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A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.

To calculate the minimum value of A we first need to establish an equation for A. The surface area of a cuboid is relatively simple to figure out we simply work out the area of the faces and sum them toge...

Answered by Jacob C. • Maths tutor

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Solve the simultaneous equations y + 4x + 1 = 0 and y^2 + 5x^2 + 2x = 0

y=-4x-1
(-4x-1)^2 +5x^2 +2x=0

16x^2 +8x +1 +5x^2 +2x=0

21x^2 +10x + 1 =0
(7x+1)(3x+1)=0

x=-1/7 or -1/3

y= -3/7 or 1/3

Answered by Dinesh J. • Maths tutor

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The curve A (y = x3 – x2 + x -1) is perpendicular to the straight-line B at the point P (5, 2). If A and B intersect at P, what is the equation of B? Also, find any stationary points of the curve A.

Firstly find the gradient of A, through differentiation: dy/dy = 3x² – 2x + 1. To find the gradient at P, substitute the x value of the P coordinate into this equation: dy/dx = 3(2)²...

Answered by James S. • Maths tutor

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C2 differentiate 2x^2 -3x +4 with respect to X

answer is 4x-3

Answered by Eloise C. • Maths tutor

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(M1) What direction does friction act in? What are the friction equations both generally and in limiting equilibrium? What does it mean for a system to be in equilibrium?

Friction always acts in the opposite direction to motion (or the potential motion) and Friction (Fr) acts as follows: In every case: Fr ≤ 𝜇R (where 𝜇 is the coefficient of friction and R is the reaction f...

Answered by Jasmine S. • Maths tutor

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