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The tangent is the straight line passing through x=1, touching the curve only at that point. For x=1, y=(4+1)^3=125 Using the chain rule we obtain dy/dx = 38x(4x^2+1)^2. To then get the gradient ...

The equations for an arithmetic sequences are 1) Un = u1 + (n - 1)d 2) Sn = n/2(2*u1 + (n-1)d) 3) Sn = n/2(u1 + un)

The first step is to calculate the common difference, d. This is done using the f...

Write x in terms of y using one of the equations. Then substitute it in the second equation, which is then only in terms of y. Find y. Then you can easily find x.

Answer: x = 6 and y = 4.

A recession is when an economy experiences negative growth in terms of GDP for two or more consecutive quarters. If an economy such as that of the US, a major trading partner, were to enter a recession it...

DNA is made of a string of nucleotide bases attached to one another by a peptide bond. A single nucleotide contains three regions: A phosphate group, a Carboxyl group and a base. Adjacent nucleotides atta...