Math Help

Archive for the ‘Math Equations’ Category

Cubic equations are equations in the following form. The highest power of x in cubic equations is 3, meaning that the coefficient a of x cube cannot be zero. If a is zero then the equation is not a cubic equation. Below are roots of cubic equations. Roots of cubic equations are useful in solving cubic equations and factoring cubic equations. We will deal with how to solve cubic equations and step by step cubic equations in another section. For this section, we introduce cubic equations and the roots of cubic equation formulas.

Cubic equations can be written in the above form.

Roots of cubic equations

When solving cubic equations, if the roots of the cubic equation are given by:

Then the following Math Formulas are true for the cube roots of the cubic equation.

Question: show dy/dx = 1 + 2x + y^2 + 2xy^2 is a separable equation?

This is a differential equations math question. thanks if you can help.

Answer: The right side factors
1 + 2x + y^2 + 2xy^2
= (1 + 2x) + (y^2 + 2xy^2)
= (1 + 2x) + y^2 (1 + 2x)
= (1 + 2x)(1 + y^2).

Thus, the DE may be rewritten
dy/dx = (1 + 2x)(1 + y^2)

Note: The algebra below has been fixed.
————-
This may be separated as follows:
dy/(1 + y^2) = (1 + 2x) dx

(For completeness, this has general solution
arctan y = x + x^2 + C, or y = tan(x^2 + x + C).)

I hope this helps!

Math: Differential Equations Introduction

Question: boring SAT math question no.2:graphing simultaneous equations.?

HI Im trying to figure out graphing simultaneous equations for my SAT from my prep book.

I have some questions. In one of the the questions in my book it gives: solve graphically the equations 4x – y = 5 and 2x+4y=16.
for 4x – y = 5 it gives y= 4x-5 I think i’ve realised you switch the constant and variables across to get -y= -4x +5 and that you take the -y as -1 and then divide -1(-y) into -4x to get +4x and then -5 divided by -1(-y) gives you +5
but can someone tell me if this is right or how much its correct.
then for the 2nd equation
(remember these are SIMULTANEOUS GRAPHICAL OR GRAPH equations) 2x + 4y = 16 it gives y = -1/2x +4. Is that bcoz first u get 4y= -2x + 16 and then you divde 4 (4y) into itself to get y and then 4 (4y) into -2x to get -1/2 x and 4(4y) into 16 to get 4?

it says the solution for x and y are 2 and 3 which is the unique solution for both – and I get that… I’ll ask more in the next post but 4now can someone please help, with this part.

Answer: No mistakes. Well done!

A14.9 Graphing Linear Equations