Dylan

Why is it that when I type a word with number 5, it's different than with no numbers? ma5 (吗） is different from ma （马）. la5（鞡） la（拉）. I know there are only 4 tone marks What does the 5 represent?

A = (1010^1010)/(2010^2010)

B = (2010^2010)/(3010^3010)

Which is larger, A or B? (no calculators)

This is supposed to be 6th grade math, but I forgot how to do it :P

(remember, 6th grade math, so no calculus, though I don't think you need it)

Prove:

Σ 1/n! = e - 1

n is every integer from 1 to ∞

Why do a lot of people always turn complex inequalities into equalities and leave it like that?

They get a problem like ax^2 + bx + c > 0 and solve it with x equal something, it makes me so angry!

You can't end it there. It's much more complicated that that! Half the time when they do turn it back, they get the signs all wrong!

I don't disagree with turning it to equal, but that's only helpful if you're solving by graph.. You need more than just that. Inequality solutions are infinite, and those answers are just marking points that help you restrict your solution.

1 + Σ 1/n!

n goes from 1 to infinity

If x + y + xy = 8, find the minimum value of P = x^2 + y^2

For reference, use the inequality a + b ≥ 2√ab (don't have to prove)

Try not to use calculus.

Thanks.

Triangle ABC is right at A. AD is the angle bisector (D ∈ BC), ∠BAD = ∠CAD.

AB = 4, DC = 5. Find AC and BD.

(solve using geometry and algebra only)

Triangle ABC is right at A, with angle bisector AD (D ∈ BC).

AB = 4, DC = 5. Find AC and BD.

(solve using geometry and algebra only)

Calculate the EXACT time between 2.00 and 3.00 when the minute hand and the hour hand are:

Touching (in the same position)

Perpendicular (forming a 90° angle)

Colinear (forming a 180° angle)

f(x) = x^2/(x - 1)

If f(x) > 0, find the minimum value of f(x) (using only algebra)

Apply the inequality:

a + b ≥ 2√ab

Prove that the quadrilateral formed by joining 4 midpoints of the sides of ANY quadrilateral is a parallelogram.

State the property of the original quadrilateral so the one joint by its midpoints is:

A rhombus

A rectangle

A square

Prove that the figure formed by joining 4 midpoints of the sides of ANY quadrilateral is a parallelogram.

State the property of the quadrilateral so that figure is:

A rhombus

A rectangle

A square

(x + y - 2√xy) / (√-x + √-y)

(No complex numbers)

1, 2, 2, 4, 8, 11, 33, 37, 148, ...

Factor:

x^(2n + 1) - y^(2n + 1)

x^(2n + 1) + y^(2n + 1)

(x - 2008)^2010 + (x - 2009)^2010 = 1

Prove that the above equation has no solutions other than 2008 and 2009.

x^2 - 2x - 7 + 3√(x + 1)(x - 3) = 0

Find a way to solve without squaring. Squaring only makes the equation harder. Nobody likes having to deal with quartics.

No calculators, also.

|x - 2007|^2007 + |x - 2008|^2008 = 1

Tại sao khi biết tin làng Chợ Dầu cải chính, mụ chủ nhà lại tỏ vẻ vui mừng chứ không cáu giận như Ông Hai dự đoán?

*Không phải bài tập, mình chỉ tò mò thôi.

x^4 - 3x^3 - 6x^2 + 3x + 1 = 0

The equation has the form a/e = (b/d)^2

No calculator. No quartic formula needed.

You can solve it using substitution.