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Find the equation of the tangent to the circle (x-3)^2 + (y-4)^2 = 13 that passes through the point (1,7)

Start with a sketch. We can see that the radius from the point (1,7) to the centre of the circle (3,4) is perpendicular to the tangent. The gradient of the radius is (4-7)/(3-1) = -3/2. We know that two p...

Answered by • Maths tutor

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How should I structure a main-body paragraph in a 25-mark essay question?

Although daunting facing a question a 25-mark question, following a template for structuring your paragraphs will help you feel more prepared and your argument will be clearer to the examiner reading it. ...

Answered by • Philosophy tutor

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The formation of new species is known as speciation. Explain the difference between Allopatric and Sympatric speciation. [1 mark]

Both allopatric and sympatric speciation occurs due to reproductive isolation between populations of the same species. Allopatric speciation involves a physical barrier such as a river or mountain separat...

Answered by Jonathan D. • Biology tutor

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What is the plus-que-parfait and when do you use it?

First of all, these more complex tenses are often very complicated and difficult so do not feel discouraged if you do not understand them initially, but once you do you will be using the plus question par...

Answered by Ella L. • French tutor

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use the substitution u=2+ln(x) to show that int(e,1(ln(x)/x(2+ln(x)^2))dx)=p+ln(q) , where p and q are rational numbers.

So u=2+lnx, therefore du/dx=1/x , we can work out the new upper and new lower limit by substitute in e and 1 into 2+lnx , and we get 2+ln(e)=3 , 2+ln(1)=2Rearrange the differential we get dx=xdu , substit...

Answered by • Maths tutor

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