The value of the integral can be calculated by using the simple rules of definite integral and double integral.
The first integral is a bit tricky, as the limits of integration are not in the standard order (with respect to x and y). However, we can change the order of integration by switching the limits of integration, so that we can use Fubini's theorem.
The double integral can be solved by converting the rectangular region R into polar coordinates.
The double integral is ∫∫R 5xsin(x+y)dA, R=[0,pi/3]×[0,pi/6]. This can be further solved as
= ∫(0,pi/3) ∫(0,pi/6) 5rrsin(rcos(θ)+rsin(θ))dθ dr
= ∫(0,pi/3) ∫(0,pi/6) 5r^2sin(r(cos(θ)+sin(θ)))dθ dr
= ∫(0,pi/3) 5r^2(-cos(r*(cos(θ)+sin(θ))) | (0,pi/6))dr
= ∫(0,pi/3) 5r^2(-cos(r*(√(2)/2)))dr
= -5/2∫(0,pi/3) r^2cos(r*(√(2)/2))dr
The integral above is not in a closed form but can be evaluated using numerical integration techniques.
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Complete Question:
Calculate the iterated integral. integral_0^3 integral_0^1 5xy Square root x^2 + y^2 dy dx = Calculate the double integral. double integral R 5x sin (x + y) dA, R = [0, pi/3] times [0, pi/6] The value of integral is
Find the area of the regular polygon. Round to the nearest tenth.
Given:
The figure of a regular polygon.
To find:
The area of the regular polygon.
Solution:
From the given figure it is clear that the regular polygon has 4 vertices. It means, it is a square.
Distance between the center and the vertex is 7 yd. So, the diagonal of the square is
[tex]d=7+7[/tex]
[tex]d=14[/tex] yd
We know that, area of a square is
[tex]A=\dfrac{1}{2}d^2[/tex]
Putting d=14 in the above formula, we get
[tex]A=\dfrac{1}{2}(14)^2[/tex]
[tex]A=\dfrac{1}{2}(196)[/tex]
[tex]A=98[/tex]
Therefore, the area of the regular polygon is 98 sq. yd.
Which sign makes the following statement true? 2/5 _____ 6/15
Answer:
2/5=6/15
Step-by-step explanation:
2/5
3x2=6
3x5=15
compare they are same
give me brainliest pls
The equal sign completes the give incomplete mathematical statement.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.The given incomplete expression is -
2/5 _____ 6/15
The given expression is -
2/5 ____ 6/15
2/5 ____ 2/5
0.4 ____ 0.4
0.4 = 0.4
Therefore, the equal sign completes the give incomplete mathematical statement.
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If a well is dug at -60 feet per day. How many days did it take to dig -5400 feet?
(Answer numerically ex: 30 Days answer = 30)
Answer:
90 days
Step-by-step explanation:
This one is just simple division, so you divide the goal number which is -5400 by -60 but in this situation you can just make them positives.
What is the area of a circle with a radius of 4 inches? Use 3.14 for π. Enter your answer as a decimal in the box.
enter your answer
in²
Answer:
A≈ 50.27in^2
Step-by-step explanation:
A= πr^2=
π·4^2≈ 50.26548
A random sample of 1175 people in a certain country
Answer:
c
Step-by-step explanation:
..........................
One side, in inches, of a triangle is 5 more than twice a number. If this is an equilateral
triangle, what is the perimeter ?
Definition of an equilateral triangle: A triangle with the exact same sides and angles, which is 60°
5 more than twice a number:
Let the number be x:
2x + 5
Since it is an equilateral triangle, multiply that by 3:
3(2x +5) = 6x + 15
The perimeter is (6x + 15) inches.
what is the difference between a quadratic function and a quadratic equation
Answer:
The roots of a quadratic equation simply tell what values of x will make the equation true. A quadratic function is a function where the largest power for the variable is 2. ... A quadratic equation is given to you so that you can solve it for the variable. A quadratic function is given to you so that you can graph it.
Write an equation for the line in slope-intercept
form.
(Use integers or fractions for any numbers in the
equation.)
Answer:
y = 3x + 5Step-by-step explanation:
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptTake two points from the graph:
(-2, -1) and (0, 5)Find the slope:
m = (5 - (-1))/(0 - (-2)) = 6/2 = 3The y-intercept is b = 5
The line is:
y = 3x + 5Find the selling price of a $30 item after a 40% markup.
Bir otobüste bulunan 45 yolcudan
Buna göre bu otobüsteki yolcuların
18'i çocuktur.
yüzde kaçı çocuktur?
Step-by-step explanation:
bence 27 cunkku yuzd sordugu icin kolaylıklar dilerim iyi günler
PC
You deposit $200 in an account that earns 4% simple interest. How much interest did you earn in 3 years? (Hint: I = prt)
Answer:
$24.
Step-by-step explanation:
Given that I deposited $ 200 in an account that earns 4% simple interest annually, to determine how much interest did I earn in 3 years, the following calculation must be performed:
((200 x 4/100) x 3) = X
((800/100) x 3) = X
(8 x 3) = X
24 = X
Thus, after 3 years of investment I will have earned $ 24 in interest.
what is estimate the product of 19.8 and 5 by grounding each factor to nearest whole number
Given:
The two numbers are 19.8 and 5.
To find:
The estimated product of given numbers by rounding each factor to nearest whole number.
Solution:
Two number are 19.8 and 5.
On rounding the given numbers to the nearest whole number, we get 20 and 5.
Now, the estimated product is
[tex]20\times 5=100[/tex]
Therefore, the estimated product of given numbers is 100.
find the area of ABC
Answer:
area of ABC=1/2 b×h=1/2×20×6=30m²
Answer:
60 m^2
Step-by-step explanation:
( Base * Hight / 2 = Area)
20 * 6 = 120
120 / 2 = 60
The equation of a line XY is (y-3)=3/2(x-4) what is the slope of the line perpendicular to XY?
Answer:
It must be 3/2.........
Answer: -2/3
Step-by-step explanation:
I wrote the equation y-3=3/2(x-4) in slope-intercept form. It's y=3/2x-5, so the slope is 3/2.
To find the perpendicular slope, I found the opposite reciprocal. The reciprocal of 3/2 is 2/3 and the opposite of 2/3 is -2/3
Select the correct option from the menu.
Raj determined that the equation 3 (x+3) = 8x - 5x +7 is equivalent to 9 = 7. This means that this equation has:
no solutions
One solution
Two solutions
Infinity many solutions
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
Required:
a. State the hypothesis that can be used to test for a significant difference between the population proportions for the two years?
b. What is the sample proportion indicating that their financial security was more that fair in 2012?In 2010?
c. Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?
d. What is the 95% confidence interval estimate of the difference between the two population proportion?
Answer:
The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.
Step-by-step explanation:
Let p1 be the sample of 1000 adults chosen in 2012 and
p2 be the sample of 1100 adults chosen in 2010
Part a:
The hypothesis that can be used to test for a significant difference between the population proportions for the two years is:
H0: p1-p2= 0 against the claim Ha: p1-p2≠0
Part b:
The sample proportion indicating that their financial security was more that fair in 2012 is
p1^= 410/1000= 0.41
In 2010 is:
p2^= 385/1100= 0.35
Part c:
p^c= 410+385/1000+1100= 0.3785
q^c= 1-p^c= 1-0.3785= 0.6124
The critical region is z > ±1.96
The test statistic is
z= p1^- p2^ / sqrt ( p^cq^c( 1/n1+ 1/n2)
z= 0.41-0.35 /sqrt( 0.3785*0.6124(1/1000 +1/1100)
z= 0.06 / 0.021036
z= 2.85
Conclusion
The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.
P- value : 0.00466
The result is significant( accept the null hypothesis) for value less than 0.05
Part d:
2012 2010
Sample 1000 1100
Proportions 0.41 0.35
Standard Error √0.41( 0.59)/1000 √0.35( 0.65)/1100
= 0.0155 0.01438
Standard Error for the difference = √0.0155² + 0.01438² =0.0211
p1-p2 ± z* standard error for the difference
0.41-0.35 ± 1.96 *( 0.0211)
0.06 ± 0.041356
-0.018644, 0.101356
The 95 % confidence interval estimate is (-0.018644, 0.10135
49 +
6. Luisa bought 23 pounds of apples,
3 pounds of oranges, and 14 pound
of pears. How many pounds of fruit
did she buy in all?
Answer:
23+3+14=40
Step-by-step explanation:
brainliest pls?
50 pounds to be exact
12. If AC=4 and CD=4 13 in the figure below, what is cos x? B 45 45° А Xº D A. 2 13 B. 3 12 C. 2 13 D. 2 E. 1 4 C С 4-13
Answer:
c
Step-by-step explanation:
Is this a proportion? 1.44/8 = 1.7/10
Answer:
No
Step-by-step explanation:
Because the equation needs to have a variable
I don't know how to solve this problem
Before you read this!! To me, it looks like 8 is the entire length of lineJL, but it may only be the length of lineJM. I've written the steps for lineJL=8 NOT lineJM=8. If this is not the case and 8 is only the length of lineJM let me know so I can fix my answer!
Step-by-step explanation:
The area of a triangle is A=1/2(b)(h)
B=base
H=height
Your height is found in the line in the middle of the triangle, for you it is 6.
The base is the long bottom line on the triangle (lineJL), for you it is 8.
So let's put it in.
A=1/2(8)(6)
A=24sq units (C)
Math question, can you guys answer this? 25 points.
Answer:
5. 1/29
Step-by-step explanation:
1/. and the bottom numbers says 30-1 which is 29 soooo 1/29
Find AB.
MN=22
DC=29
Answer:
AB=15
Step-by-step explanation:
Since DM =MA and CN=NB, then DC || MN || AB
29-22=7
22-7=15
AB=15
First to answer correctly gets brainliest
1. X+4x+6x need help ASAP 10 minutes remaining
Answer:
10x^2 or 10x because you are adding x
5
A line passes through the point (4, -3) and has a slope of
4
Write an equation in slope-intercept form for this line.
Answer:
y = 4x -19
Step-by-step explanation:
y = 4x + b
first we add the point to the equation and then we solve for b
-3 = 4 ( 4 ) + b
-3 = 16 + b
-16
-19 = b
how would i solve this?
i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+i^9+i^10
please do a step by step process
Step-by-step explanation:
step 1. I assume i is imaginary
step 2. i^2 = -1, i^3 = -i, i^4 = 1, i^5 = I. . . . and so on
step 3. i - 1 - i + 1 + i - 1 - i + 1 + i - 1
step 4. the result is i - 1.
5x - 4 = 2 (x + 3) + x
Step-by-step explanation:
5x - 4 = 2x + 6 × x
-----> 5x-3x = 6 + 4
-----> 2x = 10
----> x = 5
Mia read x pages in the book. Laurie read 1/3 more than that
Step-by-step explanation:
Laurie read x+1/3 pages.
Mia read x pages.
Anyone need help? :D
Answer:
yeah why? are you going to help?me
Answer:
Yes i actually do.
Step-by-step explanation:
5 - x/3 for x = -3
Evaluate the expression