Answers
An obvious substitution would be to take u = x - y and v = x + 2y, so that 0 < u < 1 (which follows from y = x ==> x - y = 0 and y = x - 1 ==> x - y = 1), and 0 < v < 1.
Solve for x and y in terms of u and v :
u - v = (x - y) - (x + 2y) = -3y ==> y = (v - u)/3
2u + v = 2 (x - y) + (x + 2y) = 3x ==> x = (2u + v)/3
Compute the Jacobian and its determinant:
[tex]J=\begin{bmatrix}D_ux&D_vx\\D_uy&D_vy\end{bmatrix}=\begin{bmatrix}\dfrac23&\dfrac13\\\\-\dfrac13&\dfrac13\end{bmatrix} \implies |\det(J)|=\dfrac13[/tex]
Now in the integral, we have
[tex]\displaystyle\iint_R\frac{x+2y}{\cos(x-y)}\,\mathrm dx\,\mathrm dy = \frac13\int_0^1\int_0^1\frac{v}{\cos(u)}\,\mathrm du\,\mathrm dv \\\\ \displaystyle= \frac13\left(\int_0^1v\,\mathrm dv\right)\left(\int_0^1\sec(u)\,\mathrm du\right) \\\\ \displaystyle= \frac13\bigg(\frac{v^2}2\bigg)\bigg|_0^1\bigg(\ln|\sec(u)+\tan(u)|\bigg)\bigg|_0^1 \\\\ \displaystyle= \boxed{\frac16\ln(\sec(1)+\tan(1))}[/tex]
Related Questions
Will mark Brainlest formula of (x+y)cube
Answers
Answer:
(x+y) ³
= x³+3x²y+3xy²+y³
=x³+y³+3xy(x+y)
Brainliest please~
(x+y)3= x^3+3x^2y+3xy^2+y^3
There are 3600 second in 1 hour how many second are there in 24 hour
Answers
Step-by-step explanation:
hear is your answer please
Consider two people where one person is 25% taller than the other but proportioned in exactly the same way. (That is, the taller person looks like a larger version of the shorter person.) Suppose the shorter person has a 31-inch waist. What size is the taller person's waist?
Answers
Answer:
38.75 in.
Step-by-step explanation:
[tex]125\% \times 31~in. = 1.25 \times 31~in. = 38.75~in.[/tex]
Find the slope 7-12 please
Answers
Write the next three terms in this pattern: 1, 4, 3, 6, 5, 8, 7, …
Answers
Answer:
10, 9, 12
Step-by-step explanation:
Determine the value of y.
1)
46°
2)
226°
3)
132°
4)
452°
Answers
Answer:
y = 46
Step-by-step explanation:
Angle Formed by Two Tangents= 1/2(difference of Intercepted Arcs)
We can find the other arc by the total arc of a circle minus the arc length 226
y = 1/2 ( 226 - ( 360 -226))
y = 1/2 ( 226 -134)
y = 1/2 (92)
y = 46
Ibrahim heeft een bijbaantje op de markt. Hij berekent zijn inkomsten met de formule
inkomsten in €=5+3,50 x tijd in uren. Leg de formule uit.
Answers
Answer:
Ibrahim gets 5 fixed and 3.5 per hour.
Step-by-step explanation:
Ibrahim has a side job at the market. He calculates his income with the formula income in € = 5 + 3.50 x, time in hours. Explain the formula.
Here, the fixed income is 5.
the income per hour is 3.5.
So, Ibrahim gets 5 fixed and 3.5 per hour.
!pls help!
Use a net to find the surface area
Answers
Answer:
336 square inches
Step-by-step explanation:
Nets are the spreaded out version/outline of 3d figures. It shows the faces of the figure. The figure in this case is actually a triangular prism.
find the area of each shape in the net:
Triangle A (1/2 x base x height)
1/2 • 8 x 6 = 24 square inches
Rectangle B (length x width):
6 x 12 = 72 square inches
Rectangle C:
8 x 12 = 96 square inches
Rectangle D:
10 x 12 = 120 square inches
Triangle E:
1/2 x 6 x 8 = 24 square inches
Add up all the areas of all shapes:
24 + 24 + 120 + 72 + 96 = 336
Surface area is measured in square inches
(Inches in this case)
Hope this helps
need help!! Evaluate. - 3x ^ 3 - 4x for x = - 1 . 07 0-1
Answers
Answer:
option A
Step-by-step explanation:
[tex]p(x) = -3x^3 - 4x \\\\p(x = - 1 ) = -3( - 1)^3 - 4( - 1 )[/tex]
[tex]= -3(-1) + 4 \\\\= 3 + 4 \\\\= 7[/tex]
Answer:
7Step-by-step explanation:
[tex] - {3x}^{3} - 4x[/tex]
[When x = -1 then]
[tex] = - {3( - 1)}^{3} - 4( - 1)[/tex]
= - 3 × (-1) - 4 × (-1)
= 3 + 4
= 7 (Ans)
evaluate g(x)=x/x-3, if g(1/2)
Answers
Answer:
-1/5
Step-by-step explanation:
g(x) = x/(x-3)
Substituting x = 1/2 in g(x),
g(1/2) = 1/2/(1/2-3)
= 1/2/(1/2-6/2)
= 1/2/(-5/2)
= 1/2 ÷ - 5/2
= 1/2 x -2/5
= - 1/5
Step-by-step explanation:
here is your answer
here is your answer
Which of the following is(are) the solution(s) to 17x+12= 12?
Answers
Answer:
17x+12=12
17x=12-12
17x=0
divide both sides by 17
x=0
rough check
17(0) = 12-12
0=0
I hope this helps
Type your answers into the boxes.
Complete the following questions.
4x5-(22 - 2) =
(18= 3) + (32 - 7) =
Answers
Answer:
0 and 40
Step-by-step explanation:
First expression: 4*5 - (22 - 2). We must do work inside parentheses before any other work. This, we have 4*5 - (20), which simplifies to 20 - 20 = 0
Second expression: (18 - 3) + (32 - 7 becomes (15) + 25, or 40.
ayudame y tedoy corona y puntaje
Answers
Answer:
i dont get it
Step-by-step explanation:
1. The degree of 5x³+4x²+7x degree of the quadratic Polynomial is
how tell answer crottect I mark as brilliant
Answers
Answer:
3
Step-by-step explanation:
Degree of the polynomial is the highest degree of the polynomial. Here highest degree is 3.
I NEEEEED HELP!!!!!!
Answers
Translate this phrase into an algebraic expression.
RE
16 increased by twice a number
Use the variable n to represent the unknown numbers
Answers
Answer:
16 + 2n
Step-by-step explanation:
n + n is twice of a number, but 2n is simplified. "16 increased by" just represent addition
what is the sum factor of 3600
Answers
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Find the prime factorization of the number 3,600. Factor Tree.
2|3,600.
2|1,800.
2|900.
2|450
5|225
5|45
3|9
3|3
|1
Setup the equation for determining the number of factors or divisors.
3600=2x2x2x2x3x3x5
Sum factors=2+2+2+2+2+3+3+5=24
Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $52 for 180 miles. On another day she rented a car from the same agency and paid $77.50 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.
f(x) =
Answers
9514 1404 393
Answer:
f(x) = 0.15x +25
Step-by-step explanation:
We are given two points:
(x, y) = (180, 52) or (350, 77.50)
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
m = (77.50 -52)/(350 -180) = 25.50/170 = 0.15
The y-intercept is given by ...
b = y -mx
b = 52 -0.15×180 = 25
Then the equation for the linear function is ...
f(x) = mx +b
f(x) = 0.15x +25
A florist shop represents its first month’s sales with the equation y = 168 x + 8, where x represents the number of days that the shop is open and y represents the sales in dollars. The owner of the shop would like to calculate the number of days it took to reach $3,200 in sales. Which would be used to solve the problem?
Substitute 3,200 for x.
Add 8 and 3,200.
Divide 3,192 by 168.
Isolate y in the equation.
Answers
Answer:
Divide 3,192 by 168.
Step-by-step explanation:
Given
[tex]y = 168x + 8[/tex]
[tex]y = 3200[/tex]
Required
Step to required to get x when [tex]y = 3200[/tex]
The first step is to substitute [tex]3200[/tex] for [tex]y[/tex]
[tex]3200 = 168 * x + 8[/tex]
Subtract both sides by 8
[tex]3192 = 168 * x[/tex]
Divide both sides 168 ---- [this answers the question]
[tex]19 = x[/tex]
[tex]x = 19[/tex]
Answer:
Divide 3,192 by 168.
Step-by-step explanation:
Divide 3,192 by 168.
Step-by-step explanation:
Given
Required
Step to required to get x when
The first step is to substitute for
Subtract both sides by 8
Divide both sides 168 ---- [this answers the question]
Compute ∬_R〖(7xy-5-2y^2)dxdy〗 where the domain of integration R is bounded by the lines y=0, y=4-2x and y=2x^2
Answers
Attached you'll find the region of interest, which is captured by the set of points
R = {(x, y) | √(y/2) ≤ x ≤ (4 - y)/2 and 0 ≤ y ≤ 2}
Written in this way, it's convenient to integrate with the order dx dy (that is, with respect to x first). In particular, we have
[tex]\displaystyle\iint_R(7xy-5-2y^2)\,\mathrm dx\,\mathrm dy = \int_0^2 \int_{\sqrt{\frac y2}}^{\frac{4-y}2} (7xy-5-2y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]\displaystyle = \int_0^2 \int_{\sqrt{\frac y2}}^{\frac{4-y}2} \left(\frac72 x^2y-5x-2xy^2\right)\bigg|_{\sqrt{\frac y2}}^{\frac{4-y}2}\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^2\left(\frac{15}8y^3-11y^2+\frac{33}2y-10 +\sqrt2 y^{\frac52}-\frac74y^2+\frac5{\sqrt2}y^{\frac12}\right)\,\mathrm dy[/tex]
[tex]=\displaystyle\left(\frac{15}{32}y^4+\frac{2\sqrt2}7y^{\frac72}-\frac{17}4y^3+\frac{33}4y^2+\frac{5\sqrt2}3y^{\frac32}-10y\right)\bigg|_0^2[/tex]
[tex]=\boxed{-\dfrac{95}{42}}[/tex]
Suppose 2500 dollars is invested at 4% for 5 years. Find the account balance if it is
compounded daily, monthly, quarterly?
answer step by step
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Using the compound interest formula :
A = P(1 + r/n)^nt
A = final amount ; r = rate ; n = number of compounding times per period ; t = period ; P = principal
P = 2500 ; r = 4% = 0.04 ; t = 5 years
Daily compounding, n = 365
Yearly compounding, n = 1
Quarterly compounding, n = 4
Daily compounding :
A = 2500(1 + 0.04/365)^(5*365)
A = 2500(1.0001095)^1825
A = $3053.4734
Yearly :
A = 2500(1 + 0.04/1)^(5*1)
A = 2500(1.04)^5
A = $3041.6323
Quarterly:
A = 2500(1 + 0.04/4)^(5*4)
A = 2500(1.01)^20
A = $3050.4751
4. Write an equation for the line that is parallel to the given line and that passes
through the given point.
y = 5/2x-10;(-6,-29)
Answers
Answer:
[tex]y=\frac{5}{2}x-14[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]y=\frac{5}{2}x-10[/tex]
In the given equation, [tex]\frac{5}{2}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of [tex]\frac{5}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{5}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{5}{2}x+b[/tex]
Plug in the given point (-6,-29) and solve for b
[tex]-29=\frac{5}{2}(-6)+b[/tex]
Simplify -6 and 2
[tex]-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b[/tex]
Add 15 to both sides to isolate b
[tex]-29+15=-15+b+15\\-14=b[/tex]
Therefore, the y-intercept is -14. Plug this back into [tex]y=\frac{5}{2}x+b[/tex]:
[tex]y=\frac{5}{2}x-14[/tex]
I hope this helps!
if three-fourth of a number is added to 14 gives result less than or equal to 20 .find the number,hense illustrate your answer on a number line
Answers
Answer:
see photo
Step-by-step explanation:
Jeans are on sale for 20% off the regular price. Which function would give you the total cost for purchasing a pair of jeans that costs x dollars?
Answers
Answer:
0.8X = Final cost
Step-by-step explanation:
Given that jeans are on sale for 20% off the regular price, to determine which function would give you the total cost for purchasing a pair of jeans that costs X dollars, the following calculation must be performed:
1X = Initial cost of the jeans
20% = 0.2
1 - 0.2 = 0.8
0.8X = Final cost
Part 1: Solve for the slope of the line inside of the scatter plot
Answers
Answer:
The slope is equal to 5.
Step-by-step explanation:
Point 1 (0, 5)
Point 2 (3, 20)
m=y2-y1/x2-x1
m=5-20/0-3
m=-15/-3=
m=5
Point V is located at -16. Points W and X are each 7 units away from Point V. Where are W and X located?
Answers
Answer:
Location of W is - 23, location of X is - 9.
Step-by-step explanation:
location of V = - 16
Points W and X are each 7 units away from Point V.
Let the W is at left of V and X is right of V.
location of W = -16 - 7 = - 23
location of X = - 16 + 7 = - 9
A homeowners’ association charges a $3.85 fee for each day your payment is late. If a bill was originally $98.75 and paid 13 days late, then how much is owed to the homeowners’ association?
Answers
Answer:
$148.80
Step-by-step explanation:
Find how much was charged extra with the late fee. Multiply 13 by 3.85:
13(3.85)
= 50.05
Add this to the original amount of the bill:
98.75 + 50.05
= 148.8
So, the amount owed is $148.80
Which of the folloing pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answers
Answer:
18/48 and 15/40
Step-by-step explanation:
18/48 = 3/8
15/40 = 3/8
•°• 18/48 is equivalent to 15/40
Find the distance (-2,4) and (-5,-0)
Answers
Answer:
d=√65 units
Step-by-step explanation:
Using the distance formula :
d=√((−5)−(2))2+((0)−(4))2 units
d=√(−7)2+(−4)2 units
d=√49+16 units
d=√65 units
If this helps you, please mark brainliest!
Have a nice day!
William is an electrician. He charges an initial fee of $44 per visit. If he charges $30 for every hour he works, which explicit
expression and recursive process can be used to find out how much he will charge for working n hours?
O A. Explicit Expression: 30n - 44
Recursive Process: To find out how much William will charge for working n hours, subtract $30 from how much he
charges for working n - 1 hours.
W = Wn-1 - $30, Wo = $44
OB. Explicit Expression: 30n +44
Recursive Process: To find out how much William will charge for working hours, add $30 to how much he charges for
working n - 1 hours.
W = Wn-1 + $30, Wo = $44
OC. Explicit Expression: 44n - 30
Recursive Process: To find out how much William will charge for working n hours, subtract $44 from how much he
charges for working n - 1 hours.
Wn = Wn-1 - $44, Wo = $30
OD. Explicit Expression: 44n+ 30
Recursive Process: To find out how much William will charge for working n hours, add $44 to how much he charges for
working n - 1 hours.
Answers
You times 30 by how ever many hours he worked and then add 44 at the end for the initial visit price