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Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.

In order to find the equation of the tangent to a curve at a point (x₁, y₁), we use the equation y - y₁ = m(x - x₁), where m is the gradient of the curve at (x<...

Answered by Benjamin C. • Further Mathematics tutor

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Let f(x) = x * sin(2x). Find the area beneath the graph of y = f(x), bounded by the x-axis, the y-axis and the line x = π/2.

After short consideration, we see that we must integrate f(x) with respect to x, between 0 and π/2, using integration by parts. Taking the formula for integration by parts, we set u = x and dv/dx = sin(2x...

Answered by Benjamin C. • Maths tutor

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Describe the process of transcription of DNA

DNA transcription is the process of copying the DNA strand in order to make mRNA that is needed for protein synthesis. Firstly, RNA polymerase attaches to the double helix of DNA, this unwound by the RNA ...

Answered by Matt H. • Biology tutor

3982 Views

Discuss the view that the measures taken to reduce the size of the budget deficit will inevitably result in a rise in unemployment in the UK.

The budget deficit of the government is the amount that needs to be borrowed in order to allow the government to spend what they want to. The budget deficit can be reduced by either tax increases or a red...

Answered by Cameron L. • Economics tutor

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Explain how geographical isolation can result in speciation

When two populations are geographically isolated they can no longer interbreed. There is no mixing of genes between the groups and over generations differences build up between the populations. This is ca...

Answered by Tamsyn D. • Biology tutor

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