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2x 2 < x+3, 2x 2 - x - 3 < 0, (2x - 3) (x + 1) < 0, Positive quadratic. Roots: x = -1 and x = 3/2, Therefore, x takes values greater than -1 and less than 3/2.

Using Pythagoras, x 2 + y 2 = r 2 .Using basic trigonometry, x = rsinθ and y = rcosθ. xy + 1 = r 2 sinθcosθ + 1 = (1/2)r 2 sin2θ + 1 Subbing in both halves and doubling gives:2r 2 = r 2 sin2θ + 2 -> r 2 (...

note: y' is often written as dy/dx, this doesn't change the question at all so no need to worry. Same for y'' and d 2 y/dx 2 .All second-order differential equations that don't have 0 on the right hand side ...

This is the type of question which requires some out of the box thinking. A sketch is presented below: We start by defining A = (a ij ), B = (b ij ) and C = (c ij ). We then use the definition of matrix mult...

Consider the expression (cos(theta) + i*sin(theta)) 5 . (Where theta a real parameter).By De Moirve's theorem, we know this expression is equivalent to cos(5theta) + i sin(5theta).We can also apply the binom...