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Assumption: If sqrt(2^n- 1) ∈ℕ , it means that there is a k ∈ ℕ such that (2^n-1) = k^2 ⇒ k is odd, so there is m ∈ ℕ such that (2^n-1)=(2m+1)^2 . By solving the equation we get 2^n= 4m^2+4m+2. We divide bot...

Make x the subject in the equation x+y=11(1). This will help us eliminate x in the second equation (2).x=11-y (3)Substitute (3) into (2)(11-y) 2 +y 2 =61Expanding the brackets and simplifying gives 2y 2 -22y...

Start by finding the first derivative of the function - by differentiating f(x) with respect to x. Then substitute the x-coordinate, in this case 2, into the first derivative and it will equal zero if (2,3) ...

Differentiation is something you can do to a function, to tell you about the gradient of the function. For your simple linear, quadratic, cubic, etc. equations, the process is the same every single time. You...

Let u = 3 x 4 + x du/dx = 12x 3 + 1 y = u 5 dy/du = 5u 4 Using the chain rule, dy/dx = dy/du x du/dx = 5 u 4 (12x 3 + 1) dy/dx = 5(3x 4 + x)(12x 3 +1)