Recent content by Hivoyer

Homework Statement I'm given this problem and I think I'm supposed to use the same or similar method to solve both of its parts: a) Factor 2^{15} - 1 = 32,767 into a product of two smaller positive integers. b) Find an integer x such that 1 < x < 2^{32767} - 1 and 2^{32767} is...

I thought y_o could not be equal to 0.You mean y_0 > 0 instead of y_0 \geq 0 right?

Homework Statement The problem states that: y_0 \neq 0 |y - y_0| < \frac{|y_0|}{2} |y - y_0| < \frac{\epsilon|y_0|^2}{2} And I am supposed to use these to prove that: y \neq 0 |\frac{1}{y} - \frac{1}{y_0}| < \epsilon Homework Equations |a| - |b| \leq |a - b|...

Here is the problem from the book(part (c) in the red rectangle): Here is the solution of (c) from the answer book(again surrounded in red):

Homework Statement I have the equation: x^2 + 2*x*y + 5*y^2 - 4*x - 6*y +7 and I have to find the minimum value I'm getting something that looks half like the correct answer, but not quite right... Homework Equations The answer from the answer book is: [x + 2*(y - 1)]^2 + (y + 1)^2...

Is there an exact reason for the non-uniformness or is it all just random?I mean in the early stages of Earth's development when It was still hot, shouldn't all types of substances have spread more or less evenly?

Oh yeah thanks I didn't see that, but anyway, I'm not sure about the One.Are you referring to the '1'?

Homework Statement This is the equation: x^3 - 2*x^2 + 1 = 0 Homework Equations The Attempt at a Solution If I take x out of brackets I get x*(x^2 - 2*x + 1/x) = 0 so either x = 0 or the thing inside it equals 0, however I'm not sure what to do inside the brackets now, I can't...

By doing that I get: 8*v - 7*u = u*v 12*v^2 - 196*u^2 = 3*u^2*v^2 I can't use any of them to express u = # or v = # :(

Homework Statement The system is declared as follows: 8/(2*x - y) - 7/(x + 2*y) = 1 4/((2*x - y)^2) - 7/((x + 2*y)^2) = 3/28 Homework Equations The Attempt at a Solution I define 'x' to equal k*y and I replace it inside the equation: 8/(2*k*y^2) - 7(k*y + 2*y) = 1...

Homework Statement I have a system of two equations: 3*x^2 - x + 3*y^2 = 0 2*x^2 - y + 2*y^2 = 0 Homework Equations The Attempt at a Solution I don't know how to express one with the other.I mean I can either have x = 3*y^2 + 3*x^2 or y = y = -2*y^2 - 2*x^2 and in both cases it...

oh yeah, sorry about that, so it seems that squaring them isn't the way to proceed anyway, can you offer a tip?

Homework Statement an arithmetic progression(a1-a9) has 9 numbers. a1 equals 1 The combination(S) of all of the numbers of the arithmetic progression is 369 a geometric progression(b1-b9) also has 9 numbers. b1 equals a1(1) b9 equals a9(unknown) find b7 Homework Equations...

thanks for the help, I eventually end up with (2x-4)/(x^2 - x - 2) = 1 which I turn into x^2 - x + 2 = 0 and turns out that D < 0, so no real roots.

Homework Statement This is the equation: 2/(2 - x) + 6/(x^2 - x - 2) = 1Homework Equations sqrt= square root ^ = to the power of The Attempt at a Solution First thing that comes to mind is to turn it into this: 2x^2 - 2x - 2 + 12 - 6x = (2 - 2)(x^2 -x -2) Then it gets real ugly: x^3 - x^2 -...