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At time t = 0 a particle leaves the origin and moves along the x-axis. At time t seconds, the velocity of P is v m/s in the positive x direction, where v=4t^2–13t+2. How far does it travel between the times t1 and t2 at which it is at rest?

First, you have to work out the values of t1 and t2 at which the particle is at rest. This is done by solving the quadratic equation for v, producing values for t of 13/8 +- sqrt(137): 0.1619s and 3.088s. To...
JM
Answered by Jack M. • Maths tutor
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Given that, dy/dx = 6x^2 - 3x + 4, and y = 14 when x = 2, express y in terms of x.

dy/dx = 6x 2 - 3x + 4 To retrieve the original function y from dy/dx you have to integrate the derivative with respect to x. y = ∫(dy/dx)dxy = ∫(6x 2 - 3x + 4)dx To integrate, the power is raised by one and ...
CB
Answered by Ciaran B. • Maths tutor
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Do the circles with equations x^2 -2x + y^2 - 2y=7 and x^2 -10x + y^2 -8y=-37 touch and if so, in what way (tangent to each other? two point of intersection?)

We must first complete the square for both equations and get the equations in the (x-a) 2 +(y-b) 2 =r 2 with the primary objective of determining the centres of both circles (a,b) . Through completing the sq...
SS
Answered by Shanti S. • Maths tutor
4071 Views

Factorise x^2 - 6x + 9 = 0

x 2 - 6x + 9The method for factorising quadratics is to find 2 numbers that add to make the 'x' term (-6x in this case), and multiply together to make the final term (+9 in this case). Factors of +9 are: 1x9...
KB
Answered by Kate B. • Maths tutor
9999 Views

What is 64^1/2 equal to?

A number to the power of 1/2 is the same as square rooting ( √) the number, therefore 64 1/2 is equal to √64. Remember that it can be the positive or the negative square roots, so it could be 8 2 or -8 2 .
KB
Answered by Kate B. • Maths tutor
29439 Views