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John wants to separate a rectangular part of his garden for his puppy. He has material for a 100-meter long fence and he plans to use one side of his house as a barrier. How should John select the sizes of his fence in order to gain the biggest territory?

We can denote the sides of the rectangle with a and b. As one side of the separated area is going to be the wall of the house, we do not have to use a fence there. Therefore, we will have two sides, one deno...
SG
Answered by Soma G. • Maths tutor
3335 Views

Why is the derivative of sin(x), cos(x)?

Find out what they know what the questions means, ie if they know what sinx and cosx are and then how much they understand about what derivatives are.I would explain from the point they're at, define everyth...
RA
Answered by Ryan A. • Maths tutor
4013 Views

f(x) = x^3 + 3x^2 + 5. Find (a) f ′′(x), (b) ∫f(x)dx.

(a) To find the second derivative of f(x) we must differentiate f twice.the first derivative of f is f'(x)= 3x^2 + 6xthe second derivative therefore is f''(x)= 6x +6 (b) The integral of f(x) with respect to ...
SC
Answered by Samraj C. • Maths tutor
8401 Views

Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0

2 2x - 6(2 x ) + 5 = 0let y = 2 x y 2 - 6y + 5 = 0(y-5)(y-1) = 0 y=5, y=12 x = 5, therefore, x = log 2 5 = 2.32 (3 s.f.)2 x = 1, therefore, x = log 2 1 = 0
JO
Answered by Jess O. • Maths tutor
5295 Views

Find the gradient of the function f(x,y)=x^3 + y^3 -3xy at the point (2,1), given that f(2,1) = 6.

Firstly, establish that the correct method to do this is via differentiation: specifically implicit differentiation. To find the gradient, we need to find dy/dx . The differential with respect to x of x 3 = ...
DD
Answered by Daniel D. • Maths tutor
6736 Views