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This is from the Maths in Focus textbook.

Enjoy your break! Hope you get the top marks!

How should we work out these questions? Q 16 A half-pipe is to be made from a rectangular piece of metal of length x meters. The perimeter of the rectangle is 30 meters. (a) Find the derivatives of the rectangle that will give the maximum surface area, correct to 1 decimal place. [Answer...

6. Find two numbers whose sum is 28 and whose product is a maximum. 8. A piece of wire 10m long is broken into two parts, which are bent into the shape of a rectangle and a square. Find the dimensions x and y that make the total area a maximum. (x = width of rectangle, y = length of rectangle...

Hi. So, I need to get the exact gradient of the normal of the parabola y^2=12x at the point where x=4 in the first quadrant. I get near the answer which is -(2√3)/3 but I couldn't get the working right. Any help is very much appreciated. Thank you.

Thank you very much for this very good answer! I added reputation to you as well Sir!

Thanks sir for quickly replying. So, I got y = -2x, y = x^2 and y = 3x^2 - 8x I've tried solving it but I got confused as to how to get this answer (provided by the book) y = -2x^2 + 4x -2. Can you please help me again? Thank you very much!

Question 7 of Challenge 10 Maths in Focus (Preliminary Course) Find the equation of the parabola with axis parallel to the y-axis and passing through points (0,-2), (1,0) and (3, -8). I don't know how to do this problem, can anyone please show me working onto solving this? Thank you very...

Can anyone please help me solve these problems? 1. Find the equation of the locus of a point that moves so that it is equidistant from the line 4x-3y+2=0 and the line 3x+4y-7=0. 2. Given two points A(3, -2) and B(-1, 7), find the equation of the locus of P(x, y) if the gradient of PA is twice...