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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...

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 ...

Answered by • Maths tutor

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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)

Answered by Tilly G. • Maths tutor

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Solve 5x^2 = 10x + 4 Give your answers to 2 decimal places. [4 marks]

5x^2 = 10x + 4 5x^2 - 10x = 4 5x^2 - 10x - 4 = 0 ax^2 +bx +c = 0 x = (-b (+/-) ( b²-4ac)^1/2) /(2a) x = (--10 (+/-) ((-10)²- (4 x 5 x -4))^1/2)/(2 x 5) x = (10 (...

Answered by JOSHUA T S. • Maths tutor

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