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solve the following simultaneous equations 4x + 6y = 16 and x + 2y = 5

x = 1, y = 2
BW
Answered by Billy W. • Maths tutor
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How do you know if the second derivative of an equation is a maximum or a minimum?

If the second derivative of an equation is positive (d 2 y /dx 2 > 0), we can see that this point on a curve is a minimum. This is because, where the first derivative finds the gradient of a curve (how th...
JG
Answered by Jessica G. • Maths tutor
4065 Views

Use integration by parts to find the integral of ln x by taking ln x as the multiple of 1 and ln x

For integration by parts, the integral is uv - ∫ u' v dx. First we take u = ln x and v' = 1. While we could have u and v' be the opposite at this stage, it becomes apparent later on that we can't do this bec...
JC
Answered by Jack C. • Maths tutor
5712 Views

Differentiate y=3x^2+2x+4 and find the stationary points, decide if it is a local maximum or minimum.

First Differentiate the equation to getdy/dx=6x+2Equal this to 0 to find the stationary pointdy/dx=0=6x+2 => 6x=-2=> x=-2/6=> x=-1/3 differentiate again to find the whether it is a maximum or minimu...
JG
Answered by Jemma G. • Maths tutor
4907 Views

(The question is too long so it's marked at the top of the answer space, sorry for any inconveniences)

Question: Particle P of mass m and particle Q of mass km are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the speed of P is 5u and t...
XW
Answered by Xudong W. • Maths tutor
5086 Views