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KerimF wrote:Therefore, the best thing that one can do is to present, as possible, what he has as 'new knowledge' without expecting any positive reaction... with the hope that his 'new knowledge' doesn't oppose, in any way, the interests of some powerful rich groups which are based on 'old knowledge'.
Thank you for the wise words of concern. I am a sixty percent disabled veteran, seventy-three years old, in poor health. I believe it would be like beating a dead horse if they did anything. First, it is basic mathematics because it takes random numbers to be able to see mathematics clearly. Second, I believe I have given enough to the country. NSA would not even acknowledge receiving my information, so I did my duty to the country. Third, because this is basic math, to withhold this from public knowledge would be a much larger harm, in time. Short term, it may cause some problems.
I am also former military. I have a question for you.
What's your take on illegal aliens allowed to get free medical and dental service at all VA Hospitals across the United States under the Biden/Harris administration? The VA Hospital is for VETERANS not for people who never served. I get stuck with copayments for medical service and don't qualify for dental. What do you say?
Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
A. x^6 + 2x^3 + 1
B. 3 - 27x^2
Question A
Note: x^6 = (x^3)^2
Let u = x^3
I now get u^2 + 2u + 1.
(u + 1)(u + 1) = (u + 1)^2
Back-substitute for u.
(x^3 + 1)^2 = (x^3 + 1)(x^3 + 1).
The expression x^3 + 1 can be factored using the sum of cubes.
Doing so, I get (x + 1)(x + 1)(x^2 - x + 1)(x^2 - x + 1).
Answer: (x + 1)^2 (x^2 - x + 1)^2
Do you agree?
Question B
This expression can be factored using the difference of cubes.
3(1 - 9x^3)
The difference of cubes:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Let a = 1
Let b = 3x
3(1 - 3x)(1 + 3x + (3x)^2)
3(1 - 3x)(1 + 3x + 9x^2)
Do you agree?
Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
A. x^2 + 7
B. x^4 - 1
Question A
The polynomial x^2 + 7 cannot be factored. It is prime.
Question B
x^4 - 1
(x^2 - 1)(x^2 + 1)
(x - 1)(x + 1)(x^2 + 1)...answer.
Note: x^2 + 1 is prime and thus cannot be factored.
Do you agree?
Write each number as a decimal.
A. 9.7 x 10^4
B. 9.88 x 10^(-4)
Question A
Positive exponent 4 tells me to move the decimal point 4 places to the right.
Doing so, I get 97,000.
Note: 97,000 = 97,000.00.
Question B
Negative exponent 4 tells me to move the decimal point 4 places to the left.
Doing so, I get 0.000988.
Do you agree?
A number is written in scientific notation if it is written in the form a • 10^n, where 1 ≤ | a | < 10 and n is an integer.
Write each number in scientific notation.
A. 0.00421
B. 21, 210
Question A
Moving the decimal point three places to the right, I get
4.21.
Now multiply 4.21 by 10^(-3).
Question B
The number 21,210 = 21, 210.00.
To land between 1 and 10, move the decimal point 4 places to the left.
Doing so, I get 2.1210.
Multiply 2.1210 by 10^4.
Do you agree?
Convert 9.7 x 10^3 to a number not in scientific notation.
Moving the decimal point 3 places to the right, I get 9,700.
Do you agree?
Oculus8596 wrote:Write each number in scientific notation as a decimal.
A. 9.7 x 10^3
B. 6.453 x 10^(-1)
Question A
Positive exponent 3 tells me to move the decimal point 3 places to the right.
Doing so, I get 9,700.
Question B
Negative exponent 1 tells me to move the decimal point one unit to the left.
Doing so, I get 0.6453.
Is 9700 a decimal?
Should it be 9700.0, to make it a decimal?
I edited the thread.
For example, F = ma is differential equation that is also a literal equation. However, y = x + 4 is a linear equation.
What makes the difference between the two equations?
thanks
I can help you in this forum with middle school and high school mathematics, if you are interested.
"F = ma" means that force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a); it's a fundamental equation in physics known as Newton's Second Law of Motion, which essentially states that the greater the force applied to an object, the greater its acceleration, and the more mass an object has, the more force is needed to accelerate it.
Did you know that F = ma is actually a Differential Equation?
I hope to ignite math discussions here. Hello from Great Lakes, Illinois.
Welcome to the forum. Hope you like your stay.
Facebook math groups have replaced math websites. I try to post daily problems here for a few reasons:
1. Provide members with daily practice
2. Keep my math skills sharp
3. Ignite math discussions
4. Avoid boredom
5. If possible, make a friend or two
1. Ordinary Differential Equations
2. Partial Differential Equations
3. Advanced Calculus (beyond the regular sequence of Calculus l, ll, and lll)
4. Abstract Algebra
5. Algebraic Topology
6. Complex Analysis
7. Set Theory
If you suffer from vertigo or if you are diabetic, avoid foods high on:
A. Gluten
B. Dairy
C. Sugar
What are your thoughts on anxiety attacks?
This is a good idea. What does Bob say about this?
Does it? It shouldn't. Those mm measurements are all pretty close so the miles should be too. But you've got places so close you could walk/swim the distance.
I did it this way. What do you have to multiply 58 by to get 1046. answer =what it has become, divided by what it was.
multiplier = 1046/58
Bob
ps. Maths is supposed to represent the real world so any answer should pass the 'is it reasonable?' test.
To approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale, I can use the scale of Karen’s atlas.
First, I need to find out the scale of Karen’s atlas. I'll do this by comparing a distance on her map with its corresponding real-world distance.
The measured straight-line distances are:
1. From Hamilton to Fort Lauderdale: 57 mm
2. From Fort Lauderdale to San Juan: 58 mm
3. From San Juan to Hamilton: 53.5 mm
Given that the actual distance from Fort Lauderdale to San Juan is 1046 miles, I will calculate the scale using this known value:
Scale = Actual Distance / Map Distance
For example, Scale for “From Ft.Lauderdale To Puerto Rico”= (1046miles/58mm)=18miles/mm.
Now that I found our Scale, I will apply it in order estimate other two unknowns.
So now applying same formula as above,
Actual Distance between :
1. SanJuan-Hamilton=(53.5*18)mile ≈963 mile
2. Hamilton-FtLauderale =(57 *18 )mile≈1026 mile
Is this much better, Bob?
A, B and C exactly right.
For D and E I would say the presence of another variable y is a reason. Also E has a + element as well.
Further thought about D. If we consider a = 8/y and k = 1 then it is monomial. I'm regarding y as a fixed value rather than a variable. Why not?
Bob
You said:
"Further thought about D. If we consider a = 8/y and k = 1 then it is monomial. I'm regarding y as a fixed value rather than a variable."
I don't know what you mean here.
Yes I do
Bob
I found this problem to be interestingly simple.
The first number in each sum is decreasing by 1 and the second number is increasing by 1. So I would expect the total to stay constant.
In general if a + b = c then (a+1) + (b-1) = c and more generally still, (a + n) + (b - n) = c for all n.
Bob
Thank you for a general formula explaining the clock number structure.
Find a clock in your house. The numbers given in a clockwise rotation are as follows: 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and back to 12.
From the numbers given in your clock, do this:
12 + 1 = 13
11 + 2 = 13
10 + 3 = 13
9 + 4 = 13
8 + 5 = 13
7 + 6 = 13
Creepy? Coincidence? Mysterious?
Determine the number that should be added to complete the square of each expression. Then factor each expression.
A. p^2 + 14p
B. x^2 + (1/3)x
Question A
Divide 14 by 2 and square the quotient.
So, (14/7)^2 = (7)^2 = 49
The number that should be added is 49.
p^2 + 14p + 49 factors put to be (p + 7)(p + 7) or (p + )^2.
Question B
Same steps as shown for Question A.
(1/3) ÷ 2
(1/3) (1/2) = 1/6
(1/6)^2 = 1/36.
The number that sould be added is 1/36.
x^2 + (1/3)x + (1/36) factors out to be (x + 1/6)(x + 1/6) or
(x + 1/6)^2.
Do you agree with my work?
Textbook Definition of Monomial
A monomial in one variable is the product of a constant and a variable raised to a positive integer power. A monomial is of the form ax^k, where a is a constant, x is a variable, and k => 0 is an integer. The constant a is called the coefficient of the monomial. If a does not equal 0, then k is called the degree of the monomial.
For each question, tell if the expression is a monomial.
If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not.
A. 2x^3
B. 8/x
C. -2x^(-3)
D. 8x/y
E. x^2 + y^2
A is a monomial. The variable is x. The coefficient is 2 and power is 3.
B is not a monomial. You see, 8/x can be written as 8x^(-1). The negative power indicates that it is not a monomial.
C. C is not a monomial for the same reason that B is not a monomial.
D is not a monomial for the same reason that B and C are not a monomial.
E is not a monomial. It is a binomial.
Do you agree with my reasoning and answers?
The Bermuda Triangle Karen is doing research on the Bermuda Triangle which she defines roughly by Hamilton.Bermuda; San Juan . Puerto Rico; and Fort Lauderdale, Florida.On her atlas Karen measures the straight-line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton to be approximately 57 millimeters (mm ), 58 mm, and 53.5 mm respectively. If the actual distance from Fort Lauderdale to San Juan is 1046 miles.
approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale.
I need to calculate the scale of the map.
58 mm/(1046 miles) = 1/18.03 miles per mm. This is the scale of the map.
Distance from Puerto Rico to Bermuda:
53.5 mm • 1/(1046) miles per mm is ≈ 2.97 miles.
Distance from Bermuda to Florida:
57 mm • 1/(1046) miles per mm is ≈ 3.16 miles.
It looks ok to me.