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Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.

To solve this problem we first must look into the given formula for time (T). It is stated, in the question, that the time taken is dependent on distance x. From this we can infer that the following problem ...
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Answered by Aziz H. • Maths tutor
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Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)

Normally to find a tangent we want to work out dy/dx, but since this equation is x=something, it's much easier to work out dx/dy first, then we get dy/dx by doing 1/(dx/dy)=dy/dx. By the chain rule, dx/dy = ...
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Answered by Sarah J. • Maths tutor
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Find the angle between two lines with vector equations r1 = (2i+j+k)+t(3i-5j-k) and r2 = (7i+4j+k)+s(2i+j-9k)

Explain the dot product and the relation : a.b= ¦a¦ ¦b¦ cos(x) where a.b is the dot product of two vectors, ¦a¦ and ¦b¦ are the magnitude of a and b respectively and x is the angle between them. Since the an...
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Answered by Muhammad S. • Maths tutor
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Find the intersection coordinates of both axis with the function: f(x)=x^2-3x+4/3

Find the y 1 coordinate, where x 1 = 0, this is the intersection with y-axis. f(0)=4/3, therefore one intersection P y =[0,4/3]Find the x 1,2 coordinates, where y = 0, this are the intersections with x-axis....
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Answered by Martin S. • Maths tutor
3329 Views

Integrate the natural logarithm of x (ln x) with respect to x

In order to integrate ln x you have to use integration by parts, even though it appears there is only one term to be integrated. We get around this by instead writing it as (ln x)(1), where we treat the 1 as...
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Answered by Archie D. • Maths tutor
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