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A function is defined parametrically as x = 4 sin(3t), y = 2 cos(3t). Find and simplify d^2 y/dx^2 in terms of t and y.

We first need to find dy/dx and we use the fact that dy/dx = dy/dt * dt/dx. So we have dy/dt = -6 sin(3t) and dx/dt = 12 cos(3t). Substituing these in we have dy/dx = -6*sin(3t) 1/(12 cos(3t) which simplifie...
BS
Answered by Barnaby S. • Maths tutor
7197 Views

Expand and simplify 2y+3y(5y+3)

Following the laws of BIDMAS, the bracket needs to be multiplied first (instead of adding 2y and 3y first): 2y + 15y 2 + 9y Simplify by addition of the y's: 15y 2 + 11y Optional: simplify further by grouping...
LJ
Answered by Lucy J. • Maths tutor
5298 Views

Solve 2x + 4 > 16

This is a simple GCSE inequality question. The aim is to solve the equation for x - get x on its own on the left side of the equation. Step 1. We think of equations as balanced weighing scales, so whatever w...
MP
Answered by Monique P. • Maths tutor
8320 Views

Find the coordinates of the two points where the lines y=x²+4x+6 and y=x+4 meet.

To solve these equations we must make them equal to eachother. This gives us x 2 +4x+6=x+4 , we must then subtract the ' x+4 ' from both sides to give us an equation that equals 0. This gives us the followin...
GH
Answered by Gaby H. • Maths tutor
3790 Views

All tickets for a concert are the same price. Amy and Dan pay £63 altogether for some tickets. Amy pays £24.50 for 7 tickets. How many tickets does Dan buy?

We know that Amy bought 7 tickets for £24.50. This means to find out the price for each ticket, we divide the price for 7 tickets by 7: price per ticket = (24.50/7) = £3.50 Now we can find the total number o...
SR
Answered by Sravani R. • Maths tutor
8889 Views