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The probability of passing at either the first or second time round is P(passing first time) + P(taking the test for a second time then passing)
= 0.7 + (0.85 x 0.3)= 0.7 + 0.255= 0....

Use the crab claw method to expand the bracket. Draw two lines above the equation from the 2X, one to the 3X and one to the -1. Draw another two lines below the equation from the +3, one to the 3X and one...

Factorise into (x-1)(x-2) = 0 to find that x = 1 or x = 2

R=sqrt(42)=6.48...a=arcos(4/sqrt(42))=0.905...Rsin(x+a)=6.48sin(x+0.905)

Take ln(x) = 1 * ln(x) and integrate by parts. Let u = ln(x) and dv/dx = 1 such that du/dx = 1/x and v = x. Using the integrating by parts formula, you get x ln(x) - integral(1) = x ln(x) - x + c.