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How do you show some quadratic polynomials are always greater than 0?

Usually, there are two ways to solve this kind of problems. You could re-arrange the polynomial, make it become a square plus a constant, then the polynomial is greater or equal to the constant since a squar...
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Answered by Luke W. • Maths tutor
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Differentiate the function y=4sqrt(x)

Can re-write function as y=4x 1/2 Then follow the standard steps for differentiating a power. Take the 1/2 down and multiply by the number in front of the x, in this case 4, to give 2. Now reduce the power w...
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Answered by Calum W. • Maths tutor
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A cuboid has dimensions: width = x+1, length = 2x-2, height = x+2. Work out the volume of this cuboid. Give your answer in terms of x.

Volume of cuboid = width x length x heightV = (x + 1)(2x - 2)(x + 2) For simplicity, multiply the first 2 sets of brackets first. Then multiply the result by the third set of brackets.Note: for multiplicatio...
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Answered by Sam A. • Maths tutor
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2017 Edexcel Summer 2017 Q18) 16^1/5 × 2^x = 8^3/4 Work out the exact value of x

As this is a calculator paper, it is acceptable to use one. The first step to calculating the exact value of x is to make it the subject of the equation (i.e. moving it to its own side)2^x = (8^3/4)/(16^1/5)...
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Answered by Rory P. • Maths tutor
19878 Views

What is 125^(-2/3)?

Firstly, the negative power sign flips the number the 1/125.The 1/3 part of the power means find the cubic (3rd) root. 1/5Finally the 2 of the power means square the number. 1/25 is therefore the final answe...
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Answered by Emily R. • Maths tutor
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