![Calculate The Double Integral. 4x 1 + Xy DA, R = [0, 4] [0, 1]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/MalOYzrydcX9fCxQhxVoOONe4b0HhAup.png)
Answers
Answer:
[tex]20\ln(5)-16\approx16.18876[/tex]
Step-by-step explanation:
[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]
Related Questions
2 Log y= 1/2 Log 16-Log 2 + 2 Log 3
Answers
Answer:
Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).
The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.
Evaluate (99)3 using suitable identities
Answers
Answer:
297Step-by-step explanation:
(99)3 =
(99) x 3 =
(90 + 9) x 3 =
(90) x 3 + (9) x 3 =
90 x 3 + 9 x 3 =
270 + 27 =
297
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
Correction:Evaluate (99)^3 using suitable identities.
Solution:(99)^3 = (100 - 1)^3
since, (a - b)^2 = a^3 - b^3 - 3ab (a-b)
Where,
a = 100 andb = 1Now,
(99)^3
=> (100)^3 - (1)^3 - 3(100)(1)(100 - 1)
=> 1000000 - 1 - 3(100)(100 - 1)
=> 1000000 - 1 - 300 (99)
=> 1000000 - 1 - 29700
=> 970299 Ans.
how many terms of AP - 6. - 11 by 2 .minus 5 are needed to be the sum -25
Answers
Given:
The terms of a sequence are:
[tex]-6,-\dfrac{11}{2},-5[/tex]
To find:
The number of terms whose sum is -25.
Solution:
We have, the given sequence:
[tex]-6,-\dfrac{11}{2},-5[/tex]
Here, the first term is -6.
[tex]-\dfrac{11}{2}-(-6)=-5.5+6[/tex]
[tex]-\dfrac{11}{2}-(-6)=0.5[/tex]
Similarly,
[tex]-5-(-\dfrac{11}{2})=-5+5.5[/tex]
[tex]-5-(-\dfrac{11}{2})=0.5[/tex]
The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.
The sum of n terms of an arithmetic sequence is:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where, a is the first term, d is the common difference.
Putting [tex]S_n=-25,a=-6,d=0.5[/tex], we get
[tex]-25=\dfrac{n}{2}[2(-6)+(n-1)0.5][/tex]
[tex]-50=n[-12+0.5n-0.5][/tex]
[tex]-50=-12.5n+0.5n^2[/tex]
[tex]0=0.5n^2-12.5n+50[/tex]
Splitting the middle term, we get
[tex]0.5n^2-2.5n-10n+50=0[/tex]
[tex]0.5n(n-5)-10(n-5)=0[/tex]
[tex](0.5n-10)(n-5)=0[/tex]
Using zero product property, we get
[tex](0.5n-10)=0[/tex] and [tex](n-5)=0[/tex]
[tex]n=\dfrac{10}{0.5}[/tex] and [tex]n=5[/tex]
[tex]n=20[/tex] and [tex]n=5[/tex]
Therefore, the sum of either 5 or 20 terms is -25.
Andreas patio is composed of a rectangle and a semi circle as shown in the figure below which is the best estimate of the area of Andreas patio in square meters
Answers
Answer:
38.13m²
Step-by-step explanation:
We find the area of ;
Rectangule and semicircle
Area of rectangle :
Length * width
Length = 8m ; width = 3m
Area = 8 * 3 = 24m²
Area of semicircle = 1/2 πr²
Radius, r = 3m
A = 1/2 * 3.14 * 3²
A = 1/2 * 3.14 * 9
A = 14.13 m²
Area of patio :
(24 + 14.13)m²
= 38.13m²
Find the missing side lengths. Leave your answers as radicals in simplest form. Please help!! Due today
Answers
Answer:
[tex]m = 10\sqrt 3[/tex]
[tex]n = 10[/tex]
Step-by-step explanation:
Required
Find m and n
Considering the given angle, we have:
[tex]\sin(60) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60) = \frac{m}{20}[/tex]
Make m ths subject
[tex]m = 20 * \sin(60)[/tex]
[tex]\sin(60) =\frac{\sqrt 3}{2}[/tex]
So, we have:
[tex]m = 20 *\frac{\sqrt 3}{2}[/tex]
[tex]m = 10\sqrt 3[/tex]
Considering the given angle again, we have:
[tex]\cos(60) = \frac{Adjacent}{Hypotenuse}[/tex]
This gives:
[tex]\cos(60) = \frac{n}{20}[/tex]
Make n the subject
[tex]n = 20 * \cos(60)[/tex]
[tex]\sin(60) =\frac{1}{2}[/tex]
So, we have:
[tex]n = 20 *\frac{1}{2}[/tex]
[tex]n = 10[/tex]
Hello, can somebody explain to me if my answer is correct or not. Thank you and may God bless you. Have a nice day, bye!
Answers
As you can see the circle up corresponds to the base of the cone which is a circle, and the other part is the entire surrounding of it. Here’s a picture of i wasn’t clear enough:
The coordinates of cd are C(-7,-2) and D (-3,-5) Point E is the midpoint of cd What are the coordinates of the midpoint E?
Answers
The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:
x = [(-7) + (-3)] / 2 = -5
y = [(-2) + (-5)] / 2 = -3.5
Therefore the coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
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NO LINKS OR ATTACHMENTS PLEASE. Maria had picked 6 bags of oranges. How many glasses of orange juice could she make if each glass took one-quarter of a bag?
Answers
Answer:
24
Step-by-step explanation:
You just do 6 / 1/4 = 24
I am so lost. I need help.
Answers
Answer:
136in^2
Step-by-step explanation:
A bag contains only red marbles and blue marbles.
• The number of red marbles in the bag can be represented by x.
• The number of blue marbles is 12 more than 3 times the number of red marbles.
• There are a total of 48 marbles in the bag.
What is x, the number of red marbles in the bag?
Answers
Answer:
12 red marbles in the bag
Will mark brainliest!!
Consider the circumscribed angle. Determine the value of x.
1)
x = 12
2)
x = 29
3)
x = 4.75
4)
x = 17
Answers
Answer:
x = 12
Step-by-step explanation:
i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]
ii. 29 - 5 = 2x
iii. 24 = 2x
iv. x = 24/2
v. x = 12
Help soon would be greatly appreciated
The Kimbroughs'
home has a replacement value
of $82,700. They are insuring it for 80% of the
replacement cost.
a. What is the amount of insurance?
b. What is the amount of coverage for
personal property?
c. What is the amount of coverage
for loss of use?
d. What is the amount of coverage for the garage?
Answers
According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.
How to calculate the amount of each insurance?To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.
A. What is the amount of unsurance?$82,700 / 100 = 827827 * 80% = $66,160B. What is the amount of coverage for persona property?$82,700 / 100 = 827827 * 59% = $41,350C. What is the amount of coverage for loss of use?$82,700 / 100 = 827827 * 20% = $16,540D. What is the amount of coverage for the garage?$82,700 / 100 = 827827 * 10% = $8,270Learn more about insurance in: https://brainly.com/question/27822778
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Ed is using the recipe shown to make fruit salad. He wants to use 30 diced strawberries in his fruit salad. How many bananas, apples, and pears should Ed use in his fruit salad?
Fruit Salad Recipe - 4 bananas, diced. 3 apples, diced. 6 pears, diced. 10 strawberries, diced.
Answers
Answer:
12 bananas
9 apples
18 pears
Step-by-step explanation:
You are tripling the recipe.
10 x 3 = 3
4 x 3 = 12
3 x 3 = 9
6 x 3 = 18
What is the coordinate of the vertex of this following parabola?
Answers
Comparing the parabola's equation to the formula [tex]y = ax^2 + bx + c[/tex] in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression [tex]y = ax^2 + bx + c[/tex] to obtain the vertex's y-coordinate (k).
How are the axis and vertex determined?The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, [tex]y = ax^2 + bx + c[/tex] is a vertical line, [tex]x=b^2a[/tex].
What exactly is a vertex?The intersection of two lines or rays that create an angle is known as the vertex of the angle.
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UGHH WHAT DOES THAT MEANN?!! PLEASE TELL ME HOW TO WRITE!! It
Answers
Answer:
.45
Step-by-step explanation:
it wants u to divide 5.40 by 12
HOPE THIS HELPS CHU (≧w≦)
James is playing his favorite game at the arcade. After playing the game 3 times, he has 8 tokens remaining. He initially had 20 tokens, and the game costs the same number of tokens each time.
Answers
Games:3
After num:8
Difference 20-8=12tokens
12tokens/3 games= 4tokens/1game
PLEASE HURRY AND HELP!!!
Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
Answers
Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.
By observing the given options we conclude that the third option is linear and proportional as,
6 ÷ 2 = 3 and 12 ÷ 2 = 6.
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(didnt mean to select an answer) can someone help me with this, and if possible please explain it I don't know how to do direct variation and all that
Answers
9514 1404 393
Answer:
(b) y = -5x
Step-by-step explanation:
When "y varies directly as x" the equation for that is ...
y = kx . . . . . . . for some constant k
The value of k can be found by solving for it:
k = y/x . . . . . . divide by x
So, the given point (x, y) = (2, -10) tells you the value of k is ...
k = -10/2 = -5
and the direct variation equation is ...
y = -5x
_____
Additional comments
There are a couple of other useful facts about direct variation. When you compare the equation to the slope-intercept form equation for a line, ...
y = mx + b
you see that b=0 and the slope, or rate of change, (m) is the same as k.
The y-intercept of 0 means that the graph of any direct-variation equation must go through the origin. (If it does not, then the variation is not direct.)
The area of a triangular-shaped rug is 21 square yards and the height is 3 yards. Find the base. a. 7 yd c. 16 yd b. 10 yd d. 14 yd
Answers
Area of a triangle = 1/2(base)(height)
21 = 1/2(b)(3)
Multiply both sides by 2
42 = 3b
Divide both sides by 3
b = 14
Please helps with all steps to solve the problem.
Answers
The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Find inequality ?Both equations and inequalities are mathematical phrases created by connecting two expressions.
The equal sign (=) in an equation denotes that the two expressions are regarded as equal.
In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
Given the inequality:
-3(4 – x) 6 < 9 – 2x
Solving the inequality:
(-12 + 3x)6 < 9 - 2x
-72 + 18x < 9 - 2x
20x < 81
x < 4.05
Therefore the solution to the inequality is (-∞, 4.05)
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I NEED HELP I HAVE BEEN DOING THIS FOR HOURS I ACTUALLY HAD A MENTAL BREAKDOWN PLEASE HELP ME I WILL MARK BRAINLIEST
Answers
Answer:
x=8
Step-by-step explanation
Vertical angles are always congruent which means they are equal
Since we know this we can simply set the two angle equal to each other so...
5x-5=2x+19
Now what we do is add five to 19 and subtract 2x from 5x to get
3x=24
simply divide 24 by 3 to isolate x and now we have
x=8
Hope this was helpful!
Is the point (4,0) on the parabola given by the equation: y=x^2-4x? Explain your answer
HELPP PLEASE ILL MARK BRAINIEST
Answers
Helpppppp meeeee pleaseeeeeeee
Answers
Answer:
The answer is 7/9
Step-by-step explanation:
Had this on my quiz one time
Answer:
7-9
Step-by-step explanation:
Find Area of the triangle
Answers
Answer:
A = 0.5 × [ sqrt(17^2 - 15^2) ] × 15 + 0.5 × [ sqrt(25^2 - 15^2) ] × 15 = 210 in^2
A moving sidewalk carries people at a rate of 400 feet per minute. How long is this moving sidewalk if it takes 4 minutes to travel from one end to the other?
A 25 feet
B 100 feet
C 404 feet
D 1600 feet
*process
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I really need help with this question
Answers
Answer:
S= 76, T= 76, U= 104, R= 104
Y=104, V= 104, X= 76, W= 76
Step-by-step explanation:
Opposite Angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent (equal in measure).
U and V are alternating angles
so U and are 104
i d k the last one am so sorry
The probability that you get to the bus stop on time is 0.25. The probability that the bus arrives on time is 0.55. What is the probability that you will get to the bus stop on time and the bus arrives on time?
PLEASE HELP!! i’ll mark you brainliest please !
Answers
Answer:
P(A) * P(B)
.25*.55
.1375
Step-by-step explanation:
P(A) * P(B)
.25*.55
What does the variable t stand for in parametric equations?
Answers
Answer:
t is the independent variable of time
Step-by-step explanation:
t is the independent variable of time
which of the following shows the numbers in the box shown below listed in the increasing order
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hello, i need helpw ith my math question
Answers
The three ways to purchase a vehicle include: (1) On lease (2) On hire purchased and (3) On cash basis
How to purchase a vehicle?A vehicle can be purchased on the following ways:
Lease: This involves granting the user access on the property over a period of time before he could make paymentHire purchase: In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis Cash: In this method the buyer pays cash at prompt or on the point of purchaseAdvantages include:
It places the buyer on good life without cashHe enjoys the luxurious lifeDisadvantages:
He can run away with the vehicleThe seller looses in cash of accident taking the life of the buyerAdditional expenses include
cost of maintenance repairsfuelingLearn more about leasing a vehicle on https://brainly.com/question/29216664
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