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Solve 5(x+3) < 60

Our technique here will be the same used to solve the problem 5(x+3) = 60, but we must take care at each step to decide whether our inequality changes direction.Firstly, we expand the brackets to give 5x ...

Answered by Arron B. • Maths tutor

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Solve the following simultaneous equations: 3x + 5y = 19 and 8x - 2y = -18. If both equations represent lines in a coordinate system, at which point do they intersect?

I. 3x + 5y = 19 II. 8x - 2y = -18 . We see that we can simplify the second equation, and we do so: II. x - y = -9. Now, we check to see which variable i...

Answered by Ninett A. • Maths tutor

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You are told that a straight line runs through 2 points: (1,1) and (2,3). What is the equation of the line?

Recall that all straight lines have the general equation y = mx + c, where m is the gradient of the line and c is the y intercept. First work out the gradient, m, of the line: Gradient = rise/run = (chang...

Answered by James P. • Maths tutor

2657 Views

Find the equation of the straight line passing through the origin that is tangent to the curve y = ln(x).

Firstly, recognise the relevant equations. The two functions are y = mx and y = ln(x). As the straight line is a tangent, we know that at a certain point x₀, the functions and ...

Answered by Paul S. • Maths tutor

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A stationary point of inflection implies a second derivative of 0, does this work the other way around?

No, and we may take a counterexample to see why. If y=x^5+5/3x^4, dy/dx=5x^4+20/3x^3, d2y/dx2=20x^3+20x*2=20x^2(x+1). Setting this to 0 will give us the candidates for a POI, but not all these numbers wil...

Answered by Toby R. • Maths tutor

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