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Find the exact solution to the equation: ln(3x-7) =5

Ln(3x-7)=5 Remove logs from both sides 3x-7=e⁵Rearrange to make x the subject3x=e⁵+7x=e⁵+7 3

Answered by Lily H. • Maths tutor

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Solve the simultaneous equations: 3x + y =11, 2x + y = 8

x = 3, y = 2

Answered by Nathan B. • Maths tutor

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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(b² -4 a c) ]/ (2a). You obtain two roots, x = 2 and x=3 and the integration is simpli...

Answered by Efstathios E. • Maths tutor

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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

Answered by Julianna V. • Maths tutor

3536 Views

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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