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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 = (change i...
JP
Answered by James P. • Maths tutor
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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 x 0 , the functions and their gradients are equal. Th...
PS
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 will b...
TR
Answered by Toby R. • Maths tutor
4172 Views

I buy a car from a dealership for £3500. The car depreciates in value for every year I own it. What is the value of the car after I have owned it for 18 months if it depreciates at a rate of 5 percent?

This is a compound interest problem. Here we have to put 18 months in terms of years. There are 12 months in a year, so 18 months is a year and 6 months. 6 months is half a year, so 18 months represents a ye...
LM
Answered by Lauren M. • Maths tutor
4142 Views

In triangle XYZ: XZ = 10 cm; YZ = 8 cm; cos Z = 1/8. Calculate the length of XY.

We can use the cosine rule to determine the lenght of XY. XY 2 = 10 2 +8 2 -2 10 8 cos ZXY 2 = 100+64-180 (1/8) = 144XY = 12
VH
Answered by Vencel H. • Maths tutor
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