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The surface area of a sphere can be calculated using Area = 4 x Pi x r^2. Since we know the surface are of the first sphere is 4m^2, we can write: 4 = 4 x Pi x r^2. This simplifies to r^2 = 0.318. Taking ...

Area of a triangle = 1/2 x base x height
3 x 5 = 15cm1/2 of 15 = 7.5
Area = 7.5cm²

We treat this problem as two simultaneous equations, using our knowledge that when two graphs intersect, they simultaneously have the same solution. The second equation (quadratic equation) is already in ...

A stationary point is where the curve has 0 gradient. So to prove that x=4 is a stationary point, we must find the equation of the first derivative. To do this, differentiate x² - 2x - 24sqrtx....

Initially we find the first derivative of the function y = x⁶ + sqrt(x). We achieve this by multiplying each x term by the power it is raised to, then reducing the power by 1. Solution:<...