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Solve x^2 > |5x - 6|

We need to split the problem into two cases to remove the abs sign. Case 1: 5x - 6 >= 0, equivalent to x >= 6/5. In this case the problem is now to find the values of x that satisfy x 2 > 5x - 6. Re...
JH
Answered by James H. • Maths tutor
4608 Views

What is an improper fraction, and how to I make thisproper so that it can be differentiated?

An improper fraction is any fraction where the order of the constant (power of x) is equal or greater in the nuberator than the denominator, take for example; (x 2 -3x-2)/(x 2 -3x+2) This can first be factor...
AS
Answered by Aidan S. • Maths tutor
4227 Views

1. A small stone is dropped from a height of 25 meters above the ground. i) Find the time taken for the stone to reach the ground ii) Find the speed of the stone as it reaches the ground

i) Let’s first write down, as we always should, what we know and what we are searching for. We know height is 25 meters and we are searching for time, so: ℎ = 25 �� �� =? This is a case of free fall of cours...
PM
Answered by Petar M. • Maths tutor
8212 Views

For a curve of equation 2ye^-3x -x = 4, find dy/dx

here the student needs to use both implicit differentiation and the product rule. I would differentiate term by term for this problem. for 2ye^-3x you have to use the proudct rule. uv differentiates to uv' +...
JB
Answered by Jack B. • Maths tutor
4286 Views

Differentiate with respect to x: w=4x^2 + 3sin(2x)

We will split this up and differentiate each part separately. We can differentiate 4x 2 using our normal rules for differentiating; we multiply the coefficient by the power and then subtract one from the pow...
EM
Answered by Emma M. • Maths tutor
7306 Views