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Given the function y = x^5 + x^3/2 + x + 7 Express the following in their simplest forms: i) dy/dx ii) ∫ y dx

i) 5x^4 + 3/2x^1/2 + 1ii) 1/6x^6 + 2/5x^5/2 + 1/2x^2 + 7x + c
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Answered by Liam B. • Maths tutor
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Explain Optical Isomerism

Optical Isomerism is a type of stereoisomer. The molecule has a chiral centre which is where the are four different atoms attached to the central atom. This means that they become mirror images of each other...
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Select two works of art, each by a different artist, and comment on how each artist has responded to the time in which they lived.

Both Cecil Collins (1908-1989) and Julian Trevelyan (1910-1988) and their respective works The Quest (1938) and Rubbish May be Shot Here (1937) respond directly to the period in which they are situated. The ...
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For what values of x is Cosh^2(x) - Sinh(x) = 5 Give your answer in the form of a logarithm

Substitute Cosh^2(x) = 1 + Sinh^2(x) into the starting equation (This formula should be known)Make 0 the subject 3Sinh^2(x) - Sinh(x) - 2 = 0Substitute u = Sinh(x) and solve for uSubstitute Sinh(x) back in f...
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Simplify 3/(x+1) + (3x-9)/2 = 1, to get a quadratic equation in the format ax^2 + bx + c = 0.

First, add the two fractions together. The common denominator is 2(x+1), or 2x+2. The first fraction becomes 6/(2x+2). The second fraction becomes (x+1)(3x-9)/(2x+2), or (3x 2 -6x -9)/(2x+2). Added together,...
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