ElectricPavlov

Distance from the origin for point (x,y) is    sqrt(x^2 + y^2)    (like pythagorean theorem)

2/5 * x = 42    Where x is the number of students in the class

x = 42 * 5/2 = 105 students in the class.

(2+5i)(2+5i)=

4 + 20i + 25 i^2 =

4 + 20i -25

=  20i - 21

Agree, but you cn just trial and error it to 'zero' in on n

for n C5 = 591600030      you should know that n is large    start at 100....too small     try 200   too large

150 ?   perfect          n = 150    

csc = cosecant = 1/sin x     valid for all sin values except  0

A = arcsin(36/41) = 61.4 degrees

x^2-11x+24=0   Use quadratic formula

(11+-sqrt(121-96)) /2  = (11+-5)/2 =  8   and   3 

The volume of the marbles is   26-20.9 = 5.1 l      and there ar e85 marbles

5.1/85 = .06 l/marble

then 200 marbles would requrie    .06 l/marble x 200 marbles = 12 liters

so he would only need  26-12= 14 liters of water to fill the tank !

73/99  IS in simplified form       or in decimal form = .73737373....

One more chime in...... 

x = time of one pipe   x+2 = time of other pipe

Much like two resistors in parallel:   r= (r1xr2)/(r1+r2)

x * (x+2) / (x +(x+2))  = 6

(x^2 +2x)/ (2x+2) = 6

x^2 +2x = 12x + 12

x^2-10x-12 = 0           Now use quadratic formula

x = (10+- sqrt(100+48))/2          x = 5+- 6.08     x = 11.08 hrs      the other pipe is x+2 = 13.08 hrs