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dh/dt = (6-h)/20. When t=0, h=1. Show that t=20ln(5/(6-h))

Part 1: This question requires us to first do some rearranging. The right hand side of the equation is in terms of h, and we are looking to find t in terms of h, so it won't be appropriate to simply integrat...
LA
Answered by Linetta A. • Maths tutor
4842 Views

How do you integrate (sinx)^3 dx?

Firstly, we must use the special property of trig functions which means that (sinx) n is the same as sin n x. Likewise, (cosx) n =cos n x, (tanx) n =tan n x and so on. In this case, we need to start by repla...
SS
Answered by Shanti S. • Maths tutor
9099 Views

Show that 2(1-cos(x)) = 3sin^2(x) can be written as 3cos^2(x)-2cos(x)-1=0.

Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let's t...
RS
Answered by Rebekah S. • Maths tutor
4399 Views

Given two functions x = at^3 and y = 4a, find dy/dx

Solution: Parametric Differentiation with utilisation of Chain Rule. By the chain rule: dy/dx = dy/dt * dt/dx Note: dt/dx = 1 / (dx/dt) So dy/dt = 0, dx/dt = 3at^2 So dy/dx = 0 * 1/(3at^2) and hence dy/dx = 0.
MP
Answered by Michele P. • Maths tutor
3983 Views

How do I solve a cubic?

You can solve a cubic by applying factor theorem. This is where you plug different values for x into your cubic f(x) = ax^3 + bx^2 + cx + d such that x is a factor of d, until you find a value t for which f(...
HW
Answered by Harry W. • Maths tutor
4051 Views