red balls in a game of snooker
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15 red balls in a game of snooker
No.Suppose a and b are two rational numbers.Then they can be written as follows: a = p/q, b = r/s where p, q, r and s are integers and q, s >0.Then a*b = (p*r)/(q*s).Using the properties of integers, p*r and q*s are integers and q*s is non-zero. So a*b can be expressed as a ratio of two integers and so the product is rational.
b
Suppose the points are P = (r,s) and Q = (t,u) Then gradient of PQ = (u - s)/(t - r) = m, say. Let Z = (x,y) be any point on the line. Then gradient ZP also = m that is (y - s)/(x - r) = m Equating the two expressions for m, (y - s)/(x - r) = (u - s)/(t - r) or y - s = (x - r)*(u - s)/(t - r) y = (x - r)*(u - s)/(t - r) + s = x*m - r*m - s This is of the form y = mx + b, where m is as defined above and b = -r*m + s
which function is a linear function? A. f(x)= x^3+x B. g(s)= 1-4s C. h(t)= 2t+1/t D. f(r)= square root of r