重酬!!!!! SUPER EASY MATHS(new)

Q1
opposite side=a, adjacent side=b
hypotenuse=root(a^2+b^2) [By Pyth. Theorem]
cos X=adjacent side/ hypotenuse=b/root(a^2+b^2)

Q2
x^2+bx+a^2
=(x+1/2 b)^2+(a^2-b^2/4)
The minimum value of x^2+bx+a^2
=a^2-b^2/4
The maximum value of 1/(bx+a^2+x^2)
=1/(a^2-b^2/4)
=4/(4a^2-b^2)

Q3
P(1st number smaller than 2nd number)
=P(1st=1,2,3,4,5;2nd=6)+P(1st=1,2,3,4;2nd=5)+P(1st=1,2,3,;2nd=4)+P(1st=1,2;2nd=3)+P(1st=1;2nd=2)
=(5/6)(1/6)+(4/6)(1/6)+(3/6)(1/6)+(2/6)(1/6)+(1/6)(1/6)
=5/12