geno3141

1/11 + 8/11  =  9/11

2/11 + 7/11  =  9/11

3/11 + 6/11  =  9/11

Since the number is smaller than 1, you will get a negative exponent; the number will be the number of places that you mov the decimal point from where it is until immediately after 1.

0.00 00 00 1  =  10^-7

log(0.0000001)  =  -7

From 1000° keep subtracting 360° until you get an answer in the range:  0° ≤ angle < 360°.

9x - 7  =  -7

Add 7 to both sides:

9x  =  0

Divide both sides by 9:

x  =  0

This is a quadratic, I would write it into this form and then use the quadratic formula:

2√3cos²θ - cosθ - 2√3 = 0

cosθ  =  [1 ± √( 1 - 4(2√309-2√3) ) ] / ( 4√3 )

cosθ  =  [ 1 ±  √(1 + 48) ] / ( 4√3 )

cosθ  =  8 / ( 4√3 )  =  2 / √3  --->  impossible        

or  cosθ  =  -6 / ( 4√3 )  =  - √3 / 2    --->  θ  =  5π/6  (too small)  or  θ  =  7π/6

If you mean:  (6^3) / (12^4)

This is [6 x 6 x 6] / [12 x 12x 12 x12]

  cancel the 6's into the 12's to get:  1 / [2 x 2 x 2 x 12]  =  1 / 96

Or, if you have to show all the exponential steps, 

Since  6 = 2·3,  6^3 = (2·3)^3  =  2^3 · 3^3

Since 12  =  4·3  =  2²·3,  12^4  =  (2²·3)^4  =  (2²)^4 · 3^4  =  2^8 · 3^4 

So:  (6^3) / (12^4)  =  [ 2^3 · 3^3 ] / [ 2^8 · 3^4 ]

                               =  1 / [ 2^5 ·  3 ]

                               =  1 / 96

a² / (1 - a)  =  K / b

Cross multiply:  a²b = K(1 - a)

Multiply out:     a²b  =  K - Ka

Transfer:          a²b + Ka - K  =  0

Use the quadratic formula:  a  =  [-K ± √( K² + 4bK) ] / (2b)

Yes! You are correct!

There are two log keys on your calculator:

'log'  is used for logs with a base of ten; called "common logs"; created to make calculations much easier before there were hand-held calculator.

'ln'  is used for logs with a base of e (an irrational number, approximately 2.7182818); called "natural logs"; because they occur naturally when using the base ten system (used exclusively in calculus and problems requiring calculus). 

The form is  y = mx + b;  you have y  =  (-1/2)x + 3.

For your problem,  m = -1/2  and  b = 3