CPhill

cos(sin (pi)) = cos(0)  = 1

And

tangent(1) = about 1.557     assuming radian measure

y = 8 is a horizontal line at, well, y =8

And since no single vertical line "cuts" this line in more than one place, it is a function......(this is known as the vertical line test)

sin(30)/1 = 6/x     cross-multiply

xsin 30 = 6          divide both sides by sin30

x = 6 /(sin 30)     and sin 30 = 1/2  ... so...

x = 6/(1/2)

x = 12

Call x the number of tickets they gave to employees. Then, 5x is the number they gave to the listeners.

Then

x + 5x = 294

6x = 294      divide both sides by 6

x = 49

And that's the number they gave to the employees....

log72 (x2 - x) = 1

In exponential form, we have

72^1 = x^2 - x  rearrange

x^2 - x - 72 = 0     factor

(x - 9) (x + 8) = 0   and setting each factor to 0, we have that x = 9 and x = -8

And both solutions "work".....

For the second one, we have

tan(3x)/x  = (sin3x)/x * 1/cos3x = (3sin3x/3x) * 1/(cos 3x) 

Let 3x = Θ

And  using the fact that sinΘ/Θ = 1, and cosΘ = 1   as Θ→ 0..... we have

(3sinΘ/Θ) * 1/cosΘ = (3)(sinΘ/Θ) * 1/cosΘ =

[3(1)] / [1/1]  = 3/1  = 3  

This refers to integer values of the sides in a right triangle where the sum of the squares of the lengths of the two smaller sides is equal to the square of the largest side.

Some well known ones are....

3, 4 ,5

5, 12, 13 , etc.

Also, oddly enough, any multiples of a Pythagorean Triple also generates more Triples.

So, using 3,4,5.....

6,8,10  ......9, 12, 15.....12, 16, 20  are all Triples since they are all multiples of 3,4,5 !!!!

I = Prt    ....so, to find"r," just divide both sides by Pt.....and we have

I/(Pt)  = r

Saseflower is correct.......

And, to add to what she has said, a man named Cantor showed that, between any two values on the number line, an infinite (and uncountable) number of values exist.......