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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...
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Answered by Oriane G. • Maths tutor
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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...
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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...
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Answered by Jessica C. • Maths tutor
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If a car sets off from rest with a constant acceleration of 3 m/(s^2), what would its speed be after 5 seconds?

Firstly we write down all known variables: Initial speed (u)=0 m/s, Acceleration (a)=3 m/s 2 , Time (t)=5s. Final velocity (v)=?Therefore, the equation chosen to solve the problem would be: v=u+at. Substitut...
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Answered by Shahnaan M. • Physics tutor
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Find the values of x given the equation (4x^2)-3x+1=2 using the quadratic formula.

4x 2 -3x+1=2The first step is to rearrange the equation, equating it to zero: 4x 2 -3x+1-2=0 which gives 4x 2 -3x-1=0. Next we apply the quadratic formula: x=(-b +/- sqrt(b 2 -4ac))/2a where a=4, b=-3 and c=...
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Answered by Shahnaan M. • Maths tutor
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