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Let p(x) =30x^3 - 7x^2 -7x + 2. Prove that (2x+1) is a factor of p(x).

We use the factor theorem which states that (2x+1) is a factor of p(x) if and only if the root of (2x+1)=0 is also a root of p(x). The root of 2x+1=0 is x = -1/2 (-1 from both sides and then divide both side...
HK
Answered by Henry K. • Maths tutor
9472 Views

If a circle passes through points (2,0) and (10,0) and it has tangent line along the y-axis, then what are the possible equations of the circle?

Firstly it will help to draw a diagram of our two points along the x-axis, from this we can find out the x co-ordinate of the center of the circle as these points form a chord of the circle. Where in this ca...
KM
Answered by Kieran M. • Maths tutor
4957 Views

Express (1 + 4 * 7^0.5)/(5 + 2 * 7^0.5) in the form m + n * 7^0.5

Need to make the bottom of the fraction an integer so we can simplify it. The easiest way to do that is the difference of 2 squares so multiply the whole fraction by (5 - 2 7 0.5 ). This gives us (5-56+20 7^...
EC
Answered by Ella C. • Maths tutor
3581 Views

A trolley of negilible mass on horizontal tracks is at rest. A person of mass 50kg is standing on the trolley with a bag of mass 10kg. The person throws the bag off the trolley horizontally with a velocity of 3m/s. Calculate the velocity of the man.

Establish what information you have been given in the question (mass of person=50kg, mass of bag=10kg, velocity of bag=3m/s, start velocity of both=0m/s). Use the equation momentum=mv and the principle of co...
EC
Answered by Ella C. • Maths tutor
3777 Views

y = x^2 − 2*x − 24*sqrt(x) - i) find dy/dx ii) find d^2y/dx^2

Solved by differentiation with respect to x,i) dy/dx = 2 x - 2 - 12 x^(-1/2)ii) d^2y/dx^2 = 2 + 6*x^(-3/2)
DG
Answered by Duncan G. • Maths tutor
6212 Views