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Prove that (2*a^2 + 7a + 3)/(a + 3) is an odd number for any positive integer number, a.

We see that the numerator is a quadratic, so we factorise it to obtain: (2 a + 1)(a + 3)/(a + 3) = 2 a + 1 Since a is a positive integer, we know that 2*a + 1 will always be an odd number.
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Answered by Nadia M. • Maths tutor
3697 Views

Find the length of the hypotenuse if the right angled triangle's other two sides are of length 5cm and 12cm.

Use of a^2+b^2=c^2 must be included in the answer. Furthermore the numbers must be put in the above equation to give: 5^2+12^2=c^2 This must then be solved to give: 169^0.5=c The answer can be found without ...
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Answered by Sarah W. • Maths tutor
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4x^2 + 8x + 3 can be written in the form a(x + b)^2 + c where a, b and c are whole numbers. Work out the values of a, b and c.

Factorise 4x 2 + 8x + 3 = 4(x 2 + 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x 2 +2x = (x+1) 2 -1 2 = (x+1) 2 -1 Hence, 4((x+1) 2 -1+3/4) = 4(x+1) 2 -1 which is of the form a(x + b) 2 + c So a=4, ...
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Answered by Donny W. • Maths tutor
14239 Views

Integrate (x^2+4x+13)/((x+2)^2)(x-1) dx by using partial fractions

Express (x 2 +4x+13) / (x+2) 2 (x-1) as partial fractions. (x 2 +4x+13) / (x+2) 2 (x-1) = a/(x+2) +b/(x+2) 2 +c/(x-1) where a, b and c are constants to be found. Multiplying by the denominator, we get (x 2 +...
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Answered by Donny W. • Maths tutor
5011 Views

How would I approach a source question?

Approaching source questions, whilst they may seem daunting, are reasonably straighforward. You use the simple PEA/PEE structure, whilst also taking into account the nature origin and purpose of the source. ...
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Answered by Charlotte N. • History tutor
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