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y = arcsin(x) implies sin(y) = xDifferentiating with respect to x gives: cos(y)*dy/dx = 1So: dy/dx = 1/cos(y)Noting that cos(y) = sqrt(1 - sin^2(y)): dy/dx = 1/sqrt(1 - sin^2...

method: complete the squares for (x^2 - 2x ) and ( y^2 + 14y ) using the formula (b/2)^2 (where the general equation is ax^2 + bx) so that the equation becomes ax^2 + bx ...

First let’s break this statement down. At the core of this sentence are two consecutive multiples of 5. How can we represent these using algebra? Let’s use 5a where “a” is an integer. A consecutive multip...

Note that we have a constant probability, fixed number of tests, independent patients and only two outcomes, so we can write a binomial distribution X~Bin(4000,0.0005) where X is the random variable repre...

To solve this differential, firstly note that 2cos(x)sin(x) = sin(2x) (by the Half-Angle Sine Identity), this makes computing the differential a lot easier. ...