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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)

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 (...

the remainder theorem helps us find the reminder when a polynomial of degree n f(x)=a_nxⁿ+a_n-1x^n-1+.....+a₂x²+a₁x¹+a...

If the block is at the point of sliding, we know the frictional force, F, is at it's maximuim, F = kR, where k is the coefficient of friction and R is the reaction force.As we know the mass of the block, ...

the formula for area of a trapezium = 0.5(a+b)htherefore, a = 8, b = 12.5, h = 4therefore, the total area would be 41mm squared