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A function is defined by f(x)=x/(2x-2)^(1/2): (a)Determine the maximum domain of f. (b)Differentiate f. (c)Find the inflection points of the function's graph.

This is a common A-level question tackling functions and differentiation. (a) First, it should be noted that the function f is defined within the field of real numbers and thus the value of 2x-2 in the sq...

Answered by • Maths tutor

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In a stack of CDs, there are 3 types: Rock, Pop and Jazz. There are 2 Rock CDs, x Pop CDs, and (2x+5) Jazz CDs. A CD is chosen at random. If the probability it is Rock is 1/20, work out the probability it is Jazz.

Number of Rock CDs = 2Total Number of CDs = 2 + x + (2x+5) = 3x + 7Probability of Rock CD = 2/(3x + 7) = 1/202/(3x + 7) = 1/2040 = 3x + 7x = 11Number of Jazz CDs = 2x + 5 = 27Total Number of CDs = 3x + 7 ...

Answered by Vinh L. • Maths tutor

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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.

3+4+5=12
72/12=6
36= 18 46=24 56=30
Area of a right-angled triangle= ab/2
18240.5= 216

Answered by Saif K. • Maths tutor

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Demonstrate that (2^n)-1 is not a perfect square for any n>2, n ∈ N.

Assumption: If sqrt(2^n- 1) ∈ℕ , it means that there is a k ∈ ℕ such that (2^n-1) = k^2 ⇒ k is odd, so there is m ∈ ℕ such that (2^n-1)=(2m+1)^2 . By solving the equation we get 2^n= 4m^2+4m+2. We divide...

Answered by Ionut Valeriu G. • Maths tutor

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