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]
Related Questions
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w
Answers
Answer:
A
Step-by-step explanation:
Step 1, setting variables:
We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).
Step 2, writing equations:
Great! We have everything now. Let us write the equation by substituting our variables in:
[tex]V=l*w*h\\V=6w(w+2)\\[/tex]
Ok! Let us expand the equation:
[tex]V=6w^2+12w[/tex]
[tex]\fbox{A}[/tex]
I hope this helps! Let me know if you have any questions :)
The sum of three numbers is fourteen. The first number minus three times the third number is the second number. The second number is six more than the first number. Find the three numbers.
Answers
Answer:
1st number (x) = 5
2nd number (y) = 11
3rd number (z) = -2
Step-by-step explanation:
Let the generic solution for this problem be x + y + z = 14.
The first number minus three times the third number equals the second number, so x - 3z = y. The second number is 6 more than the first number, so y = 6 + x.
x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.
After some arithmetic, we find that z = -2.
Plugging our knowns back into the generic solution becomes:
x + x - 3z + z = 14
2x - 3(-2) - 2 = 14
2x + 6 - 2 = 14
2x + 4 = 14
2x = 10
x = 5
So we know that z = -2, and x = 5, it's just simple substitution from there.
5 + y + (-2) = 14
5 + y = 16
y = 11
what is the value of x?
Answers
Answer:
46
ayo how r u doin siahsvsgshsgsgsgsg
With the help of a diagram a boy starts at a and walks 3km east to b he then walk 4km north to c find the distance and bearing of c from a
Answers
Answer:
t=3
Step-by-step explanation:
sorry if its incorrect i got it right on edgy.
Given that 4x – 5y = 12 Find y when x = -3 Give your answer as an improper fraction in its simplest form.
Answers
Step-by-step explanation:
4(-3)-5y=12
-12-5y=12
-5y=12+12
-y= 24/5
y= -24/5
y= -4⅕
hope it helps
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%:
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answers
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)
what is the sum of the angles of a triangle
Answers
Answer:
Triangle has 180 degrees
Squares have 360 degrees
Write two rational and three irrational number that are between 3and 4
Answers
a)rational number :
1)(3+4 )/2
=7/2 =3.5
2)(3.5+4)/2
=7.5/2 =3.25
b)irrational number :
1)10/3=3.33....
2)11/3=3.66....
......I hope it will help you. ..
Answer:
The real numbers, which can be represented by the ratio of two integer numbers, are called rational numbers, say P/Q where Q is not equal to zero.
The actual numbers that cannot be expressed as the two integer ratio are called irrational numbers.
Step-by-step explanation:
a)rational number :
1)
(3+4 )/2
=7/2 =3.5
2)
(3.5+4)/2
=7.5/2 =3.25
b)irrational number :
1)
10/3=3.33....
2)
11/3=3.66....
3)
√13
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Answers
Answer:
For 1: The first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2: The value of n is 27
Step-by-step explanation:
The n-th term of the progression is given as:
[tex]a_n=a_1+(n-1)d[/tex]
where,
[tex]a_1[/tex] is the first term, n is the number of terms and d is the common difference
The sum of n-th terms of the progression is given as:
[tex]S_n=\frac{n}{2}[2a_1+(n-1)d][/tex]
where,
[tex]S_n[/tex] is the sum of nth terms
For (1):The 11th term of the progression:
[tex]25=a_1+10d[/tex] .......(1)
Sum of first 4 numbers:
[tex]49=\frac{4}{2}[2a_1+3d[/tex] ......(2)
Forming equations:
[tex]98=8a_1+12d[/tex]
[tex]25=a_1+10d[/tex] ( × 8)
The equations become:
[tex]98=8a_1+12d[/tex]
[tex]200=8a_1+80d[/tex]
Solving above equations, we get:
[tex]102=68d\\\\d=\frac{102}{68}=\frac{3}{2}[/tex]
Putting value in equation (1):
[tex]25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10[/tex]
Hence, the first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2:The nth term is given as:
[tex]49=10+(n-1)\frac{3}{2}[/tex]
Solving the above equation:
[tex]39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27[/tex]
Hence, the value of n is 27
PLEASE LOOK at the photo and help me on these 2 questions :(!!!!!
Answers
Answer:
1) f(g(2)) = 24
2) f(g(-1)) = -4
Step-by-step explanation:
1) GIven f(x) = x²+2x and g(x) = 2x
f(g(x)) = f(2x)
f(2x) = (2x)² + 2(2x)
f(2x) = 4x² + 4x
f(g(x)) = 4x² + 4x
f(g(2)) = 4(2)² + 4(2)
f(g(2)) = 16+8
f(g(2)) = 24
2) f(x) = x+1 and g(x) = 5x
f(g(x)) = f(5x)
f(5x)= 5x + 1
f(g(x)) = 5x + 1
f(g(-1)) = 5(-1) + 1
f(g(-1)) = -5+1
f(g(-1)) = -4
Of the animals at a pet show, 3/8 were cats and 4/8 were dogs. The rest of the animals were rabbits. What fraction of the animals were rabbits?
Answers
Answer:
1/8 Of the animals are rabbits.
Step-by-step explanation:
3/8 Cats + 4/8 Dogs = 7/8
1/8 Is all you have room left for so 1/8 would be rabbits.
Answer:
1/8.
Step-by-step explanation:
Fraction of rabbits = 1 - (3/7 + 4/8)
= 1 - 7/8
= 8/8 - 7/8
= 1/8.
Câu ca dao sau đây bị chi phối bởi luật bài trung, Giải thích tại sao?
“Có yêu, thì yêu cho chắc,
Bằng như trúc trắc, thì trục trặc cho luôn”.
Answers
Answer:
Hi Are you from Vietnam?
Step-by-step explanation:
Sorry i cant understand
im filipino
Souta wants to compare the mean of his test scores in French class to the mean absolute deviation.
Language Test Scores
French Scores
76
62
94
80
He uses the steps below to find both the mean and mean absolute deviation.
French Scores
Step 1
Add the scores.
76 + 62 + 94 + 80 = 312
Step 2
Divide the sum of the scores by 4.
312 divided by 4 = 78
Step 3
Add the differences between the mean and each score.
(76 minus 78) + (62 minus 78) + (94 minus 78) + (80 minus 78) = 0
Step 4 Divide by 4.
StartFraction 0 over 4 EndFraction = 0
In which step did Souta make the first error?
Step 1
Step 2
Step 3
Step 4
Answers
76 + 62 + 94 + 80 + = 312
step 2 bye score 4 312 divided by 4 = 78
sana po makatulong
Estimate 481 + 223 round each number first.
Answers
Answer:
7
Step-by-step explanation:
481 + 223
approximately 481 =5
223 =2
5+2=7
Answer:
7
Step-by-step explanation:
Pppppppllllssss help
Answers
nah you good g shsgshagagagag
shshagsggsgsgwg
The length of a rectangle is 5 inches longer than it is wide. If the area is 84 square inches, what are the
dimensions of the rectangle?
The width, or shorter side is i inches
Enter an integer or decimal number (more..
inches
The length, or longer side is
Answers
Answer:
b = 7 inches and l = 12 inches
Step-by-step explanation:
Given that,
The area of a rectangle, A = 84 sq inches
Let the width is b.
Length = (5+b)
The area of a rectangle is given by :
A = lb
So,
[tex]84=b\times (5+b)\\\\b^2+5b-84=0\\\\(b-7)(b+12)=0\\\\b=7\ in, b =-12\ in[/tex]
Neglecting negative value,
b = 7 inches
Length, l = 5+b = 5+7
l = 12 inches
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answers
Answer:
D
Step-by-step explanation:
The smallest number by which 48 should be multiplied so as to get a perfect square is
Answers
Answer:
3
Step-by-step explanation:
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a trader borrowed 2500$ at a sumple interest at the end of 8 months he paid back $2500 find the rate
Answers
Answer:
8%
Step-by-step explanation:
Rate = 100×Interest ÷ Principal× Time
100× 2500/ 2500 × 8 = 800
800/100 = 8%
I hope this helps
Nia had a 20 inch by 30 inch enlargement made of a photograph. She wanted to have it framed. How many inches of frame would it take to enclose the photo?
Answers
Answer: 100 inches
Step-by-step explanation:
From the question, we are given the information that Nia had a 20 inch by 30 inch enlargement made of a photograph and that she wanted to have it framed.
The number of inches of frame that she would use to enclose the photo will be gotten by calculating the perimeter of the shape and this will be:
= 2(length + width)
= 2(30 + 20)
= 2(50 inches)
= 100 inches
To enclose the photo, 100 inches of frame is needed.
Solve the equation to find the
value of x.
8.35x – 1.5 = 71.98
Answers
Add 1.5 to both sides:
8.35x=73.48
Divide both sides by 8.35:
x=8.8
Answer:
x = 8.8
General Formulas and Concepts:
Pre-Algerba
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
8.35x - 1.5 = 71.98
Step 2: Solve for x
[Addition Property of Equality] Add 1.5 on both sides: 8.35x = 73.48[Division Property of Equality] Divide 8.35 on both sides: x = 8.8There are 25 trees on the Jackson’s property. Twenty percent of the trees are oak trees. Which equation can be used to find the number of oak trees on the property?
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
StartFraction 100 times 5 Over 20 times 5 EndFraction = StartFraction 500 Over 100 EndFraction
StartFraction 20 times 4 Over 25 times 4 EndFraction = StartFraction 80 Over 100 EndFraction
StartFraction 20 divided by 4 Over 100 divided by 4 EndFraction = StartFraction 5 Over 25 EndFraction
Answers
Answer:
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
Step-by-step explanation:
Number of trees = 25
Percentage of aok trees = 20%
To obtain the Number of oak trees :
(Number of trees ÷ 1) ÷ (percentage ÷1)
(25 / 1) ÷ (20 / 1) = (25 /1) * (20 / 1) = 25 / 20
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
Help me outtttttttttto
Answers
Answer:
,
Step-by-step explanation:
hear is your answer please give me Some thanks
A traingle has an area of 35cm2 ANSWER CORRECT WITH EXPLANATION PLEASE
GOOD POINTS UP FOR GRABS
What could its dimensions be?
Base = Height =
Answers
Answer:
Base=2 cm
Height=35 cm
or
Base=5 cm
Height=14 cm
Or
Base=7 cm
Height=10 cm
Or
Base=10 cm
Height=7 cm
Or
Base=14 cm
Height=5 cm
Or
Base=70 cm
Height=1 cm
Or
Base=35 cm
Height=2 cm
Or
Base=1 cm
Height=70 cm
Step-by-step explanation:
We are given that
Area of triangle=[tex]35cm^2[/tex]
We have to find the dimension of triangle.
We know that
Area of triangle=[tex]\frac{1}{2}\times base\times height[/tex]
Using the formula
[tex]35=\frac{1}{2}\times base\times height[/tex]
[tex]base\times height=35\times 2=70[/tex]
Factor of 70 :2,5,7,10,14,35,70
Therefore, the dimension could be
Base=2 cm
Height=35 cm
or
Base=5 cm
Height=14 cm
Or
Base=7 cm
Height=10 cm
Or
Base=10 cm
Height=7 cm
Or
Base=14 cm
Height=5 cm
Or
Base=70 cm
Height=1 cm
Or
Base=35 cm
Height=2 cm
Or
Base=1 cm
Height=70 cm
Can someone please help me out?
The difference between two numbers is 16. The first number is three times the other number. What are the numbers?
A. 8 and 25
B. 8 and 24
C. 9 and 24
D. 9 and 25
No links or fake answers pls
Answers
24 is three times the value of 8 and when you subtract 8 from 24 you receive a total of 16.
9514 1404 393
Answer:
B. 8 and 24
Step-by-step explanation:
There are a number of approaches you can use here. One of them is to choose the only answer that makes any sense in the problem.
The problem tells you the numbers have a ratio of 3, so numbers like 8 and 25, 9 and 24, 9 and 25 cannot be the answer.
The only answer choice that makes any sense is B: 8 and 24.
__
If you want to work the problem, there are different ways you can do that. One of my favorite is to consider ratio units. The ratio of the two numbers is 3:1. The difference of the two numbers is 3-1 = 2 ratio units, which we are told is 16. Then each ratio unit represents 16/2 = 8. Then the numbers are ...
3×8 and 1×8 = 24 and 8.
Or, you can let a variable represent one of the numbers. If x is the first number, then the other number is 1/3x, and their difference is ...
x -1/3x = 16
2/3x = 16
x = 16(3/2) = 24
The numbers are 24 and 24/3 = 8.
__
Additional comment
You need to talk to your teacher about this question. The answer choices list the smaller number first, but the problem statement tells you the first number is 3 times the second number. The correct answer would be 24 and 8.
Which of the following functions shows the reciprocal parent function,
F(x) = 1, vertically stretched?
LG
F(x) =
6
5
O A. G(X) = 1 + 10
B. G(x) =
X 100
1
OC. G(x) =
X-7
O D. G() =
9x
Answers
Answer:
C
Step-by-step explanation:
but it's also horizontally stretched (see screenshot)
Answer:
The correct answer is G(x)=1/9x
Step-by-step explanation:
PLEASE HELP QUICKKKKKKKK
Answers
9514 1404 393
Explanation:
Using a random number generator to choose coefficients, we can substitute the required solution to find the constants in the equations. Here is one possible set of equations.
17x +7y +8z = 6
12x -6y +z = -16
14x +8y +11z = 16
__
Additional comment
"Standard form" requires the x-coefficient be positive. Truth be told, the random number generator came up with negative numbers for the first and last equations (on the second try). On the first try, it came up with a couple of zero coefficients. Such is the behavior of random numbers.
The trick with choosing a set of numbers "by hand" is doing it in such a way that the equations are independent.
Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 16,12,17,8,15,15,10,11,19,18
Answers
Answer:
[tex]Range = 11[/tex]
[tex]\sigma^2 = 12.1[/tex]
[tex]\sigma = 3.5[/tex]
Step-by-step explanation:
Given
[tex]Data: 16,12,17,8,15,15,10,11,19,18[/tex]
Solving (a): Range
This is calculated as:
[tex]Range = Highest - Least[/tex]
Where:
[tex]Highest = 19[/tex]
[tex]Least = 8[/tex]
So:
[tex]Range = 19 - 8[/tex]
[tex]Range = 11[/tex]
Solving (b): The population variance
First, calculate the population mean using:
[tex]\mu = \frac{\sum x}{n}[/tex]
So:
[tex]\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}[/tex]
[tex]\mu = \frac{141}{10}[/tex]
[tex]\mu = 14.1[/tex]
So, the population variance is:
[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]
[tex]\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}[/tex]
[tex]\sigma^2 = \frac{120.9}{10}[/tex]
[tex]\sigma^2 = 12.09[/tex]
[tex]\sigma^2 = 12.1[/tex] --- approximated
Solving (c): The population standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{\sigma^2[/tex]
[tex]\sigma = \sqrt{12.09[/tex]
[tex]\sigma = 3.5[/tex]
What is the 45th digit in the decimal equivalent of 3/7
Answers
Answer:
1/7 = 0.142857 since this decimal is repeating divide 45/6(number of repeating numbers) and it gives you 7.5 so you know that it repeats this sequence 7 times plus an extra 3 numbers so the 45th decimal is 2
Step-by-step explanation:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
Answer:
3/7 = 0.428571 which is also considered a number that keeps repeating.