Answer: The value of the integral is 49/4 ln(2).
Step-by-step explanation:
We begin by finding a suitable change of variables that simplifies the integrand and makes it easier to integrate over the region R. In this case, we can use the transformation:
u = x - 7y
v = 3x - y
To obtain the Jacobian of this transformation, we take the partial derivatives of u and v with respect to x and y:
∂u/∂x = 1, ∂u/∂y = -7
∂v/∂x = 3, ∂v/∂y = -1
So, the Jacobian is given by: J = ∂(u,v)/∂(x,y) = (1)(-1) - (-7)(3) = 20
Now we can rewrite the integral in terms of u and v:
∬R 7x - 7y/(3x - y) da = ∬R (7u + 7v)/(20v) |J| du dv
where R is the region enclosed by the lines u = 0, u = 5, v = 2, and v = 7.
The limits of integration for u and v are determined by the intersection points of the lines that form the boundary of the parallelogram R. To obtain these points, we solve the following system of equations:
u = 0 and u = 5 - 7v/3
v = 2 and v = 7 - 3u/2
Solving for u and v, we get the following limits of integration:
0 ≤ u ≤ 5 - 7v/3
2 ≤ v ≤ 7 - 3u/2
Substituting these limits of integration into the integral expression, we have:
∬R 7x - 7y/(3x - y) da = ∫2^7 ∫0^(5-7v/3) (7u + 7v)/(20v) |J| du dv
Evaluating this double integral gives:∬R 7x - 7y/(3x - y) da = 49/4 ln(2)
Therefore, the value of the integral is 49/4 ln(2).
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33 1/3 % of what number is21?
Answer:
33 1/3% of 21 is 63.64$ or rounded to the nearest whole number it is 64%
Step-by-step explanation:
I just solved
hellppp fast plzzzzzz
Answer:
49? I think
Step-by-step explanation:
ANSWER QUICKKK
HELP !!!!! i
Answer:
its B
Step-by-step explanation:
Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th
Answer:
See solutions below
Step-by-step explanation:
Given the sequence -5, 10, -20, 40...
The nth term of the GP is expressed as;
Tn = ar^n-1
a is the first term
r is the common ratio
n is the number of terms
From the sequence, a = -5
r = 10/-5 = -20/10 = -2
Substitute
Tn = -5(-2)^n-1
This gives the explicit formula
For recursive;
a1 = -5
a2 = 10 = -2(-5) = -2a1
a3 = -20 = -2(10) = -2a2
From the shown sequence, we can see that;
an = -2an-1
This gives the recursive formula
Get the 12th term;
Using the explicit formula
T12 = -5(-2)^12-1
T12 = -5(-2)^11
T12 = -5(-2048)
T12 = 10240
Hence the 12th term is 10240
In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove that XYZ is also an equilateral triangle.
~Thanks in advance !
Answer:
See Below
Step-by-step explanation:
Statements: Reasons:
[tex]1)\text{ } \Delta PQR\text{ is equilateral}[/tex] Given
[tex]2)\text{ }PQ=QR=RP[/tex] Definition of Equilateral
[tex]3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP[/tex] Given
[tex]4)\text{ } PX=XQ[/tex] Definition of Midpoint
[tex]5)PQ=PX+XQ[/tex] Segment Addition
[tex]6)\text{ } PQ=2XQ[/tex] Substitution
[tex]7)\text{ } QY=YR[/tex] Definition of Midpoint
[tex]8)\text{ }QR=QY+YR[/tex] Segment Addition
[tex]9)\text{ } QR=2QY[/tex] Substitution
[tex]10)\text{ } 2XQ=2QY[/tex] Substitution
[tex]11)\text{ } XQ=QY[/tex] Division Property of Equality
[tex]12)\text{ } XQ=PX=QY=YR[/tex] Transitive Property
[tex]13)\text{ } RZ=ZP[/tex] Definition of Midpoint
[tex]14)\text{ } RP=RZ+ZP[/tex] Segment Addition
[tex]15)\text{ } RP=2RZ[/tex] Substitution
[tex]16)\text{ } 2XQ=2RZ[/tex] Substitution
[tex]17)\text{ } XQ=RZ[/tex] Substitution
[tex]18)\text{ } XQ=PX=QY=YR=RZ=ZP[/tex] Transitive Property
[tex]19)\text{ } \angle Q\cong \angle R\cong \angle P[/tex] Definition of Equilateral
[tex]20)\text{ } \Delta XQY\cong \Delta YRQ \cong \Delta ZPX[/tex] SAS Congruence
[tex]21)\text{ } XY\cong YZ\cong ZX[/tex] CPCTC
[tex]22)\text{ } \Delta XYZ\text{ is equilateral}[/tex] Equilateral Triangle Theorem
Answer:
this is your answer. thanks, for great point
‼️ PLEASEE HELPPP ‼️
Answer:
30
Step-by-step explanation:
3x - 27 = x +11
3x -27 +27 = 11 + 27
3x - x = x -x + 38
2x = 38
2x ÷ 2 = 38
X = 19
19 × 3 -27 = 30
The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike
this morning. Now they are at an elevation of 450 feet.
a. Explain how to find their elevation before the hike.
b. Han says the equation e + 290 = 450 describes the situation.
What does the variable e represent?
C. Han says that he can rewrite his equation as
e = 450 + -290 to solve for e. Compare Han's strategy to your
strategy for finding the beginning elevation.
Answer:
Step-by-step explanation:
A. Subtract 290 from 450, 450-290= 160
B. The variable e represents the elevation before they started the hike
C. 450+-290= 450-290
The requried elevation before the hike is given as 160 feet and the required equation model of the situation is e + 290 = 450 where e represents the elevation before the hike.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
a. To find the members' elevation before the hike, we can subtract the increase in elevation from their current elevation. So, their elevation before the hike would be 450 - 290 = 160 feet.
b. In the equation e + 290 = 450, the variable "e" represents the members' elevation before the hike.
c. Han's strategy for finding the beginning elevation involves adding -290 to both sides of the equation e + 290 = 450 to get e = 450 + -290. This is equivalent to subtracting 290 from both sides of the equation e + 290 = 450. Both strategies result in the same equation, e = 160, which tells us that the members' elevation before the hike was 160 feet.
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Independent Practice
The equation k = 1.6d gives an approximate relationship between d miles and k kilometers. The distance between Columbus, Ohio, and Des Moines, Iowa, is 665 miles. Express the distance in kilometers.
A.
1,064 km
B.
415.6 km
C.
666.6 km
D.
663.4 km
[tex]k = 1.6d[/tex]
[tex]k = 1.6(665)[/tex]
[tex]k = 1064[/tex]
The distance is 1064 km.
Answer:
A. 1,064 km
Step-by-step explanation:
1 Mile is 1,6 Kilometers
430 Miles = 688 Kilometers (430 * 1,6)
665 Miles = 1064 Kilometers (665 * 1,6)
1- 1.6(430)= 688 Km
2. 1.6(665)=1064 Km
Using 1.6 as the consant then 430* 1.6 = 688 Km
655 * 1.6 = 1048Km
if i understand what you need properly, all you do is multiply the miles x 1.6 and you will get k. so 430miles x 1.6 = 688k
and 665miles x 1.6 = 1064k
Work out, giving your answer in its simplest form:
4/7 divided by 2 1 / 3
Step-by-step explanation:
4/7÷21/3
=4/7*3/21
=12/147
Answer:
[tex]\frac{12}{49}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{7}[/tex] ÷ 2 [tex]\frac{1}{3}[/tex] ← change mixed number to improper fraction
= [tex]\frac{4}{7}[/tex] ÷ [tex]\frac{7}{3}[/tex]
To perform the division
Leave the first fraction. change division to multiplication and turn the second fraction upside down.
= [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{7}[/tex] ← multiply numerators/ denominators together
= [tex]\frac{4(3)}{7(7)}[/tex]
= [tex]\frac{12}{49}[/tex]
Cual es el 5% de 80?
Calculate the amount of work done if you use a 150N force to push a 50kg box 5m across the kitchen floor.
Answer:
750 J
Step-by-step explanation:
Factor completely
x^2 - 8x + 16
Answer:
(x - 4)^2
Step-by-step explanation:
I didn't mean to click an answer but please help me out
Answer:
135
Step-by-step explanation:
135+45=180, and supplementary angles always equal 180
Answer:
The answer is 135
Step-by-step explanation:
Definition of supplementary angles: either of two angles whose sum is 180°, so 180 - 45 = 135!
Please mark as brainliest.
what is the center of the circle?
(-5,-9)
(-4,-7)
(-6,-5)
(-5,-6)
Answer:
1000000066756355688777
Find the slope of the line passing through the points (-7, 4) & (-7, -8)
Answer:
Undefined
Step-by-step explanation:
The equation for finding the slope is:
y2 - y1
------------
x2 - x1
--------------------------------------------------------------------------------------------------------
4 - (-8)
----------
-7 - (-7)
-----------------------------------------------------------------------------------------------------------
4 + 8
--------
-7 +7
---------------------------------------------------------------------------------------------------------
12
----
0
---------------------------------------------------------------------------------------------------------
The slope is Undefined, so there is no answer
1. 2x + 7 = 2x - 7
2. 3x + 8 = -2x + 8
3. 4(x + 1) = 4x + 4
Answer:
Consider left and right sides of the equations as linear functions.
Then:
1. The equation 1 has lines with the same slope (2) but different y-intercepts (7 and -7), therefore the lines are parallel and no solution.2. The lines have different slopes (3 and 2), therefore they intersect and there is one solution.3. After opening the parenthesis we get both sides same, meaning the lines are same and overlap. The equation has infinitely many solutions.The product of two numbers is 4 2/9, if one of the number is 38, find the number
Answer:
let x and y be the two number then according to question ,
xy=4 2/9
or, xy= 38/9
if one of the number is 38 then,
38x=38/9
or, x= 1/9 is the correct ans.
Levi resolveu a expressão, 8×(-3)+7×5+(– 10)² ÷ 50, mas apagou o resultado. Resolva você também essa expressão e encontre o resultado. *
Answer:
61
Step-by-step explanation:
8×(-3)+7×5+(-10)²÷50
apply the PEMDAS rule or (parenthesis, exponent, multiplication,division,addtion,subraction)
24+7×5+(-10)²÷50
24+7×5+100÷50
24+35+100÷50
24+35+2
61
Brian is tiling a patio and ran out of tiles. The width of the remaining area of ⅔ yard. The length of the remaining area is 4 yards. What is the area Brian has left to tile?
Answer:
Area of the remaining patio = 2.67 square yards
Step-by-step explanation:
Width of the remaining area of the patio = [tex]\frac{2}{3}[/tex] yards
Length of the remaining area of the patio = 4 yards
Since, area of the remaining area of the rectangular patio
= Length × Width
= [tex]\frac{2}{3}\times 4[/tex]
= [tex]\frac{8}{3}[/tex]
= 2.67 square yards
Therefore, area of the remaining area of the patio = 2.67 square yards
CONVERTING METRIC UNITS - LENGTH WEIGHT & VOLUME 1
2)
2 kg =
B
1)
1 kg =
g
4)
2 cm =
mm
3)
1 cm =
mm
6)
2 km =
m
5)
1 km =
m
8)
2 L =
ml
7)
1 L =
mL
10)
2 m =
cm
9)
cm
1 m =
Which is the most? Circle the largest amount in each box.
1 L
1 m
560 m
2,000 cm
1 kg
1,250 mL
80 cm
300 g
980 mL
1 km
120 mm
950 g
greater than (>), less than (<) or equals (=) to compare the amounts.
2)
1 m
75 cm
590 mL
1L
1 km
250 m
2 cm
4)
20 mm
7 cm
50 mm
2 m
6)
250 cm
4 m
350 cm
8)
1 kg
-,200 g
10)
3m
2 L
20 mL
300 cm
12)
500
Om
1 km
4 kg
Answer:
2 KM 2 L 2 KG I dont know the rest i figured i could help someone but thats all i can do at the moment sorry i might come back to finish it later.
Step-by-step explanation:
If three points are coplanar, they must be collinear. Since the answer is false, state a counterexample.
Answer:
Collinear points are points that lie on a line. Any two points are always collinear because you can always connect them with a straight line. Three or more points can be collinear, but they don't have to be. … Any two or three points are always coplanar
Step-by-step explanation:
Answer:
They could be on different lines or on no line, but in the same plane.
Step-by-step explanation:
Hope This Helps!!
(brainliest please, if possible)
Can anyone help me with this question?
PLS helpp
ill give brainliest
the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress
Answer: 1 1/4
Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4
Write the number 7.8 x 10^3 in standard form.
Find the distance between (2, 8) and (−6, 2).
The distance is ( ) units.
Answer:
✓100 = 10
Step-by-step explanation:
2= x1
8= x2
-6= y1
2= y2
Then you apply your distance formula to solve.
Hope it helps
what's
[tex] \sqrt{36} [/tex]
chess ?
[tex] \huge \purple{\tt{Answer:}} [/tex]
[tex] \sf{\sqrt{36}} = \sf{6} [/tex]
Answer:
√36=6
Step-by-step explanation:
it's can also be understood by 6×6=36
HELP PLEASE!
The initial population of Rochester is 17,500 and is
projected to grow at a rate of 4.5% perdecade.
Write an expression for the projected population
of Rochester after “n” decades.
Answer:
Step-by-step explanation:
I still...really don't know
The ministry of health was interested in the relationship between the office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 5 years they gathered and analyzed the entire data.
A) Sample study
B)Experiment
C) Observational Study
The researchers found that those workers who reported taking regular 10-minute breaks during the workday were 41% percent more likely to develop cancer over the next five years than workers who didn't leave their offices during the workday
A)The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
B) The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a teacher.
C)The result suggests that if a public worker takes 10-minute breaks during the workday, he has a 41% chance of developing cancer.
D)The result suggests that starting to take 10-minute breaks during the workday will increase the risk of developing cancer for a public worker.
Answer:
Step-by-step explanation:
The answer for the second part of the question would be.
C)The result suggests that there's a positive correlation between taking 10-minutes breaks during the say and developing cancer in public workers.
The correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The health ministry only distributes forms to workers every five years to collect information on office jobs and worker health concerns. They are just monitoring the workers, and the survey allows them to assess and establish a link between office employment and worker health concerns. Therefore, it is an observational study.
The conclusion that can be concluded from this study is that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
Hence, the correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.
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Ishi has $24 in his pocket. He pays $8 to have his car washed. Write and solve an expression to show the change in Ishi's money.
Answer:
8 - 24
Step-by-step explanation:
Answer: 24 + (-8)
Step-by-step explanation:
He has 24$ do you take 8 out of it