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Prove by contradiction that sqrt(3) is irrational. (5 marks)

To the contrary assume that sqrt(3) is a rational number. Thus we can write sqrt(3) = a/b where a and b are coprime integers and b is non-zero. (1 mark for this or equivalent statement - may have that this f...
DS
Answered by Dan S. • Maths tutor
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Five numbers have a mean of 9.4 . Four of the numbers are 3, 5, 10 and 12. Work out the range of the five numbers. ( 4 marks )

9.4 =( 3 + 5 + 10 + 12 + x ) / 5=> 9.4 x 5 = 30 + x=> 47-30 = x=> 17 = x
FP
Answered by Fotini P. • Maths tutor
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Solve this simultaneous equations, clearly showing all of your workings: x^2 + 2y =9, y - x = 3

Equation 1: x 2 + 2y = 9Equation 2: y - x = 3 Rearrange equation 2: y = 3 + x Substitute y = 3 + x into equation 1x 2 + 2(3 + x) = 9x 2 + 6 + 2x = 9x 2 + 2x - 3 = 0(x + 3)(x - 1) = 0so x = 1 and -3 substitut...
EJ
Answered by Ella-May J. • Maths tutor
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Curve C has equation x^2 - 3xy - 4y^2 + 64 = 0. a) find dy/dx in terms of x and y. b) find coordinates where dy/dx=0.

a) This is no standard differentiate question. You will need identify the fact that the equation contains both x and y terms and thus you will need to differentiate with respect to both. This involves applyi...
ED
Answered by Emma D. • Maths tutor
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Solve 2y + 17 = 6y + 5

Subtract 2y from both sides:4y = 12Divide by 4:y = 3
SB
Answered by Sam B. • Maths tutor
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