CPhill

Correct answer.....

Let's "clean it up" a little

v = <5,7>

llvll = √(5² + 7²) = √(25 + 49) = √(74) ≈ 8.6

A little better, huh???

It's a THREE POINTER from the top of the arc by GL.... !!!

Thumbs Up   ......

We could do some fancy math here....but......since he gets only 1/5 of what he sells, then he has to sell 5 times as much $1000 = $5000 in order to make $1000

...Does that make sense ???

We can rewrite this as

(3^x)(3²)= 54 + (3^x)(3)         divide through by 3

(3^x)(3) = 18 + 3^x               subtract 3^x from both sides

(3^x)(3) - 3^x  = 18               factor the left side

(3^x)(3 - 1) = 18               simplify the left side

(3^x)(2) = 18                    divide both sides by 2

3^x = 9      ... so it appears that x = 2

First, only three-dimensional objects have "volume." A circle is a two-dimensional object that has an "area."

So, let's suppose you meant that it has an area of pi/6.

The "formula" for its area is   

A = pi*r^2       where r is the radius  ......     so we have

pi/6 = pi*r^2    divide both sides by pi

1/6 = r^2          take the positive square root of both sides

√(1/6) = r   ...   and "rationalizing" the denominator produces ... √(6)/6

Looks good to me, NinjaDevo.......

Let me guess...you want to find the cable length  ... ???

We have an angle and an opposite side  .....we are trying to find the hypoteneuse..so...the thing that relates these is the sine.......

sin(50) = 15/x     where x is the cable length ...  so

x = 15/sin(50)  = 19.58 ft.

The only other thing you might possibly want to know is how far the cable is anchored from the pole.

Use:    cos(50) = x / 19.58       .....and solve for x   ......!!!

18/33 = x/360

First. reduce the fraction  on the left to 6/11

So    6/11 = x/360

Cross-multiply

360*6 =  11x

2160 = 11x  ...  divide both sides by 11

x =  2160/11

sin(-1290°)

Using a trig identity, we have

sin(-1290°)  =  - sin(1290°)

First, express 1290/360 as a mixed number = 3 + 7/12

Disregard the "whole" part and multiply the fraction by 360

This gives 210...and sin(210) =  - (1/2)

But, we need the negative of this .... = 1/2

Of course.....putting the original thing into the on-site calculator would be faster ..... !!!!

(x-4) - (5x + 6) = 14

Distributing the negative outside the parenthesis changes all the signs on the things inside. So we have

x - 4 - 5x - 6 = 14     combine like terms

-4x -10 = 14           add 10 to both sides

-4x = 24                 divide both sides by -4

x = -6