hectictar

Are there any requirements or guidelines that the function has to have?

If there aren't any, here's a simple one....

function:      y = (4/5)x         , x ≥ 0

real life situation:     It costs $4.00 to buy 5 apples. What is the price for any number of apples ?

x (input)    =   number of apples

y (output)  =   total price

table:         

\(\frac{\frac1{x^4}*x^8}{1^2}\)                   1^2 = 1

\(=\frac{\frac1{x^4}*x^8}{1}\)              Any number divided by 1 equals the  original number.

\(=\frac1{x^4}*x^8\)           Multiply straight across.

\(=\frac{x^8}{x^4}\)                    Use the exponent rule that says:    \(\frac{x^a}{x^b}=x^{a-b}\)

\(=x^{8-4} \\~\\ =x^4\)

\(\frac53\,*\,3\)

That is the same thing as

\(5\,\div\,3\,*\,3\)

What happens if you take  5 , divide it by  3 , then immediately turn around and multiply it by  3 ?

\(5\,\div\,3\,*\,3\,=\,5\)      

They are on the second column from the right.

The multiplication button looks like this:      ×

The division button looks like this:               ÷

But.....you can just type the symbols into the bar.

To do      5 * 4     , type      5*4

To do      5 / 4     , type      5/4          

Rarinstraw's answer is correct if the triangle is a right triangle with C as the 90º angle, but if the triangle is not a right triangle, you can use the Law of Sines to find other two lengths.

The Law of Sines says:

\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)

where  A ,  B ,  and  C  are angles, and  a ,  b , and  c , are sides across from their respective angles.

We can find the radius using the circumference.

circumference  =  2π * radius

87.92  =    2π * radius                                        Divide both sides of this equation by 2π .

87.92 / (2π)  =  radius

43.96 / π      =  radius

volume of cylinder = ( π * radius² )(height)         Plug in what we know to be the radius and height.

                              = ( π * (43.96/π)² )(160)

                              = ( π * 43.96² / π² )(160)

                              = (1932.4816/π)(160)

                              = 309,197.056/π

                              ≈ 309,197.056/(3.14)     =     98470.4  cubic cm

The slope of this line is 3/4, which means every time the line goes up 3 units, it goes right 4 units.

The y-intercept is 3.

Here's a graph:

(x - 3)² + (y - 1)²   =   16

To get this into general form, we need to multiply out   (x - 3)²   and   (y - 1)² .

(x - 3)(x - 3)  +  (y - 1)(y - 1)   =   16                      First, let's just do (x - 3)² .

x² - 3x - 3x + 9  +  (y - 1)(y - 1)   =   16                Now, let's do (y - 1)² .

x² - 3x - 3x + 9  +  y² - 1y - 1y + 1   =   16          Subtract 16 from both sides of the equation.

x² - 3x - 3x + 9  +  y² - 1y - 1y + 1 - 16   =   0     Combine like terms.

x² - 6x + y² - 2y - 6 = 0          Rearrange.

x² + y² - 6x - 2y - 6 = 0

Gwendolynkristine, here's a trick you can use to get the picture to show:

Go to the link you just posted. Right click on the picture and select  " Copy image URL / Address / Location " * . Then, on this website click the  " Image "  button like normal and right under where it says URL,  paste the URL that you copied.

*

If you are using Internet Explorer, select "Properties" and copy the address next to "Address (URL)"

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Let's call the  base = 12.5

That makes the  height = 15sin77º

area  =  (1/2)(base)(height)

area  =  (1/2)(12.5)(15sin77º)

area  =  93.75sin77º

area  ≈  91.35  sq. un.

From looking at the graph, we can see that

the center of this circle is the point   (3, 0)      and

the radius of this circle is   5   units.

So, the equation of this circle in standard form is:

(x - 3)² + (y - 0)²  =  5²          Simplified, this is....

(x - 3)² + y²  =  25

To get this equation in general form, first multiply out the (x - 3)² .

(x - 3)(x - 3) + y²  =  25

x² - 3x - 3x + 9 + y²  =  25             Subtract 25 from both sides of the equation.

x² - 3x - 3x + 9 + y² - 25  =  0        Combine like terms and rearrange.

x² + y² - 6x - 16  =  0