Net Present Value (6 points total) The city of Corvallis is deciding whether or not to undertake a project to improve the quality of the city's drinking water. The project would require an immediate payment of $20,000 to install a new filtration system. This filtration system will require yearly maintenance costs of $1,000 after the initial period. The filtration system will be operational for 5 years. The benefits in first year are $500. At the end of year 2, the benefit received is $4000. For years 3, 4, and 5, the benefit received is $7,000. Assume that the discount rate is 6%. a. Write out the general mathematical formula you would use to determine the net present value (NPV) of this project. (2 points) b. Plug-in the appropriate numbers into the formula from above. You DO NOT need to calculate the answer, simply plug in the values in the appropriate places. (2 points) c. What criteria should the city use to decide if they should install the filtration system or not?
Answers
a. The formula for NPV is NPV = (Benefits - Costs) / (1 + Discount Rate)^n.
b. Plugging in the appropriate values, Benefits: $500 (Year 1), $4,000 (Year 2), and $7,000 (Years 3-5); Costs: $20,000 (initial payment), $1,000 (yearly maintenance from Year 2); Discount Rate: 6%.
c. The city should use a positive NPV as a criterion to decide whether to install the filtration system or not.
a. The general mathematical formula to determine the net present value (NPV) of this project is as follows:
NPV = (Benefits - Costs) / (1 + Discount Rate)^n
Where:
Benefits represent the cash inflows or benefits received from the project in each period.
Costs refer to the initial investment or cash outflows required to undertake the project.
Discount Rate is the rate used to discount future cash flows to their present value.
n represents the time period (year) when the cash flow occurs.
b. Plugging in the appropriate numbers into the formula:
Benefits: $500 in Year 1, $4,000 at the end of Year 2, and $7,000 for Years 3, 4, and 5.
Costs: Initial payment of $20,000 and yearly maintenance costs of $1,000 from Year 2 onwards.
Discount Rate: 6%.
n: 1 for Year 1, 2 for Year 2, and 3, 4, and 5 for Years 3, 4, and 5, respectively.
c. The city should use the criteria of positive net present value (NPV) to decide whether to install the filtration system or not. If the NPV is greater than zero, it indicates that the present value of the benefits exceeds the costs, suggesting that the project is financially favorable and would generate a positive return.
Conversely, if the NPV is negative, it implies that the costs outweigh the present value of the benefits, indicating a potential financial loss. Therefore, a positive NPV would indicate that the city should proceed with installing the filtration system, while a negative NPV would suggest not undertaking the project.
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Related Questions
independent variable was contact plates placed on the tile for less than 5 seconds. the standardized variables were the length of time plates were on the tiles. the control was the inoculating floor tiles for five days in chicken broth. the dependent variable was the plates placed on the tile for more than 5 seconds.
Answers
Their experimental design was Independent variable was contact plates placed on the tile for less than 5 seconds. Option D is the correct answer.
The independent variable is the factor that is being manipulated by the experimenter. In this case, the experimenter is manipulating the length of time the plates are on the tiles. The dependent variable is the factor that is being measured by the experimenter. In this case, the experimenter is measuring the amount of bacteria on the plates.
The control is a group of subjects that are not exposed to the independent variable. In this case, the control group is the floor tiles that have been inoculated with chicken broth. The control group is used to compare the results of the experimental group, which is the group of plates that have been dropped on the tiles.
The standardized variables are the factors that are kept the same for both the experimental group and the control group. In this case, the standardized variables are the type of food, the surface of the tiles, and the temperature of the room. These factors are kept the same so that the only difference between the two groups is the length of time the plates are on the tiles.
This experimental design is a well-controlled experiment because the experimenter has taken steps to ensure that the only difference between the two groups is the length of time the plates are on the tiles. This will allow the experimenter to make accurate conclusions about the effect of the independent variable on the dependent variable. Option D is the correct answer.
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The following question may be like this:
The Myth busters conducted an experiment to test the five second rule. Which of the following represented their experimental design?
The standardized variables were the length of time plates were on the tiles. The control was the inoculating floor tiles for five days in chicken broth. The dependent variable was the plates placed on the tile for more than 5 seconds. Independent variable was contact plates placed on the tile for less than 5 seconds.How do I determine whether a graph is a function?
Answers
Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.
Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.
So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.
On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.
It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.
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Please help!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
the best answer may be D because 9/3 =3 3×5=15
The average rate of change from hour 4 to 8
Answers
You would do 464-232=232
Then divide 232/2=116
Ramona is counting the posts between mile makers on the highway. In 1 mile, she counts 33 posts. If the posts are evenly spaced, how many feet apart are they? (1 mile = 5,280 feet)
Answers
Answer:
160feet
Step-by-step explanation:
5280 divided by the number of posts
count in mile= 33 posts.
to find:the distance between the posts.
solution:1 mile= 5280ft
distance= 5280/33
=160ft
so the distance between the posts are 160ft.
The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed of R. If a car traveling 80 mph can stop in 400ft, How fast can a car travel and still stop in 144ft?
Answers
Direct variation equations have the following form:
\(y=kx\)Where "k" is the Constant of variation.
In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:
\(D=kR^2\)You know that:
\(D=400ft\)When:
\(R=80mph\)So you need to make the conversion from feet to miles. Since:
\(1mi=5280ft\)You get:
\((400ft)(\frac{1mi}{5280ft})\approx0.076mi\)Then, you can find the value of "k" as following:
\(undefined\)What is the 12th term of the sequence -2,-4,-6,...........-100?
Answers
Answer:
-24
Step-by-step explanation:
The common difference (D) is -2. And A1 is -2. so if you just add -2 to the geometric sequence until A12, you would get -24.
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Answers
Hope it helps.
Do comment if you have any query.
which value of g makes 26=7(g-9)+12 a true statment
Answers
Answer:
11
Step-by-step explanation:
26=7(g-9)+12
14=7(g-9)
2=g-9
g=11
PLEASE HELP!!
Let f(x) = 8(3)^x The graph is stretched vertically by a factor of 3 to form the graph g(x). Choose the equation of g(x)
Answers:
a: g(x)=8(9)^x
b: g(x)=3(3)^x
c: g(x)=24(3)^x
d: g(x)=11(3)^x
Answers
The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).
What is function?
A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable).In contrast to the function f (x), the function g (x) is referred to as an inner function. The function g is the inner function of the outer function f, thus we can also interpret f [g (x)] in this way.For the parent function f(x) and a constant k >0,
then, the function given by
g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)
if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k
As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e
k = 3 >1
so, by definition
g(x) = 3 f(x) = 3 . 8(3)ˣ
= 8(3)ˣ⁺¹
= 24 (3)ˣ
Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).
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NEED HELP NOWWWW PLEASE HELPPPP!!!!!!!!!!
Answers
Answer:
-3 over 1
Step-by-step explanation:
Symbolab.com to help
Answer:
I’m not going to try ponte las pilas
Step-by-step explanation:
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Answers
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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Consider the statements and select the correct option below.
(a) cos(x) = 1-sin(x)/(cos(x)+cot(x))
(b) sin(x) = 1-cos(x)/(sec(x)+tan(x))
1. Only (a) is true
2. Only (b) is true
3. Both (a) and (b) are true
4. Neither (a) nor (b) are true
Answers
Option- 3 is correct that is both a and b are true.
a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)
b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)
Given that,
a. We have to prove the statement is true or false.
Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)
Now, Take the right hand side
= \(1 - \frac{sinx}{cscx+cotx}\)
= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)
By using LCM
= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)
= \(1 - \frac{sinx\times sinx}{1+cosx} }\)
= \(1 - \frac{sin^2x}{1+cosx} }\)
= \(\frac{1+cosx - sin^2x}{1+cosx} }\)
We know from trigonometric identities 1 - sin²x = cos²x
= \(\frac{cos^2x+cosx }{1+cosx} }\)
= \(\frac{cosx(1+cosx )}{1+cosx} }\)
= cosx
LHS = RHS
Therefore, The statement is true
b. We have to prove the statement is true or false.
Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)
Now, Take the right hand side
= \(1 - \frac{cosx}{secx+tanx}\)
= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)
By using LCM
= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)
= \(1 - \frac{cosx\times cosx}{1+sinx} }\)
= \(1 - \frac{cos^2x}{1+sinx} }\)
= \(\frac{1+sinx - cos^2x}{1+sinx} }\)
We know from trigonometric identities 1 - cos²x = sin²x
= \(\frac{sin^2x+sinx }{1+sinx} }\)
= \(\frac{cosx(1+sinx )}{1+sinx} }\)
= sinx
LHS = RHS
Therefore, The statement is true
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Find the area of a triangle with base of 10 inches and a height of 5 inches.
100 square inches
B 50 square inches
C) 25
square inches
D 12.5 square inches
Answers
Answer:
25 square inches
Step-by-step explanation:
just divide your base by 2 and then multiply it by the height
i need help please and thank you i will give a brainliest for the correct answers so it’s more than once it say select all that apply
Answers
Answer:
I would say C or B
Step-by-step explanation:
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x² – 9
x² - 2x - 15
Simplify
Answers
Answer:
x^2 - 9 = (x + 3)(x - 3) = (x - 0)^2 - 9.
x^2 - 2x - 15 = (x - 5)(x + 3) = (x - 1)^2 - 16.
I assume you mean factored form?
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Answers
The length of the shorter leg will be 2.5 feet and the length of the longer leg is 4.5 feet.
How to calculate the value?The Pythagoras theorem will be used in calculating the lengths.
This will be:
a = First leg = x
b = Second leg = x + 4
c = Hypothenuse = 7
In this case, the values will be substituted into the formula given below:
a² + b² = c²
x² + (x + 4)² = 7²
x² + x² + 8x + + 16 = 49
Collect like terms
2x² + 8x + 16 - 49
2x² + 8x - 33
By using the quadratic formula, the value of x will be 2.5. This is the shorter leg. The Longer leg will be: 2.5 + 4 = 6.5 feet
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If a bank doubles in size every 5 years, then by what percent does it grow after only 3 years? Round to nearest tenth of percent.
Answers
could you help me with 11% and 9% thank you Assuming that the current interest rate is 10 percent, compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 11 percent? What happens when the interest rate goes to 9 percent?
Answers
As the interest rate increases from 10 percent to 11 percent, the present value of the bond decreases from $1,074.47 to $1,058.31. Conversely, when the interest rate decreases to 9 percent, the present value increases to $1,091.19. This is because the discount rate used to calculate the present value is inversely related to the interest rate, meaning that as the interest rate increases, the present value decreases, and vice versa.
To compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000, we need to discount the future cash flows (coupon payments and face value) by the appropriate interest rate.
Step 1: Calculate the present value of each coupon payment.
Since the bond has a 10 percent coupon rate, it pays $100 (10% of $1,000) annually. To calculate the present value of each coupon payment, we need to discount it by the interest rate.
Using the formula: PV = C / (1+r)^n
Where PV is the present value,
C is the cash flow,
r is the interest rate, and
n is the number of periods.
At an interest rate of 10 percent, the present value of each coupon payment is:
PV1 = $100 / (1+0.10)^1 = $90.91
Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of the fifth year. We need to discount it to its present value using the interest rate.
At an interest rate of 10 percent, the present value of the face value is:
PV2 = $1,000 / (1+0.10)^5 = $620.92
Step 3: Calculate the total present value.
To find the present value of the bond, we need to sum up the present values of each coupon payment and the present value of the face value.
Total present value at an interest rate of 10 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,074.47
When the interest rate goes to 11 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 11 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,058.31
When the interest rate goes to 9 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 9 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,091.19
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Julie is tracking the growth of a plant for a science project. The height of the plant on the 2nd day she measured was 8 inches and on the 7th day, it was 20.5 inches find and interpret the rate of change.
Answers
This means that the plant grow at a rate of 2.5 inches per day.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the height of the plant after x days.
The height of the plant on the 2nd day she measured was 8 inches. It is given by:
(2, 8)The height of the plant on the 7th day she measured was 20.5 inches. It is given by:
(7, 20.5)The rate of change (m) is:
\(m=\frac{y_2-y_1}{x_2-x_1} =\frac{20.5-8}{7-2} =2.5\)This means that the plant grow at a rate of 2.5 inches per day.
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The formula for the area of a rhombus is A = a equals StartFraction one-half EndFraction d 1 d 2.d1d2, where d1 and d2 are the lengths of the diagonals.
Which are equivalent equations? Select two correct answers.
Answers
The two equivalent equations are d₁= 2a/d₂ and d₂= 2a/d₁ , Option 2 and 5 is the right answer.
What is a Rhombus ?Rhombus is a quadrilateral with all the sides equal to each other.
It is given that d₁ and d₂ are the lengths of the diagonals.
and Area = a
a = (1/2) d₁ * d₂
2a = d₁ * d₂d₁ * d₂ = 2a
It can be written as
d₁= 2a/d₂
a = (1/2) d₁ * d₂
d₁ * d₂ = 2ad₂= 2a/d₁
Therefore Option 2 and 5 are the correct answer.
The options of this question are:
1. d₁=2Ad₂
2. d₁= 2A/d₂
3. d₂= d₁/2A
4. d₁= 2A/d₂
5. d₂= 2A/d₁
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How long would it take R20000 invested today at a simple interest rate of 9% p.a. to reach an investment goal of R30000.
A Approximately 5.6 years
B Approximately 6.1 years
C Approximately 4.7 years
D Approximately 5.1 years
Answers
\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)
Q15) I CAN COMPUTE THE MEAN, MEDIAN, AND MODE OF A SET OF DATA The data represent a number of texts received over an 8-day period: 5, 6, 8, 13, 9, 1, 8, 4 Find the mean, median, and mode. Mean = Median = Mode =
Answers
Answer:
median=10
mode=8
mean=42,63
Answer:
Mean:7
Median:8
Mode:8
Solution:Mean: The sum of all observation divided by several observation
6+8+13+9+1+8+4=4949÷7=7Median: it is the middlemost observation of data arraged in increasing or decreasing order of values
(1,4,6,8,8,9,13)\( \sf{( \cancel1,4,6,8,8,9, \cancel{13})}\)\( \sf{ \cancel4,6,8,8 ,\cancel9}\)\( \sf{( \cancel6,8 ,\cancel8)}\)(8)Mode: it is the value that accurs most frequently in a set of data
\( \sf {1,4,6 ,\red{8,8},9,13}\)Hope it helps!!
using only words solve 8x+3=27 step by step
Answers
Answer:
X=3
Step-by-step explanation:
Subtract 3 from both sides
Simplify 27-3 to 24
Divide both sides by 8
Simplify 24/8 to 3
Step-by-step explanation:
Your goal is to isolate x, so your first step is to subtract by 3 on both sides. That leaves you with the equation 8x=24. Divide by 8 on both sides (since x is being mutliplied b 8) and you get x=3
Rewrite 40 − 8x^3 using a common factor.
Answers
Answer:
4(10-2x³)
Step-by-step explanation:
4×10=40
4×-2x³ = -8x³
final answer = 40 - 8x³
Write an explicit formula for each geometric sequence. 1,2,4,8, . . .
Answers
The explicit formula for a geometric sequence is \(a_{n}\) =\(a_{1}^{r-1}\)
The sequence is:
1, 2, 4, 8..........
The formula for a geometric sequence,
\(a_{n}\) = \(a_{1}^{r - 1} }\)
a, ar, \(ar^{2}\), \(ar^{3}\)
r = common ratio
n = number of sequences in a series.
Let us understand by the sequence,
Here r = 2 , a = 1
Therefore by putting these values in the equation we get,
\(a_{n}\) = \(a_{1}r^{n-1} }\)
= a, ar, a\(r^{2}\), a\(r^{3}\), ........
1, 2, 4, 8 .........
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Find the perimeter of the parallelogram whose vertices are A (-1,1), B (-9,6), C(-12,11) and D(-4,6) Give your answer correct to one decimal place
Answers
Answer: 30.5
Step-by-step explanation:
Help me with question 12 pls pls someone
Answers
The value of n from the given expression is m/p-6
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the expression
m/n = p - 6
Cross multiply
m = n(p - 6)
Divide both sides by p - 6
m/p-6 = n
Swap
n = m/p-6
Hence the value of n from the given expression is m/p-6
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how do I answer these questions?
Answers
Answer:
cross multiplication would be the quickest technique that works to visualize this set of questions..
if \(\frac{a}{b} = \frac{c}{d}\) then ad = bc
each item that does not have a denominator add a "1" as the denominator
so first item... \(\frac{sin(50)}{1} = \frac{x}{4}\)
\(\frac{4 * sin(50) }{1} = x\) x = \(4\sin \left(50^{\circ \:}\right)=3.06417\dots\)
#b) \(3\tan \left(81^{\circ \:}\right)=18.94125\)
#c) \(6\cos \left(33^{\circ \:}\right)=5.03202\)
.
.
#g)\(7.1\tan \left(18.4^{\circ \:}\right)=2.36185\)
Step-by-step explanation:
Answer:
First we extract the sin or the tan according to the question and multiply the number with the denominator and extract the x .
a)\( \sin(50) = \frac{x}{4} \\ 0.766 = \frac{x}{4} \\ x = 3.06\)
b)\( \tan(81) = \frac{x}{3} \\ 6.31 = \frac{x}{3} \\ x = 18.93\)
C)\( \cos(33) = \frac{x}{6} \\ 0.83 = \frac{x}{6} \\ x = 0.83 \times 6 \\ x = 4.98\)
d)\( \cos(75 ) = \frac{x}{3.5} \\ 0.258 = \frac{x}{3.5} \\ x = 0.2588 \times 3.5 \\ x = 0.90\)
e)\( \sin(24) = \frac{x}{4.2} \\ 0.406 = \frac{x}{4.2} \\ x = 0.406 \times 4.2 \\ x = 1.70 \)
f)\( \tan(42) = \frac{x}{10} \\ 0.9 = \frac{x}{10} \\ x = 9\)
g)\( \frac{x}{7.1} = \tan(18.4) \\ \frac{x}{7.1} = 0.33 \\ x = 0.33 \times 7.1 \\ x = 2.34\)
h)\( \frac{x}{5.3} = \sin(64.7) \\ \frac{x}{5.3} = 0.9 \\ x = 4.77\)
i)\( \frac{x}{12.6} = \cos(52.9) \\ \frac{x}{12.6} = 0.6 \\ x = 0.6 \times 12.6 \\ x = 7.56\)
I hope I helped you^_^
Define a relation ~ on R' by stating that (a, b) ~ (c, d) if and only if a3+ b' transitive but not symmetric.
Answers
A relation ~ on R' is defined as a relation where (a,b) ~ (c,d) if and only if a3+b3=c3+d3. This relation is transitive but not symmetric.
Transitivity of the relation states that if (a, b) ~ (c,d) and (c, d) ~ (e, f) then (a, b) ~ (e, f). This means that if a3+b3=c3+d3 and c3+d3=e3+f3 then a3+b3=e3+f3, thus, the relation is transitive.
Symmetry of the relation means that if (a, b) ~ (c, d) then (c, d) ~ (a, b). This, however, does not hold in this relation since it is possible for a3+b3=c3+d3 and yet c3+d3≠a3+b3. For example, (1,2) ~ (8,4), this is true since 13+23=83+43, however, this does not mean that (8,4) ~ (1,2) since 83+43≠13+23. Therefore, this relation is not symmetric.
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