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x^2 - 10x + 21 = 0

First, factorise the quadratic equation. Find two numbers that multiply to give 21 and add to give 10. 7 and 3 (x-7)(x-3)=0 Now find the value x so that when these brackets are multiplied together the answer...
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Answered by Ben S. • Maths tutor
4977 Views

rex Aegypti duos liberos habebat. hi liberi erant Cleopatra et Ptolemaeus. per multos annos liberi vitam laetam cum patre habebant. deinde post mortem patris Cleopatra erat regina. [passage taken from sample paper, own questions below]

How many children did the king have and what were their names? We look at the first line, which translates to: The king of Egpyt had two children, Cleopatra and Ptolemaeus. The nominative is 'rex' (king), th...
RA
Answered by Rania A. • Latin tutor
6258 Views

Find the derivative of f(x)=x^2*e^x+x

You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x) For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule V'=dx/dy(e^x) dx/dy(x)=e^x 1=e^x Returning t...
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Answered by Benedict R. • Maths tutor
4130 Views

We have the curve f(x) = (x^2-5x)(x-1)+ 3x. Sketch the graph y=f(x), making sure to plot the co-ordinates where the curve meets the axes.

The first thing we want to do is re-write the curve f(x) in a format in which we can read and easily plot a graph. If we can include the '3x' in the factorised part of the equation, it will be neater and we'...
RA
Answered by Rania A. • Maths tutor
3776 Views

What is a balance of payments deficit and why might this be damaging to the economy?

In Macroeconomics, a balance of payments or balance of trade deficit is where the total imports (M) received by an economy exceed that of exports (X). The balance of payments is a component of aggregate dema...
AJ
Answered by Ayrton J. • Economics tutor
18204 Views