# Beat Unknown Soldier at his own game of math.

#### Unknown Soldier

##### Senior Member
Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax2+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n2+ n.

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
Another desecrate cry for attention and self affirmation.

US seeks recognition he is a mathematician.

My kind of logic puzzle is my last post in the programming thread.

Perhaps you could chnge it from 2d to 3d for me. Beat me at my own game......

#### Tigers!

##### Veteran Member
Why do we feel the need for a pissing competition at IIDB?

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
Why do we feel the need for a pissing competition at IIDB?
You are alwys free to put me on ignore if you do not like what I say. Said without prejudice or malice.

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax2+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n2+ n.
Seriously your mathematical problem statement is incomprehensible.

Here is one,

You have $10.00 total. You have 3$1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form. #### Tigers! ##### Veteran Member Why do we feel the need for a pissing competition at IIDB? You are alwys free to put me on ignore if you do not like what I say. Said without prejudice or malice. I was not referring to you, rather unknown soldier #### steve_bank ##### Diabetic retinopathy and poor eyesight. Typos ... Why do we feel the need for a pissing competition at IIDB? You are alwys free to put me on ignore if you do not like what I say. Said without prejudice or malice. I was not referring to you, rather unknown soldier Let him have his say. He is not hurting anybody. #### Swammerdami ##### Squadron Leader Staff member Here's a somewhat challenging math quiz. ... VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2. None of these problems are of interest or challenge to any "math expert," self-proclaimed or otherwise, but VI is somewhat nifty: This fact follows directly from the fact that the square of a real number is never negative. (a - b)2 ≥ 0 a2 + b2 - 2ab ≥ 0 a2 + b2 ≥ 2ab (a2 + b2) / ab ≥ 2 . . . . . . . # Note that ab > 0 a2/ab + b2/ab ≥ 2 a/b + b/a ≥ 2 QED. #### Unknown Soldier ##### Senior Member Here's a somewhat challenging math quiz. ... VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2. None of these problems are of interest or challenge to any "math expert," self-proclaimed or otherwise, but VI is somewhat nifty: This fact follows directly from the fact that the square of a real number is never negative. (a - b)2 ≥ 0 a2 + b2 - 2ab ≥ 0 a2 + b2 ≥ 2ab (a2 + b2) / ab ≥ 2 . . . . . . . # Note that ab > 0 a2/ab + b2/ab ≥ 2 a/b + b/a ≥ 2 QED. Excellent! That's exactly right. How about the other problems? #### Shadowy Man ##### Veteran Member Here's a somewhat challenging math quiz. ... VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2. None of these problems are of interest or challenge to any "math expert," self-proclaimed or otherwise, but VI is somewhat nifty: This fact follows directly from the fact that the square of a real number is never negative. (a - b)2 ≥ 0 a2 + b2 - 2ab ≥ 0 a2 + b2 ≥ 2ab (a2 + b2) / ab ≥ 2 . . . . . . . # Note that ab > 0 a2/ab + b2/ab ≥ 2 a/b + b/a ≥ 2 QED. Excellent! That's exactly right. How about the other problems? But what does that prove to you? Did Swammerdami just figure that out on their own? Did they know of the proof already? Why is this proof even of interest? As a physicist, I consider math a tool. I am interested in some of the pure math niftyness but I don’t spend a lot of time thinking about it. If I need it for my work I will depend on mathematicians to have figured it out already. #### Unknown Soldier ##### Senior Member Seriously your mathematical problem statement is incomprehensible. I can offer hints if you think they would help. If you're lost, then please admit it. And in any case, if you're rude to me, then I will ignore your posts. Here is one, You have 10.00 total. You have 3 1 bills. You have 5 quarters. You have 8 nickles, You have 2 dimes. How would you algebraically find how many pennies and additional nickels would you need you have to equal$$10.00? In equation form.
I will post my answer to this problem if you explain that you cannot complete the problems in the OP.

#### Unknown Soldier

##### Senior Member
As a physicist, I consider math a tool. I am interested in some of the pure math niftyness but I don’t spend a lot of time thinking about it. If I need it for my work I will depend on mathematicians to have figured it out already.
If that's true, then you should have no difficulty figuring out IV and V. All you need is knowledge of basic calculus and linear algebra, respectively.

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
If US is an expert in linear algebra show how to solve this simple problem using matrices.

x + 2y = 10
2x + 3y = 18

The solution is obvious from simple inspection. How using matrices and linear algebra wold yiu solve it? ... without looking it up on the net. Trivial stuff in engineering and science. More like high school algebra.

Show your work, partial credit will be given.

Then solve

(3xy) + (2xy) = 20
x^2 + y^2 = 16

Show the process of a solution. A tpyical kind of an engineering problem. This one should be easy for a mathematician.

There is a common way to solve it.

If you can not then I'll say you are beaten at your own game.

Please no hints from the peanut gallery,

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
Oops

Should be

(3xy) + (2xy) = 20
x^2 + y^2 = 8

##### Veteran Member
As a physicist, I consider math a tool. I am interested in some of the pure math niftyness but I don’t spend a lot of time thinking about it. If I need it for my work I will depend on mathematicians to have figured it out already.
If that's true, then you should have no difficulty figuring out IV and V. All you need is knowledge of basic calculus and linear algebra, respectively.
Maybe I could. I just don’t care to.

#### Juvenal

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.
One form of the definition is (A-B) U (B-A).
II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?
Assumes incorrectly those are the only colas.
III. If x is any real number and a, b, and c are real numbers where f(x) = ax2+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.
a+b+c=1
4a+2b+c=1
9a+3b+c=3
IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.
Area = G(pi)-G(0) with G(x)=-2 cos 3x / 3
(y-2 sin 3pi/6)/(x-pi/6) = 6cos 3x
V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?
xy-6=4 iff xy=10
VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.
a, b both positive or both negative -> x=a/b >0 and x+1/x ≥ 2 -> x^2-2x+1 ≥ 0 -> (x-1)^2≥0, corollary ab<0 then a/b+b/a ≤2
VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n2+ n.
if n≠0 mod 2, then n+1=0 mod 2 for all n in Z.

These are beyond trivial.

Try some real math. Prove any group of prime order is cyclic.

#### Juvenal

If US is an expert in linear algebra show how to solve this simple problem using matrices.

x + 2y = 10
2x + 3y = 18
(x | y) = (1 2 | 2 3 )^-1 (10 | 18)
The solution is obvious from simple inspection. How using matrices and linear algebra wold yiu solve it? ... without looking it up on the net. Trivial stuff in engineering and science. More like high school algebra.

Show your work, partial credit will be given.

Then solve

(3xy) + (2xy) = 20
x^2 + y^2 = 16
xy=4 -> 2xy=8 -> (x+y)^2=8 -> x+y = ±2√2
Show the process of a solution. A tpyical kind of an engineering problem. This one should be easy for a mathematician.

There is a common way to solve it.

If you can not then I'll say you are beaten at your own game.

Please no hints from the peanut gallery,
I was bored.

#### Juvenal

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax2+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n2+ n.
Seriously your mathematical problem statement is incomprehensible.

Here is one,

You have $10.00 total. You have 3$1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal 10.00? In equation form.
Ill-formed. 3+1.25+.40+.20 ≠ 10

Here's one for you.

Find the generating function that counts how many ways \$10 can be made up from dollar bills, quarters, nickels, and dimes.

#### Unknown Soldier

##### Senior Member
x + 2y = 10
2x + 3y = 18
Using the Desmos online graphing calculator, I get x = 6, y = 2.
(3xy) + (2xy) = 20
x^2 + y^2 = 8
Using the Desmos online graphing calculator, I get x = y = 2, and x = y = -2.

Would you prefer if I work these out manually?

#### steve_bank

##### Diabetic retinopathy and poor eyesight. Typos ...
x + 2y = 10
2x + 3y = 18
Using the Desmos online graphing calculator, I get x = 6, y = 2.
(3xy) + (2xy) = 20
x^2 + y^2 = 8
Using the Desmos online graphing calculator, I get x = y = 2, and x = y = -2.

Would you prefer if I work these out manually?
That was the idea. You loose......as I asked, work the first problem using matrices. Linear Algebra 101. You obviously don't even understand the question.

And then the second problem.

I used math tools extensively. My 'calculators' were Matlab, Scilab, and Mathcad. To use them intelligently I had yo know how the math worked, not be an expert.

I like the Penne and Teller TV show Fool Us. Magcians try to fool Penne and Teller with magic tricks. Hard to do with ther combined experince md knowledge of magic.

You are not fooling anyone here.