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How do you solve a quadratic inequality eg find the values of x for which x^2 -6x +2 < -3

First we must change our inequality so that we have a zero on one side, In this case we can add three to both sides of the inequality, this gives: x^2 - 6x +5 < 0 Now let's consider the equation y = x^...

Answered by Isobel R. • Maths tutor

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2 equations intersect each other, y = x + 2 and y = x^2. Find the area of the shaded region between the points of intersection giving your answer to 3 significant figures. (shaded region will be shown)

points of intersection are (-1,1) and (2,4). Area of the shaded region is 4.5.

Answered by Syed A. • Maths tutor

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What is the differential of y =sin(2x)?

For this question we have to use the chain rule. The chain rule is dy/dx (the differential you are looking for) = du/dx (the differential of u with respect to x) * dy/du(the differential of y with respect...

Answered by Cem U. • Maths tutor

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Given that y=ln([2x-1/2x=1]^1/2) , show that dy/dx= (1/2x-1)-(1/2x+1)

y=ln([2x-1/2x=1]^1/2)- can be written as y= [0.5ln(2x-1)]-[0.5ln(2x+1)] due to laws of logs. Take first term -- (0.5ln(2x-1)) and substitute 2x-1 for u. so u=2x-1 and y=0.5lnu Now dy/du=1/2u and du/dx=2. ...

Answered by Sam F. • Maths tutor

10461 Views

A man travels 360m along a straight road. He walks for the first 120m at 1.5ms-1, runs the next 180m at 4.5ms-1, and then walks the final 60m at 1.5ms-1. A women travels the same route, in the same time. At what time does the man overtake the women?

In order to answer this question we will break it down into several pieces. Firstly, using physical arguments, can we narrow down which interval the man must overtake the women? After some thought, it mus...

Answered by James G. • Maths tutor

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