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Integrade the function f(x) = 1/(x^2 - 5x +6) with respect to x.

First, we need to factorise the denominator and therefore we use this formula: x 1,2 =[ -b + sqrt(b 2 -4 a c) ]/ (2a). You obtain two roots, x = 2 and x=3 and the integration is simplified to : 1/[(x-2)(x-3)...
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Answered by Efstathios E. • Maths tutor
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Solve by completing the square: x^2 - 8x + 12 = 0

x 2 - 8x + 12 = 0 (x - 4) 2 - 16 + 12 = 0 (x - 4) 2 - 4 = 0 (x - 4) 2 = 4 x - 4 = +- 2 x = 6 x = 2
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Answered by Julianna V. • Maths tutor
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Which adjective ending should I use for a masculine noun?

The adjective ending depends on the case and the article in which you are speaking. If it's the definite article you use -e for nominative, and -en for accusative, genitive, and dative. If it's the indefinit...
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Answered by Francis W. • German tutor
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Consider the functions f(x) = −x^3 + 2x^2 + 3x and g(x) = −x^3 + 3x^2 − x + 3. (a) Find df/dx (x) and hence show that f(x) has turning points at when x = 2 /3 ± √ 13/ 3 . [5] (b) Find the points where f(x) and g(x) intersect. [4]

a) First differentiate f(x) using standard polynomial derivative rules which gives, df/dx=-3x^2+4x+3. The derivative function gives the gradient of f for any value of x. Turning points occur when the gradien...
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Assess the economic effects of a depreciation on a countries currency

Depreciation involves reducing the value of the nations currency against others. Under a managed float this could be achieved by a central bank selling its own currency in exchange for foreign currency. This...
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Answered by Oliver B. • Economics tutor
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