Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
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A bicycle wheel has a diameter of 559 mm and has 32 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3. 14 for π. Show your work
The approximate arc length rounded to the nearest hundredth, between each spoke is 54.9 mm.
Diameter = 559 mm, r = d/2 = 279.5 mm
Number of spokes = 32
π = 3.14
To solve this question, we have to use the formula of the length of an arc which is given as
L = θ/360 × 2πr
To calculate the angle between each spoke, let's divide 360 by 32
θ = 360/32
θ = 11.25°
Now we have the value of the angle, substitute it and solve for the length of the arc.
[tex]L_{arc}[/tex] = θ/360 × 2πr
= 11.25/360 × 2 × 3.14 × 279.5
= 54. 9 mm
Therefore the length of the arc is approximately 54.9 mm.
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Trey and three of his friends are ordering a pizza. They plan to split the cost, and the want to spend at most $3.50 per person. Write and solve an inequality to find the cost of the pizza they should order.
The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.
How to express the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:
c ≤ (3.50 × 4)
c ≤ 14
The cost will be at most $14.
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Hannah is recovering hundreds of treasure chest from an ancient shipwreck she is able to recover a test every four hours to complete the table using equivalent ratios
A table of equivalent ratios for the number of treasure chests and hours that Hannah recovered is as follows:
Treasure chests Hours
8 4
12 6
10 5
What is a proportional relationship?In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 4/8
Constant of proportionality (k) = 0.5.
When hours y = 6, the number of treasure chests x is given by:
x = y/k
x = 6/0.5
x = 12.
When treasure chests x = 10, the number of hours y is given by:
y = kx
y = 0.5(10)
y = 5.
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Complete Question:
Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests every 4 hours.
Complete the table using equivalent ratios. Select all the answers that will fill the table.
How do you know if there are 2 real solutions?
For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
discriminant : [tex]b^2-4ac[/tex]
if [tex]b^2-4ac[/tex] is positive, Both solutions are real.
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Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years: f(x)
Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.
It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.
It should be also noted that the interest rate is given as a decimal and not a percentage.
For example, if the interest rate is 5%, then r = 0.05.
In order to use this equation, the value of P, r and x should be known
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Help please with this maths
Answer:
9 cm
Step-by-step explanation:
You want the radius of the sphere that has a surface area of 324π cm².
AreaThe area of a sphere is given by the formula ...
A = 4πr²
Filling in the given values, we can solve for r:
324π = 4πr²
81 = r² . . . . . . . . . divide by 4π
9 = r . . . . . . . . . . . take the square root
The radius of the sphere is 9 cm.
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PLEASE HELP!!!
Will give brainliest!
The value of h'(2) = 50.
What do you mean by function?
A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
here we are given a function h(x)
here h(x) = - 5f(g(x)) ------(i)
and we are given the value of
g(2) =3 ; f(2) = 1 ; g'(2) = -2
f(3) = 4 ; f'(3) = 5 ; f'(2) = 6.
and we need to find the value of h'(2).
here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.
so we are given ,
h(x) = - 5f(g(x))
differentiating with respect to x both side
h'(x) = -5 f'(g(x).g'(x).
at x =2,
h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]
and we know g(2) = 3 and g'(2) = -2.
so,
h'(2) = [tex]-5*f'(3)*-2[/tex]
h'(2) = [tex]-5*5*-2\\[/tex] ( as f'(3) = 5 )
h'(2) = 50
so Option C is correct, the value of h'(2) = 50.
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For a project in her Geometry class, Violet uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 6.65 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.
Since similar triangles have the same angle measures, we can set up the following proportion:
(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)
We can now use the information provided in the problem to solve for the height of the goalpost.
(6.65+4.25)/x = 1.75 / H
x = (6.65+4.25) * (1.75/H)
Where x is the distance from mirror to top of the goalpost.
Substitute the known values and solve for H
H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x
We know that x = 4.25, so
H = 1.75*10.9 / 4.25 = 4.093 m
The height of the football goalp
Step-by-step explanation:
Olivia is making greeting cards, which she will sell by the box at an arts fair. She paid $24 for a booth at the fair, and the materials for each box of cards cost $2. She will sell the cards for $6 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? How many cards will that take?
Answer:
$8
Step-by-step explanation:
distance of -6,8 and 1,7
Answer:
d ≈ 7.07 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )
d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]
= [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]
= [tex]\sqrt{7^2+1}[/tex]
= [tex]\sqrt{49+1}[/tex]
= [tex]\sqrt{50}[/tex]
≈ 7.07 units ( to 2 decimal places )
A specialty foods company sells "gourmet hams" by mail order. The hams vary in size from 4. 15 to 7. 45 pounds, with a mean weight of 6 pounds and standard deviation of 0. 65 pounds. The quartiles and median weights are 5. 6, 6. 2, and 6. 55 pounds.
a) Find the range and the IQR of the weights.
b) Do you think the distribution of the weights is symmetric or skewed? If skewed, which way? Why?
c) If these weights were expressed in ounces ( 1 pound = 16 ounces) what would the mean, standard deviation, quartiles, median, IQR, and range be?
d) When the company ships these hams, the box and packing materials add 30 ounces. What are the mean, standard deviation, quartiles, median , IQR, and range of weights of boxes shipped (in ounces)?
e) One customer made a special order of a 10-pound ham. Which of the summary statistics of part d might not change if that data value were added to the distribution?
The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.
What is Mean , Median and Standard Deviation ?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
a) the range is the difference between the highest and lowest value:
range =7.5-4.15 =3.3 pounds
the IQR is the difference between the third and first quartile
IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds
b) Skewed because the mean and median are not the same value.
c) All values will be multiplied by 16
Mean: 96 ounce
Standard deviation: 10.4 ounce
Quartiles: 89.6 ounce and 104.8 ounce
Median:99.2 ounce
IQR: 15.2 ounce
Range: 52.8 ounce
d) The mean,quartiles and median increase by 30,the result remain unchanged:
Mean: 126 ounce
Standard deviation: 10.4 ounce
Quartiles: 119.6 ounce and 134.8 ounce
Median:129.2 ounce
IQR: 15.2 ounce
Range: 52.8 ounce
e) The median, quartiles and IQR might not changed,because they are unaffected by an outlier.
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How do you use log and e?
The value of e (exponential) is approximately equal to 2.718281 which is rounded to 6 digits. The exponential constant frequently happens in mathematics every time the exponential functions are involved.
Log mention to a logarithm to the base 10. Ln mentions a logarithm to the base e. This is also known as a common logarithm. This is also known as a natural logarithm.
The first common log is represented as log 10 (x) The second natural log is represented as log e (x) The exponent form of the common logarithm is 10 x =y.
An exponential function is a function in which a number or data is raised to the power of another number or a variable.
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Reflect shape A in the line y = -x. (See picture)
Answer:
See picture below
Step-by-step explanation:
What is the coefficient of y2 in the expression 2x2y 15xy2 7y?
Let x be the coefficient of y^2 in the expression 2x^2y+15xy^2-7y. So x=0.
What is co-efficient?
A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.
Write an example of co-efficient.
As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
The given algebraic expression is 2yx^2+15xy^2-7y.
The terms are xy^2, yx^2 any y^2
So the co-efficient of y^2 is 0
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Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
The required value of x is 17 for the given equation 11 = x - 6.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question, as follows:
11 = x - 6
We can determine the value of x by adding 6 to both sides of the equation.
As per the question, we have
⇒ 11 = x - 6
⇒ 11 + 6 = x - 6 + 6
⇒ x = 11 + 6
Apply the addition operation, and we get
⇒ x = 17
Therefore, the required value of x is 17.
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A ball bounces to a height of 6.7 feet on the first bounce. Each subsequent bounce reaches a height that is 81% of the previous bounce. What is the height, in feet, of the sixth bounce
After solving, the height in feet of the sixth bounce is 1.892 feet.
In the given question, we ave to find the height, in feet, of the sixth bounce.
From the given question,
Height on the first bounce = 6.7
Subsequent bounce reaches a height of the previous bounce = 81%
Suppose the height is h.
So according to the question:
h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6
h(6) = 6.7*(81%)^6
h(6) = 1.892 feet
So the height of sixth bounce is 1.892 feet.
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Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
2x³ +x² -25x +12 factorised
The correct solutions for "x" after factorizing the cubic equation are:
x1 = -4
x2 = 0.5
x3 = 3
Cubic Equation:
A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.
Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.
Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0
Given: 2x³ +x² -25x +12
On comparing with the standard form of the cubic equation, we get;
a=2
b=1
c=-25
d=12
After factorizing the cubic equation, we have three roots.
x1 = -4
x2 = 0.5
x3 = 3
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You decide you want to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only (not the bus). What is the total cost for your fun day out? (round to the nearest hundredth)
The total cost for your fun day out is $23.82.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that you decided to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only.
Assume that the total cost for your fun day out is ${x}. Then, we can write the equation as -
{x} = 15% of (75 + {5% of 75}) + 12
{x} = 15% of (75 + {5/100 x 75}) + 12
{x} = 15% of (75 + {1/20 x 75}) + 12
{x} = (15/100) x (75 + 75/20) + 12
{x} = (3/20 x 78.75) + 12
{x} = 11.82 + 12
{x} = 23.82
Therefore, the total cost for your fun day out is $23.82.
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i need help with number seven with a full explanation please
The value of x would be 32.
What are a congruent quadrilaterals?
In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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By analyzing the figure, The value of x would be 32.
What are a congruent quadrilaterals?In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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Square root of 16b power four
Answer: 256b
Step-by-step explanation: So, first we need to find the square root of 16b.
That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b
So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.
So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.
So, I'd be 256b
If you have 10 friends and make two equal teams, what fraction do you use?
Please answer the 4th and 6th one
Answer:
5
Step-by-step explanation:
0-6x will be -6x if we divide that six then we will get -30/-6 since minus gets cancelled we will be left with 5
If Y=6 and X=10 then find the value of y when x=8
Answer:
when x=10 & y=6
10-6=4 so,
x=8
y=4
Find output, g, when the input, r, is 4. g= 25-3r
when the input r, is 4, then the output g, is 13.
The function g = 25 - 3r gives the output g when the input r is given.
If we substitute r = 4 into the equation, we get:
g = 25 - 3×4
g = 25 - 12
g = 13
Therefore, when the input, r is 4, the output g, is 13.
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How doe etimation help you place the decimal point in a product correctly?Explain
By counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
What is Estimation?A high number of a certain number is estimated to be the closest whole number or significant number.
When estimating, the use of decimal points aids in separating the fractional portion from the entire figure.
For instance, we have a total of three integers after the decimal point if we want to calculate the product of 4.23 and 2.1.
4.23
× 2.1
4 2 3
________
8 4 6
8 8 8 3
Therefore, we shall move the decimal point three places, working our way from the back to the front.
The result of 4.23 and 2.1 is 8.883 then.
We can therefore say that we completely understand how estimating helps you accurately set the decimal point in a product.
Therefore, by counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
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Correct question:
How does estimation help you place the decimal Point in a product correctly?
Equivalent expression
The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.
What is right-angled triangle?The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.
What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters
we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,
then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters
the ladder touches the build at 4.53 meters vertical distance from the ground.
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I really also need help on this question lol
Answer:
13/15
For this question, you could type it into the calculator.
Hence, this question is too trivial, and your question might get deleted as a result. Since this is your first question, I will help you out but subsequently, do use a calculator to solve this kind of questions.
Step-by-step explanation:
4 1/3 can be converted to 13/3 as an improper fraction.
Next, evaluate 13/3 divided by 5
(13/3) / 5 = (13/3) x (1/5)
= 13/15
Answer:
Step-by-step explanation:
There are a number of ways to do this. I am going to take a little longer, but I am hoping that it will make sense to you.
4[tex]\frac{1}{3}[/tex] ÷ 5
Another name for 1 is [tex]\frac{3}{3}[/tex] I am going to rewrite 4[tex]\frac{1}{3}[/tex] knowing this.
[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]
Another way to write 5 is [tex]\frac{5}{1}[/tex].
I want both of my fraction to have the same denominator so I will multiple
[tex]\frac{5}{1}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{3}[/tex] I am now ready to divide by fractions
[tex]\frac{13}{3}[/tex] ÷ [tex]\frac{15}{3}[/tex] Divide across
[tex]\frac{\frac{13}{15} }{\frac{3}{3} }[/tex] = [tex]\frac{\frac{13}{15} }{1}[/tex] = [tex]\frac{13}{15}[/tex]
probability:
a) A family wants to have 4 children. Design and do a simulation to determine the probability that, if they do have 4 children, they will have two boys and two girls. (Hint: Use coins.)
b) A basketball player is shooting free throws blindfolded. He shoots in groups of 4 shots. Assume that it is equally likely that he will hit or miss a shot. Design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (Hint: Use coins.)
a) A simulation of the probability that a family with 4 children will have 2 boys and 2 girls can be done using coins. We can represent boys as heads (H) and girls as tails (T).
To simulate the birth of one child, we will flip a coin. If it comes up heads, it represents the birth of a boy, and if it comes up tails, it represents the birth of a girl. We will repeat this process four times to simulate the birth of four children.
We can use the simulation to estimate the probability of the family having 2 boys and 2 girls. We can do this by performing the simulation multiple times (e.g. 100, 1000 or more) and counting the number of times that the family has 2 boys and 2 girls.
The probability can be calculated by dividing the number of successful outcomes (2 boys and 2 girls) by the total number of simulations.
b) A simulation of the probability that a basketball player will hit at least 75% of his shots within the groups can be done using coins. We can represent hitting a shot as heads (H) and missing a shot as tails (T). To simulate one shot, we will flip a coin. If it comes up heads, it represents hitting the shot, and if it comes up tails, it represents missing the shot. We will repeat this process four times to simulate the shooting of four shots.
To determine the probability of hitting at least 75% of the shots, we will perform the simulation multiple times (e.g. 100, 1000 or more) and count the number of times that the player hits at least 3 out of 4 shots.
The probability can be calculated by dividing the number of successful outcomes (3 or 4 shots hit) by the total number of simulations
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What are the factors of x^3 Y^3?
The factors of (x^3 + y^3) are ( x + y )(x^2 - x . y + y^2).
In order to find the factors of (x^3 + y^3), you need to apply the sum of cubes formula:
(x^3 + y^3) = ( x + y )(x^2 - x . y + y^2)
(x^3 + y^3) = ( x + y )(x^2 - x y + y^2)
Therefore, in order to find the factor of the given expression, you just simply need to learn the sum of cubes formula.
Similarly, the difference of cubes formula is as follows:
(x^3 - y^3) = ( x - y )(x^2 + x y + y^2)
Which gives factors of (x^3 - y^3).
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