The valid proof approaches are: b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) and e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1))
Approach a is invalid because it only shows that P holds for some integers, but not for all integers.
Approach c is invalid because it only shows that P holds for non-negative integers, but not necessarily for negative integers.
Approach d is invalid because it only shows that P holds for non-negative integers and negative even integers, but not necessarily for negative odd integers.
Approach f is invalid because it only shows that P(0) and P(1) imply P(-k) for all positive integers k, but not necessarily for all integers.
Approach b is a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1) and P(-1), and that if P holds for an arbitrary integer k, then it also holds for k+1.
Approach e is also a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1), P(-1), and that if P holds for a positive integer k, then it also holds for k+1, and if it holds for a negative integer -k, then it also holds for -(k+1).
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Happy Corporation leased a building from Sensor Company. The ten-year lease is recorded as a capital lease. The annual payments are $10,000, and the recorded cost of the asset is $67,100. The straight-line method is used to calculate depreciation. Which of the following statements is true?
a. Depreciation expense of $6,710 will be recorded each year.
b. Depreciation expense of $10,000 will be recorded each year.
c. No depreciation expense will be recorded by Happy Corporation.
d. No interest expense will be recorded by Happy Corporation.
2. In 2017, Aspinwall Company issued $200,000 of bonds for $175,000. If the face rate of interest was 9% and the effective rate of interest was 7.99%, how would Aspinwall calculate the interest expense for the first year on the bonds using the effective interest method?
a. $175,000 × 7.99%
b. $175,000 × 9%
c. $10,000 × 7.99%
d. $10,000 × 9%
3.
Use the information below for Focal Point Corp. for 2017 and 2018 to answer the following question:
Retained earnings, December 31, 2017 $300,000
Retained earnings, December 31, 2018 345,000
Dividends payable, December 31, 2017 19,000
Dividends payable, December 31, 2018 29,000
Net income—2018 150,000
Assume that there were no retained earnings transactions other than those dealing with dividends and net income. How much dividends did Focal Point declare during 2018?
a. $95,000
b. $105,000
c. $140,000
d. $150,000
1) Option a. Depreciation expenses of $6,710 will be recorded each year. is correct.
2) Option c. 175,000 × 7.99% is correct
3) Option b. $105,000 is correct.
1) The annual payments of $10,000 and the recorded cost of the asset of $67,100 are used to calculate the annual depreciation expense using the straight-line method.
Depreciation expense = (Recorded cost of the asset - Residual value) / Useful life
= ($67,100 - $0) / 10 years
= $6,710 per year.
2) The effective interest method calculates interest expense by multiplying the carrying value of the bond (i.e., the amount at which it was issued minus any discount or plus any premium) by the effective interest rate (i.e., the rate that discounts the bond's future cash flows to the carrying value).
Therefore, the interest expense for the first year on the bonds would be $175,000 × 7.99% = $13,965.
3) The dividends declared during the year can be calculated as follows:
Dividends declared = Net income - Increase in retained earnings - Decrease in dividends payable
= $150,000 - ($345,000 - $300,000) - ($29,000 - $19,000)
= $105,000.
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The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent
If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%
To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.
Let the cost price of each article be "C" and the selling price of each article be "S".
Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:
20C = 16S
We can simplify this equation to:
S = (20/16)C = (5/4)C
Now, let's calculate the profit earned on the sale of 16 articles:
Profit = Total Selling Price - Total Cost Price
Profit = 16S - 20C
Profit = 16(5/4)C - 20C
Profit = 5C/2
The profit earned is 5C/2. The profit percent can be calculated as:
Profit Percent = (Profit / Cost Price) x 100
Profit Percent = (5C/2) / (20C) x 100
Profit Percent = 25%
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At maxs party 3/12 of the guests are 10 year old and 7/12 of guests are 11 year old what fraction of the guests are 10 or 11 years old
The fraction of the guests are 10 or 11 years old is 5/6
A fraction represents a part of a whole, where the whole is divided into equal parts.
To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.
3/12 of the guests are 10 years old, which can be simplified to 1/4.
7/12 of the guests are 11 years old.
Therefore, the fraction of guests who are 10 or 11 years old is
1/4 + 7/12 = 3/12 + 7/12
Add the fractions
= 10/12
Simplify the fraction
= 5/6
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What is the area of this figure?
6 mm
4 mm
3 mm
5 mm
3 mm
15 mm
3 mm
9 mm
Write your answer using decimals, if necessary. Square millimeters
Based on the given data, The shape's whole surface area is about 252 mm².
Based on the image, the shape appears to be a set of rectangles with different lengths and widths.
To find the area of this shape, we can break it down into smaller rectangles and add up their areas.
Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:
Area1
= 6 mm × 4 mm
= 24 mm²
Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:
Area2
= 6 mm × 3 mm
= 18 mm²
The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:
Area3
= 6 mm × 5 mm
= 30 mm²
The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:
Area4
= 6 mm × 3 mm
= 18 mm²
The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:
Area5
= 6 mm × 15 mm
= 90 mm²
The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:
Area6
= 3 mm × 9 mm
= 27 mm²
Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:
Area7
= 5 mm × 9 mm
= 45 mm²
To find the total area of the shape, we can add up the areas of all seven rectangles:
Total Area
= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7
= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²
= 252 mm²
Therefore, the total area of the shape is approximately 252 mm².
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The volume of two similar figures are given. The surface area of the larger figure is given. Find the surface area of the smaller figure.
V=4000m^3
V=6912m^3
S.A.=2304m^3
Te surface area of the smaller figure based on the ratio is 1600m²
Calculating the surface area of the smaller figure.The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding sides.
Let x be the scale factor between the smaller and larger figures.
Then we have:
(x³)/(4000) = 6912
x³ = 6912/4000
x³ = 1.728
Taking the cube root of both sides, we get:
x = 1.2
So the scale factor from the larger figure to the smaller figure is 1:1.2.
The surface area of a similar figure is proportional to the square of the scale factor.
So we can use the scale factor to find the ratio of the surface areas:
SA(smaller) / SA(larger) = 1/(1.2)²
We know that the surface area of the larger figure is 2304m^2, so we can solve for the surface area of the smaller figure:
SA(smaller) = 2304 * 1/(1.2)²
SA(smaller) = 1600m²
Therefore, the surface area of the smaller figure is 1600m²
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Maggie crochets squares to make a blanket. She has 6 squares made. She then makes 6 squares each hour for 3 hours. Determine which of the following represent the linear relationship described.
The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)
How to determine the linear relationshipLet x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.
Initially, Maggie has 6 squares made,
so y = 6 when x = 0.
For each hour that she spends crocheting squares, Maggie makes 6 more squares.
Therefore, the relationship between x and y is:
y = 6 + 6x
This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.
This is represented by graph (b)
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h(x)= -x + 5, solve for x when h(x) = 3
According to the given information, the solution to H(x) = 3 is x = 2.
What is equation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS
To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:
H(x) = -x + 5
3 = -x + 5
Subtracting 5 from both sides, we get:
-2 = -x
Multiplying both sides by -1, we get:
2 = x
Therefore, the solution to H(x) = 3 is x = 2.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A coffee maker is on sale for 45$. If the sales tax is 7%, how much will the buyer spend altogether?
Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at
Step-by-step explanation:
Let X >0 denote a random variable with p.d.f. fx(2) and c.d.f. Fx (I). Assume Fx() is monotone increasing, and let Y = FX(X). That is, Y is a random variable that takes the value Fx (1) when X = r. Find fy(y). Mark the correct answer (a) fy(y) = 1,0
The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).
We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).
Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).
To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).
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Use the internet or some other reference to find the populations and areas(in square miles) of India, China, Argentina, the United States, and Egypt. Round each population to the nearest million and each area to the nearest thousand square miles
The populations of the listed countries are
India is 1.366 billion
China is 1.397 billion
Argentina is 45 million
the United States is 332 million
and Egypt is 102 million people.
Let's start with India. According to the World Bank, India's population is approximately 1.366 billion people, which is the second-largest population in the world after China. India's land area is approximately 1.269 million square miles.
Moving on to China, it has the largest population in the world, with approximately 1.397 billion people. China's land area is approximately 3.705 million square miles, making it the fourth-largest country in terms of land area.
Argentina, on the other hand, has a population of approximately 45 million people, with a land area of approximately 1.073 million square miles. This makes it the eighth-largest country in the world in terms of land area.
The United States has a population of approximately 332 million people, and its land area is approximately 3.796 million square miles. It is the third-largest country in terms of land area and the fourth-largest in terms of population.
Lastly, Egypt has a population of approximately 102 million people, with a land area of approximately 386 thousand square miles. It is the 30th largest country in terms of land area and the 14th most populous country in the world.
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x + 3y = 12 x = -2y + 8
Answer:
x = 0
y = 4
Step-by-step explanation:
x + 3y = 12 x = -2y + 8
-2y + 8 + 3y = 12
y + 8 = 12
y = 4
Now put 4 in for y and solve for x
x + 3(4) = 12
x + 12 = 12
x = 0
Let's Check
0 + 3(4) = 12
12 = 12
So, x = 0 and y = 4 is the correct answer!
Tell me pls what is the answer to this question? 3=x+3-5x??????????
Answer:
[tex]\boxed{x=0}[/tex]
Step-by-step explanation:
We need solve for x
[tex]3=x+3-5x[/tex]
substract 3 to both sides of the equation:
[tex]3-3=x+3-5x-3\\0=-4x[/tex]
divide both sides of the equation by -4
[tex]\frac{0}{-4}=\frac{-4x}{-4}\\0=x\\\equiv x=0[/tex]
The value of "x" that satisfies the equation is x=0,
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
12. INTERPRETING A LINEAR FUNCTION The table shows the length y
(in inches) of a person's hair after x months.
a. Write and graph a linear function that relates y to x.
b. Interpret the slope and the y-intercept.
Months, Hair
X
0
3
6
Length, y
11.0
12.5
14.0
Answer:
a. To write a linear function that relates the length of hair to the number of months, we need to find the slope and y-intercept of the line that passes through the given points. We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Using the given data, we can find the slope as:
m = (y2 - y1) / (x2 - x1) = (14.0 - 11.0) / (6 - 0) = 0.5
And we can find the y-intercept as:
b = y - mx = 11.0 - 0.5(0) = 11.0
So, the linear function that relates the length of hair to the number of months is:
y = 0.5x + 11.0
We can also graph this function as a straight line, passing through the given points (0, 11.0), (3, 12.5) and (6, 14.0), as shown below:
linear function graph
b. The slope of the function is 0.5, which means that the length of hair increases by 0.5 inches every month. In other words, the slope represents the rate of change of hair length with respect to time.
The y-intercept of the function is 11.0, which means that if the person doesn't cut their hair at all (i.e., x = 0), their hair length would still be 11.0 inches. In other words, the y-intercept represents the starting value of the hair length.
(please mark my answer as brainliest)
The selling price of a table is ₹ 5400.If the shopkeeper makes a profit of 20%, find the cost
price of the table?
Sure! I can help you with that.
First, we should calculate the profit made by the shopkeeper. To calculate the profit, we will multiply the selling price of the table with 20%, which is 20% of 5400, or 1080.
Next, we should subtract the profit from the selling price to find the cost price of the table.
The cost price of the table = 5400 - 1080
The cost price of the table = 4320
Therefore, the cost price of the table is ₹ 4320.
A triangle can have sides with measures: 10, 12, 24
True
False
Answer:
False.
Step-by-step explanation:
A triangle's two smaller sides have to add to be bigger than the larger side.
Answer:
False, that cannot exist by the hypotenuse rule
Hope it helps!
1 Find the value of x.
i’m like struggling
Answer: 23 degrees
Step-by-step explanation:
Assuming that 117 is the entire angle we can find that:
94+x = 117
Subtract 94 from both sides:
x = 117-94
x = 23 degrees
Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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what is the specificity for the test based on these screening results (rounded to three decimal places)?
The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).
To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).
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What is the answer I keep getting 32
Answer:
2 9/14
Step-by-step explanation:
Consider the following equation
-16p + 37 = 49 - 21p
the solution to the equation -16p + 37 = 49 - 21p is p = 12/5. The equation -16p + 37 = 49 - 21p is a simple linear equation with one variable, p.
Linear equations are equations where the highest exponent of the variable is one, and they can be solved using algebraic techniques.
To solve this equation, we need to isolate the variable, p, on one side of the equation. We can start by simplifying the equation by combining like terms. To do this, we can add 21p to both sides of the equation, which gives us:
-16p + 37 + 21p = 49
Next, we can combine the terms -16p and 21p, which gives us 5p. So, the equation becomes:
5p + 37 = 49
We can further simplify the equation by subtracting 37 from both sides, which gives us:
5p = 12
Finally, we can solve for p by dividing both sides of the equation by 5:
p = 12/5
So, the solution to the equation -16p + 37 = 49 - 21p is p = 12/5.
In summary, the given equation is a simple linear equation that can be solved using algebraic techniques. We can isolate the variable, p, on one side of the equation by combining like terms and simplifying the equation. Finally, we can solve for p by dividing both sides of the equation by the coefficient of p.
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How many students are in the band this year? how do you know?
Answer:
Step-by-step explanation:
which band?
A beverage company delivers three type of drinks which are Milk(M), Carbonateddrinks(C ) and Juice (J) to four stores ( A, B, C, D) for a period of two month. The number of pets of each type of beverage delivered to four stores in first monthis
represented in Matrix K and second month is Matrix L
8 4 3
2 2 2
1 3 1
3 1 3
M C J
A
B
K
C
D
1 3 1
2 7 2
8 3 4
9 2 6
MCJ
A
B
L
CD
i. Calculate the total number of pets delivered over the period of 2 months to eachstore. Suppose, the price charged for pet of each type of drink is given by the matrix. 225
195
212
M
C
J
ii. Calculate the cost of each store ( A, B, C, D) on the beverages in two months
The cost of each store in two months is: Store A is 4281, Store B is 5485, Store C is 3153, and Store D is 6413.
To calculate the total number of pets delivered over the period of 2 months to each store, we need to add the corresponding elements of matrix K and matrix L. The result will be a new matrix representing the total number of pets delivered to each store.
So, we have: Matrix K:
| 8 4 3 |
| 2 1 3 |
| 1 3 2 |
| 7 2 6 |
Matrix L:
| 1 3 2 |
| 8 4 9 |
| 2 6 3 |
| 4 9 2 |
Total pets delivered to each store:
| 9 7 5 |
| 10 5 12 |
| 3 9 5 |
| 11 11 8 |
To calculate the cost of each store in two months, we need to multiply the total number of pets delivered to each store by the price of each type of drink, as given by the matrix:
| 225 195 212 |
So, the cost of each store in two months is:
Store A: (9 × 225) + (7 × 195) + (5 × 212) = 4281
Store B: (10 × 225) + (5 × 195) + (12 × 212) = 5485
Store C: (3 × 225) + (9 × 195) + (5 × 212) = 3153
Store D: (11 × 225) + (11 × 195) + (8 × 212) = 6413
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Divide negative 6 and 2 over 5 ÷ negative 4 and 3 over 7. Negative 224 over 155 224 over 155 negative 519 over 35 519 over 35
By dividing we get: -6/2 ÷ 5 = -6/10 = -3/5, -4/3 ÷ 7 = -4/21, -224 ÷ 155 = -1.445, 224 ÷ 155 = 1.448, -519/35 = -14.83, 519/35 = 14.83.
.
To divide fractions, we need to remember the rule: "invert and multiply." This means that we take the reciprocal of the second fraction and then multiply it by the first fraction. For example, to divide -6/5 by 2/5, we invert 2/5 to get 5/2 and then multiply it by -6/5 to get -6/5 x 5/2 = -15/2. Similarly, to divide 224/155 by -1, we invert -1 to get -1/1 and then multiply it by 224/155 to get -224/155. To divide 519/35 by itself, we simply get 1 as the answer.
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Complete question:
Divide:
1. negative 6 and 2 over 5
2. negative 4 and 3 over 7
3. negative 224 over 155
4. 224 over 155
5. negative 519 over 35
6. 519 over 35
Let X be a random variable with the probability mass function (PMF) given below (figure not drawn to scale), where a=0, b=0.23, c=0.13, d=0.10, e=0.15. a. Find the cumulative distributive function (CDF) Fx(3). Round answer to two decimal points.
The cumulative distributive function (CDF) Fx(3) is 0.61.
The cumulative distributive function (CDF) of a random variable X is the probability that X takes a value less than or equal to x. In this case, we are asked to find Fx(3).
Since the random variable X is given with a probability mass function, we can calculate the CDF by summing the probabilities of X being less than or equal to 3. This can be expressed as: [tex]Fx(3) = P(X<=3).[/tex]
For X = 0, P(X<=3) = 0.23.
For X = 1, P(X<=3) = 0.23 + 0.13 = 0.36.
For X = 2, P(X<=3) = 0.23 + 0.13 + 0.10 = 0.46.
For X = 3, P(X<=3) = 0.23 + 0.13 + 0.10 + 0.15 = 0.61.
Therefore, the cumulative distributive function (CDF) Fx(3) is 0.61.
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6(x - 2) -3 ≥ -4 ( -3 + 9) +10
Answer:
2x=5 > -14
Step-by-step explanation:
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3 3
2x=5 > -14
What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
The surface area of the rectangular prism is 170 square yards.
What is the surface area formula?Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.
To calculate the surface area of the rectangular prism, add the areas of each of its faces.
The front and back faces are 5 yards by 6 yards in size, so each has an area of:
5 yards x 6 yards equals 30 square yards
The top and bottom faces are 5 yards by 5 yards, so each has an area of:
5 yards x 5 yards equals 25 square yards
The two side faces have dimensions of 6 yards by 5 yards, for a total area of:
30 square yards = 6 yards x 5 yards
As a result, the surface area of the rectangular prism is as follows:
Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area
= 30+30+25+25+30+30
= 170 square yards
As a result, the rectangular prism has a surface area of 170 square yards.
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hi could someone help me
The listed price of the TV that Wayne bought was $947.37
What was the listed price of the TV?Here we know that Wayne pays $660 for a TV whose price was marked down by (30 + 1/3)%
We can rewrite that discount as 0.30333... in a decimal form (get that just by dividing the percentage by 100%)
Then if the lited price of the TV is P, we can write the equation for the discount as follows:
660 = P*(1 - 0.3033...)
The number that we subtract is the percentage in decimal form.
Solving this for P gives:
P = 660/(1- 0.3033...) = 947.37
The listed price was 947.37 dollars.
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HELP!!
Write a quadratic equation in standard form that has solutions of -3 and -4.
Answer:
If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:
(x + 3)(x + 4) = 0
To convert this to standard form, we can multiply out the factors:
x^2 + 7x + 12 = 0
Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:
x^2 + 7x + 12 = 0
Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order.
y dA, D is bounded by y = x − 6; x = y2
D
The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.
The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.
Given, the double integral ∫∫yA and the region y = x-6 and x = y²
y = x-6
x = y²
y² = y +6
y² - y - 6 = 0
y² - 3y +2y - 6 = 0
(y-3) (y+2) = 0
y = 3 and y = -2
[tex]\int\int\limits_\triangle {y} \, dA\\ \\[/tex]
= [tex]\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}[/tex]
The value for the double integral is 125/12.
Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.
Learn more about Double Integral:
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What sum of money amounts to Rs 8700 in 3 years at the rate of 24% per annum?
Answer:
e. 8/00 ggg： What sum of money amounts to Rs. 8700 in 3 years at the rate of 24% per annum? [Ans: Rs. 5058.14]
Step-by-step explanation: