Alan

The following should help:

Just use the standard ! character on your keyboard.  e.g. 5! followed by Enter or = results in 120.

"Find a polynomial f(x) of degree 5 such that both of these properties hold:
 f(x) is divisible by x^3.
 f(x)+2 is divisible by (x+1)^3."

COB = 2*CDB = 60º

CAB + COB = 180º

You can finish from here.

sin(pi/6) = 1/2

cot(45º) = 1

cos(pi) = -1

You can insert these into 6sin(pi/6)+2cot(45º) + 5cos(pi)

Вы можете вставить их в 6sin (pi / 6) + 2cot (45º) + 5cos (pi)

For a.  ask yourself if the boat is accelerating in the tangential direction.

For b. Normal force is mass.v²/R  and here, mass.g = 1200 N, v = 20 m/s, R = 40m.

The appropriate equations are as follows:

\(\text{a. and b. }T_B\sin(45°)-mg=0\\\text{ and }T_A-T_Bcos(45°)=0\\\text{c. }T_B-mg\sin(45°)=0\)

I'll leave you to take it from here.

"Solve the system

a^2 + b = 7

a + b^2 = 11

in real numbers."

I get a the same answer as Geno, obtained in a different way:

"A hat contains 2 red marbles, 3 blue marbles, and 4 green marbles.  You choose two different marbles at random.  What is the probability that they are the same color?"

            red           blue          green  

\(p=\frac{2}{9}\times \frac{1}{8}+\frac{3}{9}\times \frac{2}{8}+\frac{4}{9}\times \frac{3}{8}=\frac{5}{18}=0.278\)