welcome.
The part that's cut off it says To the nearest tenth of a percent, what's percent...
and is the answer 3.3?
Answer:
Yes you are correct.
1 point
8. Find a positive angle that is less than 360° that is coterminal with a -80°
angle
*
260°
440°
-440°
None of the above
can someone please help me I only have a few minutes
Answer:
(x + 8)(y - 3)
Step-by-step explanation:
Since you have a few minutes left, I will make this quick.
Focus on one letter within the trapezoid ABCD. Pick a certain letter that can correlate to trapezoid A'B'C'D'.
If we move B to B', we would notice it takes 8 skips,therefore (x + 8). If we do the same for y, we would notice it takes 3 skips down. Therefore (y - 3)
10v2 + 50
o Linear binomial
o Constant binomial
Quadratic binomial
Quadratic trinomial
Answer:
So what is the question? probably to describe the polynomial 10v^2 + 50. okay. the polynomial is a quadratic (it is to the 2nd power) and a binomial (2 terms).
The table shows the participation in a school’s debate club during the last four years. Year 1 2 3 4 Students 14 19 25 33 Between which two years did the club see the greatest growth? By what percent did it grow? Round to the nearest percent. Use the drop-down menus to show and explain your answer. The greatest growth was between years Choose... and Choose... . The growth between those years was about Choose... .
Answer:
Year 1 and 2
36%
Step-by-step explanation:
Given the data :
Year ______1 ___ 2 ____ 3 ___ 4
Students __ 14 __ 19 ___ 25 __ 33
Greatest growth is observed between year 1 and 2
Growth percent :
(year 2 - year 1) / year 1 * 100%
(19 - 14) / 14 * 100%
5 / 14 * 100%
0.3571 * 100%
= 35. 71%
= 36%
The growth percent between year 1 and 2 is greater than between the other years
Year 2 and 3 = (6/19) * 100% = 31.57%
Year 3 and 4 = (8/25) * 100% = 32%
Answer:
1 and 2 x=32%
Step-by-step explanation:
1. 5/14=x/100
2. 500/14=14x/14
so you get 36%
BTW the quiz 3-4 and 3-5 sucks lol
A room has a perimeter of 40 feet. The length is 4 less than 2 times the width. What are the dimensions of the room?
Answer:
First, develop an equation for this scenario. The formula to find the perimeter of a quadrilateral is 2l+2w. Because the length is 4 less than twice the width, this would be translated to (2w-4). Plug this into the variable for the length to get 2(2w-4)+2w=40. Distribute the 2 to get 4w-8+2w=40. Add the like terms to get 6w-8=40. Add 8 to both sides and get 6w=48. Divide 6 to result with w=8.
Now that we know w, we can substitute 8 into the variable to solve for the length. 2l+2(8)=40. Multiply 8 and 2 to get 2l+16=40. Subtract 16 to both sides to get 2l=24. Divide 2 to both sides to result with l=12.
Length = 12 feet
Width = 8 feet
What is the slope of the line in the graph? HELPPPPPPPP WILL GIVE BRAINLYIST TO CORRECT ANSWER!!!!!
Answer:
(-1,1),(-2,-1)
Step-by-step explanation:
brainliest please
Which of the following could be the side lengths of a right triangle?
Question 1 options:
1 in, 2, in, 3 in
2 m, 5 m, 5 m
12 ft, 16 ft, 20 ft
3 in, 4 in, 6 in
Answer:
its C
Step-by-step explanation:
it cant be b because there would be no longest side
neither d or a because ive done the math for it
a^2 + 6=
a=5
Evaluate
Answer:
31
Step-by-step explanation:
[tex]a^{2} +6=?[/tex]
[tex](5)^{2} +6=?[/tex]
[tex]25+6=?[/tex]
=31
Help me please!!!! I really need help ty!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please please help asap!!! I will mark brainliest!!!
Answer:
The other angle is 63 if it is asking what I think it is asking
Step-by-step explanation:
If it is right can you mark brainliest
Answer:
63 or 72
Step-by-step explanation:
please help this is algebra II
Answer:
m=5
Step-by-step explanation: