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Solve the equation x^6 + 26x^3 − 27 = 0

While this equation may look complicated, it's actually much easier than it looks - this equation is called a hidden quadratic. This is because it can be rewritten and solved the same way you would solve a q...
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Answered by Saachi P. • Maths tutor
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Find the equation of the normal to the curve 2x^3+3xy+2/y=0 at the point (1,-1)

Step 1 Use Implicit differentiation with respect to x and y - 6x^2+3y + 3x(dy/dx) - 2/y^2(dy/dx) = 0Step 2 Write the equation as dy/dx =... - dy/dx = (6x^2 + 3y)/(2/y^2 - 3x)Step 3 Input (1,-1) into the equa...
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Find the exact value of the integral of (2+7/x), between x=1 and x=e. Give your answer in terms of e.

1.) Find the integral of each term. --> [2x +7ln(x)]. --> Uses standard integrals--> e.g. that the integral of 1/x is ln(x). 2.) substitute values into the integral. --> [2(e)+ 7ln(e)]- [2(1)+7ln...
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The velocity of a car at time, ts^-1, during the first 20 s of its journey, is given by v = kt + 0.03t^2, where k is a constant. When t = 20 the acceleration of the car is 1.3ms^-2, what is the value of k?

Our task is to find out the value of k, which we can determine from the equations for velocity or acceleration if we know 2 of the 3 variables in either equation. We are given the value of acceleration at t(...
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Answered by Lascelle M. • Maths tutor
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y=x^2 +4x-12, Find the Range (co-domain) when the domain of x is (1) -6 to 2 inclusive (2) the set of real numbers, R.

This question usually comes up at AS level where students have prior knowledge of quadratic functions:We need to 1) understand the 'shape' 2) locate the roots 3) Find the turning point 4) sketch the graph 5)...
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Answered by Pascal T. • Maths tutor
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