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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:

(2a + 1)(a + 3)/(a + 3) = 2a + 1

Since a is a positive integer, we know that 2*a + 1 will always be an odd nu...

Answered by Nadia M. • Maths tutor

3062 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 answ...

Answered by Sarah W. • Maths tutor

3048 Views

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 4x²+ 8x + 3 = 4(x²+ 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x²+2x = (x+1)²-1² = (x+1)²-1 Hence, 4((x+1)²

Answered by Donny W. • Maths tutor

12651 Views

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

Express (x²+4x+13) / (x+2)²(x-1) as partial fractions. (x²+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 fou...

Answered by Donny W. • Maths tutor

4308 Views

Given the parametric equations x = lnt+t and y = sint calculate d^2y/dx^2

First we can write d²y/dx² as (d/dx)(dy/dx). Now we need to find dy/dx. This can be further written as (dy/dt)(dt/dx). These derivatives can be obtained from the given parametric equ...

Answered by Agnieszka R. • Maths tutor

3472 Views