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Solve simultaneously 2x + 3y = 18 and y = 3x – 5 to find the value of x and y.

sub the y value into the first eqn 2x + 3(3x-5) = 18 expand the brackets 2x +9x-15 = 18 add up the x values 11x -15 = 18 add 15 to both sides to cancel it out on the l.h.s 11x = 33 divide by 11 to get value ...
JG
Answered by Jessica G. • Maths tutor
4196 Views

Given that x = cot y, show that dy/dx = -1/(1+x^2)

Identify that we are looking at dy/dx, not dx/dy and realise the relationship that dy/dx=1/(dx/dy)2)Try find dx/dy;cot = 1/tan or (tan) -1 Hence, x=(tan y ) -1 implying dx/dy = (-1)(tan y) -2 (sec 2 y ) =(-1...
JF
Answered by Jacob F. • Maths tutor
12737 Views

Work out the gradient of the tangent to the curve (y=x^2-x-2) at the point where x=2

y=x^2-x-2y=(x+1)(x-2)The gradient (dy/dx) measures the rate of the change in y with respect to x. So this can be used to help us find the gradient of a function at any point along it. The question asks the t...
OG
Answered by Oriane G. • Maths tutor
4858 Views

Define Economies of Scale stating an instance when this might occur.

This is when a company's costs decrease as a result of increased production. This may occur when two companies decide to merge in order to grow the business by pooling their individual resources. As a result...
SM
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How do you factorise the algebraic expression x^2 +5x+ 6?

Factorising is all about writing algebraic expressions using brackets, to separate x terms.(x + ... )(x +... ) when multiplying out the brackets there will be an x 2 term, an x term and a numerical term. Bre...
JC
Answered by Jessica C. • Maths tutor
3685 Views