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Bayes' rule is a really neat equation that's used everywhere, including in Artificial Intelligence! Most things in the real world aren't certain: that's why we use probabilities. Also, we often can't dire...

This question tests fundamental understanding of integration and checks that the student is not simply memorizing the simple examples for the test. Most students will remember that the integral of 1/x is ...

y = x^x, by taking logs:ln(y) = ln(x^x )By log laws:ln(y) = xln(x)From implicit differentiation; d/dx = y'*d/dy, so:d/dx[ln(y)] = y'*d/dy[ln(y)] = y' * 1/yFrom the product rule; d/dx[...

There are two main steps. First find the gradient of the curve at x = 2 (m). This is done by differentiating the curve equation y = 3x^2 + 4 to get dy/dx = 6x. By plugging in x = 2, we get the gradient of...

First, we make the standard assumption that there is no air resistance, meaning that gravity is the only force acting on our cannonball. We then use the SUVAT equations, so: S = 0m (because it will return...