Tetration

$$10(\frac{1}{2})^{0/29}$$

0/x is 0 for all x ≠ 0, so the exponent will simply be 0. 

x⁰ is 1 for all x ≠ 0, so the second factor will simply be 1:

$$10(\frac{1}{2})^{0/29} = 10(\frac{1}{2})^{0} = 10*1 =10$$

1. Do the division

2. Multiply the answer by 100...

...and you have your percentage.

This is because percent means "per hundred" i. e. x% is x hundredth of something.

So we get:

7/13 ≈ 0.54

7/13 ≈ 54%

3 1/2 * 5/6      

Transfom the mixed numbers into improper fraction, using this formula (can you see why it's correct?)

$$a\frac{b}{c}=\frac{ac + b}{c}$$       We get:

$$3\frac{1}{2}=\frac{3*2+1}{2}= \frac{7}{2}$$    Thus the whole expression is:

$$\frac{7}{2}*\frac{5}{6}$$      Multiply numerator (top) by numerator, and denominator (bottom) by denominator:

$$\frac{7}{2}*\frac{5}{6}= \frac{7*5}{2*6}=\frac{35}{12}$$  

Remember that:

a + (-b) = a - b

So, we get:

1 + (-3) = 1 - 3 = -2

 8 is not that far from 10. So it isn't unlikely that 8²⁰¹⁵ has at least more than 1000 digits. Thus I use Wolfram Alpha to calculate this:

8²⁰¹⁵ ≈ 5.33 * 10¹⁸¹⁹.

Guess I was right ;)

Do you mean, solve: 3h² + 8h + 5 = 0 ?

Use the quadratic formula:

$$h = \frac{-b +/- sqrt(b^{2}-4ac)}{2a}$$

We get:

$$h = \frac{-8 +/- sqrt(8*8 - 4*3*5)}{2*3}$$

$$h= \frac{-8 +/- sqrt(64-60)}{6}$$

$$h = \frac{-8 +/- 2}{6} => h= \frac{-10}{6} ...v... h=\frac{-6}{6}$$

h = - 5/3  v  h = -1 

Where v is latin for "vel", indicating inclusive disjunction:

A v B means "A or B", or more precise: "either A, or B, or both"

Remember the order of operations:

1. Solve what's inside the paranthesis

2. multiply(*)  /  divide  (:)

3. Add(+)   /   subtract   (-)

y = 2x - 3 = 2(-1) - 3 = -2 - 3 = -5

$$\frac{x}{2}= \frac{1}{7}$$

Multiply both sides by 2:

$$x = \frac{2}{7}$$

.06 = 0.06

The 6 is on the hundredth place, so the fraction is:

6/100 = 3/50

Percent means "per hundred", thus: 7% = 7/100

7% of somehing means 7% * something.

We get:

7% * x = 154=

$$\frac{7}{100}* x = 154$$

$$\frac{7x}{100} = 154$$

Multiply both sides w/ 100:

$$7x = 15 400$$

Divide both sides by 7:

x = 2200