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Given y=rootx + 4/rootx = 4, find the value of dy/dx when x=8, writing your answer in the form aroot2, where a is a rational number.

First, we will write out the equation, writing the root x values in a way that allows us to differentiate them. Root x can be written as x^1/2 and 4/rootx can be written as 4x^-1/2. Now we can differentiate....
Answered by • Maths tutor
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What is the gerundival attraction?

Although the name sounds scary, it is easier that it seems. In Latin when a gerund has an object, there is a tendency to harmonise the terminations of the two, so the object will agree with the sense of the ...
Answered by • Latin tutor
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P is a point on the circle with equation x^2 + y^2 = 80. P has x-coordinate 4 and is below the x-axis.Work out the equation of the tangent to the circle at P.

Point P has x-coordinate 4, to work out the y-coordinate you should substitute x=4 into the equation of the circle. This gives you 16 + y^2 = 80. this can be rearranged to y^2 = 80 - 16 = 64. Therefore y = +...
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Answered by Faaris K. • Maths tutor
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There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is 2/3 The probability that a girl chosen at random studies French is 3/5. Work out the number of students in the school who study French.

Let x denote the number of boys studying French and y the number of girls studying French. Then the probability that a boy chosen random studies French is x/720 and the probability that a randomly chosen gir...
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Make a the subject of a + 3 = (2a + 7) / r

Multiply both sides by r: ra+3r = 2a + 7Move a to one side: ra -2a = 7-3rFactorise left hand side: a(r-2) = 7-3rMultiply both sides by (r-2): a= (7-3r) / (r-2)
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Answered by Tilly G. • Maths tutor
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