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Given that F(x) = X^2 - 10X + 17. Write F(x) in the form of (x+a)^2 + b = 0, where a, & b are constants.

So we know that our equation is: X²- 10X +17 = 0. STEP 1: rearrange this equation to get x on one side: X²- 10X = -17. Lets call this, "equation 1". STEP 2: Understand th...

Answered by Rumit M. • Maths tutor

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Let p(x) = 30 x^3 -7 x^2 - 7 x + 2. Prove that (2x + 1) is a factor of p(x) and factorise p(x) completely.

Using the Factor Theorem, we know that (2x + 1) = 2(x + 1/2) = 2(x - (-1/2) ) is a factor of p(x) if and only if p(-1/2) = 0, which is true. Now that we know a factor of ...

Answered by • Maths tutor

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proof for the derivative of sin(x) is cos(x) (5 marks)

let f(x)=sin x f'(x) lim h-> 0 = ( sin(x+h) - sin(x))/h. f'(x) lim h-> 0 =( sin(x)cos(h) + cos(x)sin(h) - sin(x))/ h. f'(x) lim h-> 0=(sin(x)(cos(h)-1)/h + cos(x) (sin(h))/h. then as h tends to z...

Answered by Nicola P. • Maths tutor

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Find the total area enclosed between y = x^3 - x, the x axis and the lines x = 1 and x= -1 . (Why do i get 0 as an answer?)

Our first step should always be to make sure we understand what the question actually wants from us, in the case of most polynomial questions a rough sketch with any information we know is very useful. Fi...

Answered by George B. • Maths tutor

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The Tour de France is 2162miles long. A cyclist knows his average speed his 12.37 miles/hour from his previous races. For the Tour de France the cyclist knows he will cycle for 10 hours a day. Estimate how many days it will take him to complete the race.

First you must figure out your estimates, in this case you can round 2162 down to 2000 and 12.37 to 10 to make your solutions easier. First you must calculate the total number of hours it is going to take...

Answered by • Maths tutor

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