geno3141

Since all the particles have the same charge, you must divide the charge equally;

          -56  ÷  8  =  -7

(7y³ - y² + 9)(3y² + y + 1)

Use the distributive property (an extended FOIL):

=  7y³(3y² + y + 1) - y²(3y² + y + 1) + 9(3y² + y + 1)

=  7y³(3y²) + 7y³(y) + 1(7y³)     - y²(3y²) - y²(y) - y²(1)     + 9(3y²) + 9(y) + 9(1)

=  21y^5 + 7y^4 + 7y³    - 3y^4 - y³ - y²    + 27y² + 9y + 9

=  21y^5  + 4y^4 + 6y³ + 26y² + 9y + 9

Simple interest formula:  I = P ·r·t

where:  P  =  Principal (amount invested)         r  =  rate (as a decimal)         t  =  time (years)

           I  =  interest earned (not the final amount; the final amount will be  P + I)

-----     the time is usually in years because the rate is usually a yearly rate     -----

Compound interest formula:        A  =  P(1 + r/n)^(n·t)

where:  P  =  Principal (beginning amount)         r  =  rate (as a decimal)          t  =  time (number of years)

            A  =  final amount (not just the interest earned)        n  =  number of compounding periods per year         

Both functions will be undefined when x = 1.

Beside this:

The denominator of g(x) is undefinded whenever x < 1. therefore, g(x) will be undefined for any x < 1.

In f(x), when both the numerator and the denominator are both negative, the quotient will be positive, therefore, f(x) will be defined. The only time that f(x) will be undefined will be when only one of the numerator/denominator group is negative. So, f(x) will be undefined only in the section -1 < x ≤ 1.

The functions are not equivalent when x ≤ -1; otherwise, they are.

Multiply the number times the number, add the exponents of 10 together.

For example:  (3 x 10^7)  x (5 x 10^6)  =  (3 x 5) x (10^7 x 10^6)  =  15 x 10^13  = 1.5 x 10^14

When a rational number is written as a decimal, it either terminates or repeats.

Example:

     8  =  8.0

     3/2  =  1.5

    2/3  =  0.66666...

An irrational number does not have a decimal portion that either repeats or terminates.

    √2  =  1.414213562...

    Π  =  3.14159265359...

    e  =  2.718282828459...

    0.101001000100001000001000000...

There are two ways that you can get the answer:

One way:  remove the powers:

     4 x 10³ =  4000         and         2 x 10²  =  200         and            4000 x 200  =  800 000

Other way:  when you multiply two numbers that have the same base, add the exponents:

    4 x 10³ x 2 x 10²   =  4 x 2 x 10³ x 10²  =  8 x 10^5  =  800 000

    because the exponents were added (2 + 3 = 5). 

x  =  y² + 2

To get the y-term alone on one side, subtract 2 from both sides:

x - 2  =  y²

Take the square root of both sides; remember to use the  ±  sign:

± √(x - 2)  =  y

Since P.E. depends upon height, if it's halfways down, it's P.E. will only be one-half of what it was.

What does the '&' mean? Are you supposed to add them together?