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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)^-1Hence, x=(tan y )^-1 implying dx/dy = (-...

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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 th...

Answered by Oriane G. • Maths tutor

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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 x² term, an x term and a numeri...

Answered by Jessica C. • Maths tutor

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Find the values of x given the equation (4x^2)-3x+1=2 using the quadratic formula.

4x²-3x+1=2The first step is to rearrange the equation, equating it to zero: 4x²-3x+1-2=0 which gives 4x²-3x-1=0. Next we apply the quadratic formula: x=(-...

Answered by Shahnaan M. • Maths tutor

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Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.

To solve this problem we first must look into the given formula for time (T). It is stated, in the question, that the time taken is dependent on distance x. From this we can infer that the following probl...

Answered by Aziz H. • Maths tutor

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