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Solve by completing the square: x^2 - 8x + 12 = 0

x² - 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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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 indefi...

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 grad...

Answered by George Alexander L. • Maths tutor

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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. T...

Answered by Oliver B. • Economics tutor

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Solve the following: sinx - cosx = 0 for 0≤x≤360

We know that sinx/cosx = tanx. Therefore we can write sinx - cosx = 0 as sinx = cosx . By diving both sides by cosx, we get tanx = 1. By taking tan inverse of both sides, we can see that for 0≤x≤360, we g...

Answered by Aaman K. • Maths tutor

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