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The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.

(a) If we consider the intersection of these two lines then, 3x-7=2px^2-6px+4p.This can be rearranged into the form ax^2+bx+c=0 such that, 2px^2+(-6p-3)x+4p+7, where a=2p, b=-6p-3 and c=4p+7.However, sinc...

Answered by Will G. • Maths tutor

8496 Views

How do you differentiate using the chain rule?

The chain rule is used where the equation you are looking to differentiate is a function that is itself raised to a power. For example, we might have y = (x²-2)³ and want to differen...

Answered by Oliver B. • Maths tutor

3423 Views

Derive the following: f(x)=(96/x^2)+kx

f'(x)=(-192/x^3)+k

Answered by Adrien D. • Maths tutor

1819 Views

A family go into a shop, they buy three sandwiches and two packets of crisps. It costs them £9. Another family buy five sandwiches and six packets of crisps. It costs them £19. How much does two sandwiches and five packets of crisps cost?

We will call sandwiches S and packets of crisps C. These are the 'unknowns'. From the information we can write down two equations. Equation 1: 3S + 2C = 9 and Equation 2: 5S + 6C = 19. We need two equatio...

Answered by Nicholas W. • Maths tutor

3063 Views

Line A is parallel to the line 4y+12x=24. Find the equation of Line A if it passes through the point (5,40/3).

Line A and line 4y+12x+24 are parallel. This means that they have the same gradient. In y=mx+c the gradient of the line is m. We can rearrange the equation 4y+12x+24 to find m. To begin with subtract 12x...

Answered by Chloe B. • Maths tutor

3040 Views