geno3141

Since each bus holds 47 passengers, divide the number of passengers (1222) by 47 to get the number of busses that you need.

If the quotient is a whole number, fine, that's your answer; if it isn't a whole number, you'll have to increase the quotient by 1, so you don't leave any passengers behind.

√x > 13

Square both sides:    ( √x )²  >  ( 13 )²

--->                             x      >    169

So, every number greater than 169 is a corrent answer. 

Check by using the convers of the Pythagorean Theorem:  If c²  =  a² + b², then the triangle is a right triangle.

'c' must be the longest side; the other two sides are interchangeable; so,  c = 29.

Does  29²  =  18² + 23² ?

If so, it is a right triangle, if not, it isn't.

Can you take it from here?

When simplifying complex numbers, add/subtract the real parts and add/subtract the imaginary parts -- use the same rules that you use to simplify algebraic expressions.

(3 + 4i) - (2 - 5i)  =  3 + 4i - 2 + 5i  =  3 - 2 + 4i + 5i  =  1 + 9i

(8 - 6i) + (7 + 4i)  =  8 - 6i + 7 + 4i  =  8 + 7 - 6i + 4i  =  15 - 2i

When adding/subtracting, you aren't really using the idea that i = √-1.

However, when multiplying/dividing, you will use the idea that i = √-1.

A proportional relationship grows (or shrinks) at the same rate.

Examples:  If a basketball team scores 15 points in the first quarter, then a proportional relationship predicts that they score 15 points in each quarter, so they would have 30 points by half-time, 45 points at the end of the third quarter, and 60 points at the end of the game.

Another example: If you make $10.00 per hour, then after two hours, you have $20.00; after 6 hours, you have $60.00; and after 20 hours, you have $120.00.

Example of relationships that is not proportional:

Human growth rate: as a baby, you grow by the greatest amount of increase, as you get older, your growth rate slows, and stops.

Assuming a constant growth rate: 

Final Number  =  Beginning Number x ( rate ^ time )              (time:  1998 - 1994 = 4)

81 000 000  =  72 000 000 · r ^ 4

Dividing both sides by 72,000,000:          1.125  =  r^4

Finding the fourth root of both sides:              r  =  1.030

Using the formula to estimate the population iin 2016 (2016 - 1994 = 22):

    Final Number  =  72 0000 000 · 1.030 ^ 22  =   138, 000, 000  (rounded)

The total surface area of a cylinder can be found with this equation:   TSA  =  2·π·r·h  +  2·π·r² 

Changing 30 inches into feet:  30 inches ÷ 12 inches/foot  =  2.5 feet.

Since you didn't specify the 30 inches to be a radius or a diameter, I'll take it to be a diameter.

Changing a diameter of 2.5 feet into a radius:  2.5 feet ÷ 2  =  1.25 feet 

TSA  =  2·π·1.25·30  +  2·π·1.25²  =  245.4 square feet

If you don't want to include the area of the two ends, don't include the  2·π·r²  term.

Assuming a regular rate:

Final Amount  =  (Initial Amount) x (rate ^ time)

           2200  =  2000 · r^4

Dividing by 2000:         1.1  =  r^4

Finding the fourth root:    r  =  1.024

After 9 hours:  Final Amount  =  2000 · 1.024^9

     --->   Final Amount  =  2478 

log(x) + log(2x)  =  log(18)

In the beginning, you can't find the antilog of both sides because the left side isn't just one log. But, you can turn the addition of two logs into one log by combining them this way:

log(x · 2x)  =  log(18)

log(2x²)  =  log(18)

Once you have the equation so that both sides are logs, find the antillog of both sides:

   2x²  =  18

    x²  =  9

Either x = 3    <---   answer!

or      x = -3   <---   impossible because the log of a negative number, such as log(-3), is undefined

π · 34 ÷ 4 - 56  =  34π ÷ 4 - 56  =  (34π/4) - 56  =  (34/4)π - 56  =  (17/2)π - 56