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Find all real solutions of (x^2 +4x +3)^(x^2 -6x+8) = 1

Rewrite as a^b = 1, where a = x^2+4x+3 and b = x^2-6x+8List the cases for which a^b = 1Case 1: a = 1:So x^2+4x+3=1 => x^2+4x+2=0 => x=-2 +/- sqrt(2)Case 2: b=0, a ≠ 0:b=(x-4)(x-2) => x = 2, x=4Ch...

NM
Answered by Nicholas M. PAT tutor
1305 Views

A function is defined piecewise f(x) = ( e^x for x<0, e^(-x) + 2x for x>= 0). Sketch f(x) and its first, second and third derivatives

f(x) = ( e^x for x<0, e^(-x) + 2x for x>= 0)f'(x) = ( e^x for x<0, -e^(-x) + 2 for x>= 0)f''(x) = ( e^x for x<0, e^(-x) for x>= 0)f'''(x) = ( e^x for x<0, -e^(-x) for x>= 0)(Will s...

NM
Answered by Nicholas M. PAT tutor
1430 Views

A business is planning to invest in a new machine which will cost £220 000. The machine will lead to an annual increase in revenue of £75 000. It will also lead to extra labour costs of £28 000 per annum but will reduce the firm’s energy costs by £4 000

Annual return is £75 000 – £28 000 + £4 000 = £51 000 Return on investment = annual return x 100 = £51 000 x 100 = initial cost £220 000 Answer = 23.2% or 23%

DS
3250 Views

Given two strings s1 and s2 return the location of each permutation of the s1 string within the s2 string.

Solution: Iterate through s2 and select blocks of characters of length equal to that of s1 (for simplicity let's call this block string ref). Now, check if ref is a per...

VH
Answered by Vlad H. Computing tutor
1279 Views

Explain some of the differences between an entrepreneurial endeavour an established business.

Established businesses focus on three main strategies to grow their business and increase profits: aggregation, arbitration, and adaptation. These strategies rely on a level of certainty not available to ...

AC
1142 Views

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