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The Tour de France is 2162miles long. A cyclist knows his average speed his 12.37 miles/hour from his previous races. For the Tour de France the cyclist knows he will cycle for 10 hours a day. Estimate how many days it will take him to complete the race.

First you must figure out your estimates, in this case you can round 2162 down to 2000 and 12.37 to 10 to make your solutions easier. First you must calculate the total number of hours it is going to take hi...
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How do you find the gradient of a line?

There are 2 methods used for finding the gradient of a line in 2D space, depending on whether it is a straight line or a curve. To find the gradient a straight line you must first take the equation of the li...
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Let f(x)= x^3 -9x^2 -81x + 12. Calculate f'(x) and f''(x). Use f'(x) to calculate the x-values of the stationary points of this function.

To answer this question we need to first decide what the question is asking for. In this case the question is asking for the first and second differential of a given function. If we have a function f(x) = x ...
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Answered by Jazz P. • Maths tutor
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Differentiate y=(sin(x))^(2)

Using the chain rule of dy/dx=dy/du * du/dx we label sin(x) as u. Now we differentiate u with respect to x, getting cos(x). Then we differentiate u 2 , getting 2u. Mutiplying these together gets us 2u*cos(x)...
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Answered by Bill H. • Maths tutor
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The equation x^2 + (k-5)x + 1 = 0 has equal roots. Determine the possible values of k.

So the first part of this question is regarding your knowledge and understanding on the subject matter. You should know that for real and equal roots, (b 2 - 4ac)=0. (For real and unequal roots, it is >0 ...
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