geno3141

Divide  3  by  8  and multiply your answer by  100.

3/8  =  .375                            .375 x 100  =  37.5%

2^x  =  3

Whenever the unknown is in the exponent, use logarithms. You can use either log (common logs) or ln (natural logs).

Take the log of both sides:

log(2^x)  =  log (3)                       

A property of logarithms is that the exponent comes out as a multiplier:

x·log(2)  =  log(3)

x  =  log(3) / log(2)

x  ≈  1.585

I could have used  ln  instead of  log ; the steps and the answer would be the same.

Be careful with your spelling!

"pi" is the symbol for that weird number ...

"pie" has an extra "e" and you've learned in science class that "e" stands for "energy"; the energy that you have to expend going to a bakery to buy a pie or the energy that you need to bake a pie at home!

Rewrite 2 as 18/9

18/9 - 7/9  =  11/9

Let's check!

Replace x with 4 and y with -3

  Does  -3  =  3(4) - 2 ?

  Does  -3  =  12 - 2 ?

no!

(f + g)(x)  =  f(x) + g(x)

               = [4x + 3] + [2x - 3]

                =  6x 

16000  =  70000e^(-3a)

Divide both sides by 70000:

8/35  =  e^(-3a)

Take the ln of both sides:

ln(8/35)  =  ln(e^(-3a))

Exponents come out as multipliers:

ln(8/35)  =  -3a ·ln(e)                                   ln(e)  =  1

ln(8/35)  =  -3a

a  =  ln(8/35) / -3     ≈     .4919688...

Divide both sides by -9:

-22 / -9  =  -9v / -9

22/9  =  v

Is there more to this problem?

For the third problem:

Use deMoivre's Theorem:

Write the  complex number in r[cos(θ) +i·sin(θ)] form:          r = √(x²+y²)      θ = invTan(y/x)

z  =  1 + i   --->  x = 1 and y = 1         r = √(1²+1²)    --->   r  =  √2                  θ = invTan(1/1)   = 45°   

z^(1/3)  --->   r^(1/3)[cos(θ/3) + ·isin(θ/3)  --->  (√2)^(1/3)[cos(45°/3) +i·sin(45°/3)]

     --->  (2)^(1/6)[cos(15) + isin(15)]

then, add two more values by adding 360°/3  =  120°  and 2·360°/3 =  240°

--->    (2)^(1/6)[cos(135°) + isin(135°)]   and    (2)^(1/6)[cos(255°) + isin(255°)]