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Solve the Simultaneous equations 4x - y = 8 and x + y = 12

One basic method used here, when you have an equation and you add, subtract, multiply or divide one side of the equation from the equal sign, you must add, subtract, multiply or divide by the same value on t...
CE
Answered by Cameron E. • Maths tutor
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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 squar...
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 = 4...
VL
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 3 6= 18 4 6=24 5 6=30 Area of a right-angled triangle= a b/2 18 24 0.5= 216
SK
Answered by Saif K. • Maths tutor
3338 Views

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 bot...
IV
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