geno3141

P.E.  =  mass x g x height

P.E.  =  54 kg x 9.8 N/kg x 8.0 m

P.E.  =  4200 J   (rounded)

The domain consists of all the x-values:  domain = {-1}

The range consists of all the y-values:  range = {1}

Usually, the domain and range is defined for a more extensive function.

10^(-1)  =  1/(10^1)  = 1/10

Also:  3^(-1)  =  1/3

and:  4^(-2)  =  1/(4^2)  =  1/16

         2^(-5)  =  1/(2^5)  =  1/32

Is the score + 13; can you tell us the rest of the problem?

Authors have agreed to  define the set of "natural numbers" to be the same set as the set of "counting numbers", which is:  {1, 2, 3, 4, 5, ...}.

They then define the set of "whole numbers" to be: {0, 1, 2, 3, 4, ...}.

Thus, yes, 0 is a whole number.

You want to get the 'x' alone on the left side. If you have any number added to, or subtracted from, the x-term get rid of it first.

3x + 17 = -7

Subtract 17 from both sides:                (-7 - 17 = -24)

3x = -24

Divide both sides by 3:

x = -8

6% written as a decimal is .06

To calculate 6% of 29, find .06 x 29.

There is a calculator at this site to help you.

It is worth knowing that 1/3 = .333333...

and                              2/3 = .666666...

So,  6.66666...  = 6 2/3  or  20/3.

20000  =  9330(1.10)^n

First, divide by 9330:

20000/9330  = (1.10)^n

To solve an equation that has the variable as an exponent, find the log of both sides:

log(20000/9330)  =  log(1.10^n)

The reason to find the log of both sides is that an exponent in the log will come out s a multiplier:

log(20000/9330)  =  n·log(1.1)

Divide both sides by log(1.1);

log(20000/9330) / log(1.1)  =  n

Enter this into a calculator to get your answer.

cot(x) = 1/tan(x)

The period of tan(x) and cot(x) is the same; it equals π.

If there is a multiplier of x, so that you have cot(ax), the period will be π/a; this means that the period of this function is π/(2π) = 1/2. The entire function will make one period between 0 and 1/2.

At 0, tan(x) = 0, so cot(x) is undefined; because the period is 1/2, it will also be undefined at 1/2.

Halfway between, at 1/4, 2cot(2π(1/4)  =  2cot(π/2) = 0.

The graph starts with a y-value of +∞ at x = 0, waves down through the point (1/4,0), and continues down to   -∞ at x = 1/2.

Graph it on a calculator, restrict the x-values to between -1/2 and +1/2.