Answer:
Step-by-step explanation:
The following methods can be used by Kaitlyn to check her work:
She could substitute 7 for n and add.
This is a valid way to check her work as she found the value of the unknown to be 7, so substituting 7 for n should give her the same result.
She could subtract 6 from 13 and check that the answer is 7.
This is also a valid way to check her work as n + 6 = 13 can be rewritten as n = 13 - 6, which simplifies to n = 7.
She could put all the tiles in 1 pile and count them to see if there are 13.
This is a practical way to check her work, as she started with 6 tiles and added 7 more to make 13, so there should be a total of 13 tiles. Counting all the tiles would confirm this.
Therefore, the correct options are:
She could substitute 7 for n and add.
She could subtract 6 from 13 and check that the answer is 7.
She could put all the tiles in 1 pile and count them to see if there are 13.
Can someone help me with this math problem, ASAP?
Answer: [tex]\sqrt{\text{x}-7}-10[/tex]
Work Shown:
[tex]f(\text{x}) = \sqrt{\text{x}-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-1-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-7}-10[/tex]
Explanation:
I replaced each copy of x with x-1. Then I combined like terms. Doing this will shift the graph 1 unit to the right.
in any given month there are at least 20 workdays each week, then how many workdays would roger have in the month if the month starts on a monday ? (hint: Draw a calendar to show how you arrive at your answer)
Answer:
120 because 20 x 6 = 120 when u take of sunday it will be 6 days
Step-by-step explanation:
d(t) = 16t2 -23t + 18
Answer:
t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32
Step-by-step explanation:
Solve for t:
16 t^2 - 23 t + 18 = 0
Divide both sides by 16:
t^2 - (23 t)/16 + 9/8 = 0
Subtract 9/8 from both sides:
t^2 - (23 t)/16 = -9/8
Add 529/1024 to both sides:
t^2 - (23 t)/16 + 529/1024 = -623/1024
Write the left hand side as a square:
(t - 23/32)^2 = -623/1024
Take the square root of both sides:
t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32
100 POINTS HELPP PLEASE BRAINLIEST
The percent abundance of the medium nails in the sample is given as follows:
27.07%.
How to obtain the percent abundance?The percent abundance is obtained applying the proportions in the context of the problem.
The total length of nails is given as follows:
67 x 2.5 + 18 x 5 + 10 x 7.5 = 332.5 cm.
The length relative to medium nails is given as follows:
18 x 5 = 90 cm.
Meaning that the percent abundance is given as follows:
90/332.5 x 100% = 27.07%.
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If Catlain had 3 apples and Josh had 75% more apples than Catlain. How many apples did Josh have?
Answer:
5 apples
Step-by-step explanation:
Find the slope of the tangent line to the curve defined by 4x2+5xy+y4=370
at the point (−9,−1)
Answer:
The slope of the tangent line to the curve at the given point is -11/7.
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve. At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
[tex]4x^2+5xy+y^4=370[/tex]
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
Begin by placing d/dx in front of each term of the equation:
[tex]\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370[/tex]
Differentiate the terms in x only (and constant terms):
[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0[/tex]
Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:
[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]
Use the product rule to differentiate terms in both x and y.
[tex]\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}[/tex]
[tex]\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]
[tex]\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]
Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:
[tex]\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}[/tex]
To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}[/tex]
Therefore, slope of the tangent line to the curve at the given point is -11/7.
By first calculating the size of angle LMN,
calculate the area of triangle MNL.
You must show all your working.
I
+
M
4.8 cm
Answer cm²
38/43 Marks
L
8
7.2 cm
38°
14%
Not drawn
to scale
N
The area of triangle MNL is approximately 10.44 cm².
What is the sine rule?
The sine rule, also known as the law of sines, is a formula used in trigonometry to find the lengths of the sides and the measure of the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:
[tex]a/sin A = b/sin B = c/sin C[/tex]
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides. The sine rule can be used to find the length of a side of a triangle or the measure of an angle if the other two sides and the included angle are known, or if two sides and the angle opposite one of them are known.
To find the area of triangle MNL, we need to first calculate the length of side NL using the sine rule:
sin(38°) / NL = sin(90°) / 4.8
NL = sin(38°) / sin(90°) * 4.8
NL = sin(38°) * 4.8
NL ≈ 2.9 cm
Now we can find the area of the triangle using the formula:
[tex]Area = (1/2) * base * height[/tex]
[tex]Area = (1/2) * 7.2 * 2.9[/tex]
Area ≈ 10.44 cm²
Therefore, the area of triangle MNL is approximately 10.44 cm².
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write two monomials with the quotient:
[tex]24 {a}^{2} {b}^{5} [/tex]
Answer:
Two monomials with the quotient 24a2b5 are:
12a b³
48a³ b²
Step-by-step explanation:
Can you please solve? Thanks
The numeric values of the composite functions are given as follows:
u(w(3)) = 19.w(u(3)) = -8.How to define the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the equation with rile presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, which for this example is g(x), serves as the input of the outer function, which for this example is f(x).
Hence the functions are given as follows:
u(w(x)) = u(-2x²) = -(-2x²) + 1 = 2x² + 1. w(u(x)) = w(-x + 1) = -2(-x + 1)².At x = 3, the numeric values are given as follows:
u(w(3)) = 2(3)² + 1 = 19.w(u(3)) = -2(-3 + 1)² = -2 x 4 = -8.More can be learned about functions at https://brainly.com/question/24808124
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Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is B. x² + y² - 41 = 0.
What is Circle?A circle is a round, two-dimensional shape with all points on its boundary equidistant from its center.
Since the center of the circle is O(0,0), the equation of the circle will have the form x² + y² + ax + by + c = 0. To find the values of a, b, and c, we can use the fact that point B(4, 5) lies on the circle. Substituting the coordinates of B into the equation and simplifying, we get:
4² + 5² + a4 + b5 + c = 0
16 + 25 + 4a + 5b + c = 0
41 + 4a + 5b + c = 0
We now have one equation with three variables, so we need more information. Since the center of the circle is (0,0), we know that the distance from the center to any point on the circumference is equal to the radius of the circle. The distance between points (0,0) and (4,5) is the length of the line segment joining them, which can be found using the distance formula:
[tex]\sqrt{(4-0)\² + (5-0)\²} = \sqrt{(16+25) }= \sqrt{41}[/tex]
Therefore, the radius of the circle is √(41). We can use this fact to eliminate one of the variables in the equation we derived earlier. Since point (0,0) lies on the circle, we can substitute its coordinates into the equation to get:
41 + 0a + 0b + c = 0
c = -41
Now we can substitute this value of c back into the equation we derived earlier to get:
41 + 4a + 5b - 41 = 0
4a + 5b = 0
Finally, we have two equations with two variables, which we can solve to get:
a = -5/4
b = 4/5
Substituting these values into the equation of the circle, we get:
x² + y² - 5x/4 + 4y/5 - 41 = 0
Multiplying by 20 to eliminate fractions, we get:
20x² + 20y² - 25x + 16y - 820 = 0
Simplifying, we get:
x² + y² - 25/4x + 4/5y - 41 = 0
Which is equivalent to:
x² + y² - 41 = 0
So the answer is B. x²+ y² - 41 = 0.
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Question 3
Mr Dladla wants to open a training company, he will be training Learnerships and
ABET. He plans to operate at South Gate Mall with the total Market share of 4500
customers per month. He knows that he can only expect 50% of the market share for
the year.
His selling price will be R500 and the cost of running his course in R300. His training
company opens 20 days per month.
(10)
3.1 Calculate his gross profit per day and thereafter
Answer:
To calculate Mr. Dladla's gross profit per day, we first need to calculate his total revenue and total cost per month:
Total revenue per month = Selling price x Expected market share per month
Total revenue per month = R500 x (50% of 4500 customers) = R112,500
Total cost per month = Cost per course x Number of courses per month
Total cost per month = R300 x 20 days = R6,000
Gross profit per month = Total revenue per month - Total cost per month
Gross profit per month = R112,500 - R6,000 = R106,500
To calculate his gross profit per day, we can divide the gross profit per month by the number of days the training company opens per month:
Gross profit per day = Gross profit per month / Number of days per month
Gross profit per day = R106,500 / 20 days = R5,325 per day
Therefore, Mr. Dladla's gross profit per day is R5,325.
Step-by-step explanation:
Compare center and variations of histograms 1 questions with part A, B, C, D PLEASE HELP ME 40 POINTS SUPER EASYY
The requried (a) median for the chocolate candy and nonchocolate candy sales are $3040 and $1566.5 respectively. (b) The range for the chocolate candy sales, the range is ($1941, $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).
What is a histogram?A histogram is a graphical representation of the distribution of a set of numerical data. It consists of a set of rectangles, where the area of each rectangle is proportional to the frequency (or count) of the observations falling within a particular interval, called a bin.
Here,
A. The interval for the median for each data set can be found by arranging the data in ascending order and finding the middle value. For the chocolate candy sales, the median falls in the interval of 2800-3,099 dollars. While for the Nonchocolate candy, it falls under 1300 -1599
The median for the chocolate candy sales = $3040
The median for the Nonchocolate candy sales = $1566.5
B. The range for each data set can be found by subtracting the minimum value from the maximum value. For the chocolate candy sales, the range is ($1941, to $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).
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how do you get an answer for dot plots
By answering the above question, we may state that Find any dots that expressions are distant from the other dots to identify outliers. They might be anomalies and need more research.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. .
You should check for the following data when interpreting a dot plot:
Determine the dot plot's lowest and maximum values by using the range concept.
Shape: Search for any patterns or groups of dots that could point to a certain data distribution.
Central Tendency: Locate the dot plot's centre to ascertain the typical value of the dataset. Finding the data's median or mean can be used to achieve this.
Find any dots that are distant from the other dots to identify outliers. They might be anomalies and need more research.
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13. Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area y in square feet that she can surround with the fencing that she has, where x is the width in feet of the rectangle.
We can write the quadratic equation as -
y = - (x - 25)² + 625
What is the general form of a quadratic equation?The general form of a quadratic equation is -
y = ax² + bx + c
where -
a, b and c are constants.
Given is that Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area {y} in square feet that she can surround with the fencing that she has, where the breadth is width {x} in feet of the rectangle.
The given coordinates on the parabola are -
(8, 336)
(42, 336)
(25, 625)
Here, the point (25, 625) represents the vertex (h, k) of the parabola.
We can write the equation of parabola as -
y = a(x - h)² + k
y = a(x - 25)² + 625
For the point (8, 336), we can write -
336 = a(8 - 25)² + 625
336 - 625 = a(8 - 25)²
a(8 - 25)² = - 289
a(- 17)² = -289
a = -289/289
a = -1
So, we can write the quadratic equation as -
y = - (x - 25)² + 625
Therefore, we can write the quadratic equation as -
y = - (x - 25)² + 625
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I need help, please its due today
Answer:??? Bio?
Step-by-step explanation:give a good expample
Amira has 27 feet of ribbon to make 5 braided bracelets.How much ribbon goes to each bracelet
27 ÷ 5 = 5.4
∴ 5.4 feet of ribbon goes to each bracelet.
Solve for x:
−2x+5=19
Answer: -7
Step-by-step explanation:
-2x+5=19
-5 |-5
-2x=14
-2x/-2 = 14/-2
x = -7
Solve the inequality
The value if x in the inequality is x > -2 2/13
What is inequality?The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.
greater than is represented by >
less than is represented by <
greater than or equal to is represented by ≥
less than or equal to is represented by ≤
-5/7(21x+35)<1/3(9-6x)
-15x -25 < 3-2x
collect like terms
-25-3 < 15x -2x
-28 < 13x
-28/13 < x
therefore x > -28/13
x> - 2 2/13
therefore the value of x in the inequality is x > -2 2/13
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How many sixths does it take to make the same amount as 1/3
Answer: Two 1/6
Step-by-step explanation:
It takes two 1/6 to make the same amount as 1/3 because 1/6 is half of 1/3, so all it takes is two 1/6 to make 1/3.
Answer:
1/3 is equal to 2/6, so it takes 2 sixths to make the same amount as 1/3.
Select the correct answer. What are the solutions to the equation x2 − 1 = 399? A. B. C. D.
Answer:
x = 20
Step-by-step explanation:
x² − 1 = 399
x² = 400
x = 20
15. Complete the table showing cost price, selling price and profit or loss. SP Profit Loss R320 CP R850
The selling price is the cost a customer pays for a good or service.
(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .
(4) Profit = Rs.9712 . (5) Loss % = 7.5% .
What is the selling price?The amount a buyer pays for a good or service is known as the selling price.
It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.
The cost price of an item is the sum paid for it or the cost at which it was produced. C.P. stands for "cost price." Selling Price: The selling price of a good is the price at which it is sold.
So, the table would be:
(1)
CP = Rs.8000 , SP = Rs.10000
if SP > CP, we have profit.
Profit = SP - CP = 10000 - 8000 = Rs.2000 .
Profit % = (Profit * 100) / CP = (2000 * 100) / 8000 = 25% .
(2)
SP = Rs.6890 , Profit = Rs.390 .
CP = SP - Profit = 6890 - 390 = Rs.6500 .
Profit % = (Profit * 100) / CP = (390 * 100) / 6500 = 6% .
(3)
CP = Rs.25000 , Loss = Rs.1000 .
SP = CP - Loss = 25000 - 1000 = Rs.24000 .
Loss % = (Loss * 100) / CP = (1000 * 100) / 25000 = 4% .
(4)
CP = Rs.48560 , Profit = 20% .
SP = CP * (100 + Profit%) / 100 = (48560 * 120) / 100 = Rs.58272 .
Profit = SP - CP = 58272 - 48560 = Rs.9712 .
(5)
CP = Rs.28320 , SP = Rs.26196 .
CP > SP, we have a Loss.
Loss = CP - SP = 28320 - 26196 = Rs.2124 .
Loss % = (Loss * 100) / CP = (2124 * 100) / 28320 = 7.5% .
Therefore, the selling price is the cost a customer pays for a good or service.
(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .
(4) Profit = Rs.9712 . (5) Loss % = 7.5% .
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Complete question:
Find the profit or loss and complete the table.
Cost Price Selling Price Profit () Loss
Profit Loss
Percentage Percentage
6000
1000
6000
(a) 5000
(b) 6200
(c) 2400
(d) 1900
400
300
1590
190
42 + z= 131
what is z?
Answer:
z=89
Step-by-step explanation:
42+z=131
take 42 away from both sides
z= 89
Answer:
z = 89
Step-by-step explanation:
42 + z = 131
z = 131 - 42
z = 89
Graph the image of the triangle after a rotation 90° counterclockwise around the origin.
Answer:
The answer you're looking for is: (4, -9), (6, -9), (4, -1)
Step-by-step explanation:
When translating an image 90º counterclockwise you go one quadrant to the right and use the scale factor: (x, y) --> (y, -x).
When using this scale factor you switch the x and y coordinates and also make sure that x is the opposite operation, it doesn't always mean it's going to be negative.
In this case points (-9, -4), (-9, -6), and, (-1, -4) were translated to (4, -9), (6, -9), (4, -1) accordingly.
I hope this was helpful!
What is the mathematical expression for 21 fewer stars than three times a number h??
The mathematical expression for 21 fewer stars than three times a number h is : 3h - 21
Explain about the mathematical expression?A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtract, multiplication, division, exponents, and other as-yet-unlearned operations and functions.
Every mathematical statement that includes numbers, variables, and also an arithmetic operation in between them is known as an expression as well as algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.The given statement is-
21 fewer stars than three times a number h
so,
mathematical expression is:
3h - 21
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Emily took an airplane trip. Her plane flew and equal numbers of miles each hour. Let m stand for the miles flown each hour. Write an equation to represent one way you can find how many miles Emily’s plane flew each hour.
An equation to represent one way you can find how many miles Emily’s plane flew each hour is y = 182x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Assuming the variable m represent the miles flown each hour, an equation for the number of miles Emily’s plane flew each hour can be calculated as follows;
y = kx
y = (2184/12)x
y = 182x
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Complete Question:
Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
A survey of 1,033 tourists visiting Orlando was taken. Of those surveyed:
256 tourists had visited the Magic Kingdom
267 tourists had visited Universal Studios
52 tourists had visited both the Magic Kingdom and LEGOLAND
75 tourists had visited both the Magic Kingdom and Universal Studios
82 tourists had visited both LEGOLAND and Universal Studios
33 tourists had visited all three theme parks
93 tourists did not visit any of these theme parks
How many tourists only visited the LEGOLAND (of these three)?
There are 509 tourists only visited the LEGOLAND (of these three).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, To find the number of tourists who only visited LEGOLAND, we need to subtract the tourists who visited LEGOLAND and another theme park from the total number of tourists who visited LEGOLAND.
Calculation:
First, we can find the total number of tourists who visited LEGOLAND:
Total = Tourists who visited only LEGOLAND + Tourists who visited LEGOLAND and another park
Hence, Total = (Total visitors to LEGOLAND) - (Tourists who did not visit any of the parks)
Total = 1,033 - (256 + 267 + 75 + 93 - 52 - 82 - 33)
Total = 1033 - 260
Total = 509
Hence, There are 509 tourists only visited the LEGOLAND (of these three).
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WW
the same area without any on
square? How many such squares can the rectangle be cut into?
15 In the figure below, point B is the corner of street ABC. If streetlights are to be
installed along one side of the street with equal distance between the lights, and a
streetlight must be installed at points A, B and C, at least how many streetlights
can be installed along the street?
1625 m
B
1170 m
The minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.
Describe Distance?In Euclidean geometry, the distance between two points is defined as the length of the shortest path between them. This is often referred to as the "straight-line distance" or "Euclidean distance." It is calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The total distance between A and C is the sum of the distances AB and BC:
AC = AB + BC = 1625 + 1170 = 2795 m
Since we need to install streetlights at points A, B, and C, there will be two segments of the street with streetlights:
From A to B, which has a distance of 1625 m
From B to C, which has a distance of 1170 m
We want to install streetlights along each segment with equal distance between the lights. Let's call the distance between each pair of adjacent streetlights "d".
For the first segment, there will be "n" streetlights, so the total distance covered by the streetlights will be (n-1)d. Similarly, for the second segment, there will be "m" streetlights, and the total distance covered by the streetlights will be (m-1)d.
The total distance covered by the streetlights should be equal to the distance AC, so we have:
(n-1)d + (m-1)d = AC
Substituting the values we know, we get:
1624d + 1169d = 2795
2793d = 2795
d = 2795/2793
d ≈ 0.999
We can round down to 0.99 to ensure that we don't have more streetlights than necessary.
Therefore, the distance between each pair of adjacent streetlights should be 0.99 m. To find the minimum number of streetlights required, we can divide the distance of each segment by 0.99 and round up to the nearest integer:
For the first segment: ceil(1625/0.99) = 1641
For the second segment: ceil(1170/0.99) = 1182
So the minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.
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Let D= Ф(R), where Φ(u,v)= (u^2, u+v) and R= [1,9] x [0,5]. Calculate \int \: \int \: _D ydA
The value of the double integral of y over D is 160.
The region D is defined as the image of the rectangle R under the transformation Φ(u,v) = (u², u+v). To find the integral of y over D, we need to express y as a function of u and v, and then compute the double integral in terms of u and v.
From the definition of Φ, we have:
u² = x
u + v = y
Solving for v in terms of u and y, we get:
v = y - u
Substituting this expression for v into the second equation, we get:
y = u + (y - u) = y
Therefore, y does not depend on u, and we can write:
y = f(v) = v + u
The integral of y over D can then be written as:
∫∫D y dA = ∫∫R f(v) |J| dA
where J is the Jacobian of the transformation Φ.
The Jacobian of Φ is given by:
J = ∂(x,y)/∂(u,v) =
| 2u 1 |
| 1 1 |
The determinant of J is:
|J| = 2u - 1
Substituting this expression for |J| and the expression for f(v) into the integral, we get:
∫∫D y dA = ∫∫R (v + u)(2u - 1) dudv
To evaluate this integral, we can integrate first with respect to u and then with respect to v:
∫∫D y dA = ∫[0,5]∫[1,9] (v + u)(2u - 1) dudv
= ∫[0,5] [(v+9)³/3 - (v+1)³/3] dv
= [(5+9)⁴/12 - (1+9)⁴/12]
= 480/3
= 160
Therefore, the value of the double integral of y over D is 160.
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Complete question:
Let D= Ф(R), where Φ(u,v)= (u², u+v) and R= [1,9] × [0,5].
Calculate [tex]\mathrm{\int \: \int \: _D ydA}[/tex]
Can you help on this fast
The table that shows proportional relationship is x = 1,3,4,5 and y = 50, 150, 200,250 ( table 1).
What is proportionality?The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
To determine the proportionality the ratio of x toby must be thesame Ina table
in table 1
x/y = 1/50 = 3/150 = 4/200 = 5/250 = 1/50
table 1 show proportional relationship
in table 2
3/1.5 is not equal to 7/3 , therefore table 2 does not show proportional relationship
in table 3
1/1.5 is not equal to 3/6 , therefore table 3 does not show proportional relationship
therefore the table that show proportional relationship is table 1
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hElp!!! quick!!!! p.s i’ll give brainliest
The required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.
What is the rate of change?Rate of change is defined as the change in value with rest to another value is called rate of change.
Here,
In Frank's city,
y = 0.3x + 2
The rate per mile is represented by the slope of the linear equation.
So,
m = $0.3 per mile
For Seattle
The rate per mile is given by the slope of the relation shown in the graph. So,
m = 3.2 - 2.4 / 6 - 2
m = $0.2 per mile
Similarly,
For Orlando, m = $0.25 per miles
For Miami, m = $0.4 per mile
For Honolulu m = $0.75 per mile
Thus, the required from Frack's city rate of miles, Seattle and Orlando are less expensive while Miami and Honolulu are more expensive.
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