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Find the coordinates of the point where lines 3x+5=y and 6y+x=11 intersect

To find the coordinates of the point, we have to solve the equations simultaneously. To do this, we need the same number for the coefficient of x or y in each equation. Arbitrarily, we will chose to match th...
AP
Answered by Adeoluwa P. • Maths tutor
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Find the stationary points of the curve y=x^4-8x^2+3 and determine their nature.

First we will differentiate y to find dy/dx= 4x 3 -16x. Stationary points exist at dy/dx=0 so we set 4x 3 -16x=0 and solve for x. x(4x 2 -16)=0. So x=0 or 4x 2 -16=0. If 4x 2 -16=0 then x 2 =4 and so x=2 or ...
Answered by • Maths tutor
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Determine the first derivative of the following curve defined by parametric equations x = 20-5t and y = t^5.

First remember that a parametric curve z = (x(t), y(t)) can be differentiated using the following formula (derived using the chain rule): dz/dt = (dy/dt)/(dx/dt). We should now find dy/dt and dx/dt (which ar...
FC
Answered by Federico C. • Maths tutor
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I don't fully understand the purpose of integration. Could you please explain it to me?

I have written "… " where I would imagine the student is replying. I have then provided prompts assuming that the student did not come up with the answer straight away. Integration can be useful in...
RL
Answered by Rebecca L. • Maths tutor
3466 Views

Write down the value of 27^(-2/3)

We are trying to solve 27 -2/3 . Firstly, using the index rule a xy = (a x ) y , this can be rewritten as (27 1/3 ) -2 . Lets tackle the value inside the bracket first: 27 1/3 means the cube root of 27, and ...
ML
Answered by Matt L. • Maths tutor
6964 Views