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Find the equation of the tangent at x=1 for the curve y=(4x^2+1)^3

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 = 3 8x (4x^2+1)^2. To then get the gradient of the tan...
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Answered by Jacob H. • Maths tutor
4055 Views

If the fourth term in an arithmetic sequence is, u4 = 12.5, the tenth is u10 = 27.5. Find the common difference and the 20th term.

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 first equat...
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Answered by Ndalukile K. • Maths tutor
3105 Views

Solve these simultaneous equations: 3y + x = 18 and x - 4y = -10.

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.
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Answered by Tess E. • Maths tutor
3778 Views

Analyse the effects on the UK economy of a recession in another economy with trade ties.

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 co...
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Answered by Luke J. • Economics tutor
10292 Views

Describe the structure of DNA.

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 attach ...
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Answered by Bethan P. • Biology tutor
12154 Views