CPhill

(x^2/3)^(4/5)  =   [multiply the exponents ]

x^(8/15)

tan = y/x = 3/4  

We need to find r  =  sqrt(y^2 + x^2) =   sqrt(3^2 + 4^2)  =  sqrt(25)  = 5

And csc  =   r / y   =   5 / 3

You are correct, Guest....!!!

40.18 /  796  = about  5%

e^(-t)=0.01   take the ln   of both sides

ln e^(-t)=  ln(0.01)     and by a log property, we can write

(-t) ln e  = ln (0.01)     and ln e  = 1, so we can forget this term

-t = ln (0.01)    multiply both sides by  -1

t = -ln(0.01) =  about 4.605

I guess you want to evaluate  x^2 + 6x + 9   when x = -4   ???

So we have

(-4)^2 + 6(-4) + 9   =

16 - 24 + 9  =

25 - 24  =

1

In scientific notation, it's

5.8 x  10¹⁰    

 But  since 5.8 is close to 6 and you want an estimate, we can write....   ≈ 6 x 10¹⁰        

2.38656 x 10⁷

I assume this is

[3 *45] / [ 16 + 5]  =

(3/21) * 45 

(1/7) * 45  =

45/7

             2x - 5

             2x - 5

         -------------

          -10x + 25

4x^2  -10x

----------------------

4x^2  - 20x  + 25