Melody

That is neat Chris :))

2sin^2x+cosx=1

\(2sin^2x+cosx=1\\ 2(1-cos^2x)+cosx=1\\ 2-2cos^2x+cosx=1\\ -2cos^2x+cosx+1=0\\ 2cos^2x-cosx-1=0\\let\;\;m=cosx\\ 2m^2-m-1=0\\ m^2-(1/2)m-(1/2)=0\\ (m-1)(m+1/2)=0\\ m=1 \;\;or\;\; m=-1/2\\ cosx=1\qquad or \qquad cosx=-1/2\\ x=0+360n \qquad or \qquad 180\pm60+360n\qquad where\;\;n\in z\\ x=360n \qquad or \qquad x=180+60+360n\qquad or \qquad x=180-60+360n \qquad where\;\;n\in z\\ x=360n \qquad or \qquad x=240+360n\qquad or \qquad x=120+360n \qquad where\;\;n\in z\\ \mbox{x is in degrees}\)

Hi, I really do not understand this question?: "Calculate the effective annual interest rate for 20% p.a., compounded every 4 months?". Could someone please help me with this??. Thank you kindly..

\(1(1+0.20/3)^3=1(1+r)^1\\ 1(1+0.20/3)^3=1(1+r)^1\\ 1.21362963=1+r\\ r=0.21362963\\ \mbox{effective rate is 21.362963% p.a.} \)

If Rx is invested now, and at the end of every year for 4 years into an account that earns 7.2% interest per annum, compounded monthly. If the investment should grow to R20 000, calculate x. NB: a Hint is given to use a timeline?...

Ok,

x is invested now

In another 4 years another x is added to the account

Then another 4 years after that another x is added to the account.

etc,etc

The interest rate is    7.2% / 12 = 0.6% per month = 0.006

It grows to 20000 BUT you have not said how long it takes to grow to 20000.

Hence information is missing and this question cannot be answered !

Maybe you forgot to put something ?

square root of one minus four divided by two?''

\(\sqrt{1-4/2} = \sqrt{1-2}=\sqrt{-1}=i\)

This is an imaginary number.  There is no real number solution.

Nothing multiplied by itself = a negative number in the real number system.

Just google "difference of 2 cubes"

You will find lots :))

Flag pole erected and held in place by 3 wires. one wire is at the angle of 72° to ground and others 55° what is total length of wire?

Let the flag pole be h tall

Let the wire lengths be L1, L2, and L3      (L2=L3)

\(sin72=\frac{h}{L1}\qquad sin55=\frac{h}{L2}\\ L1=\frac{h}{sin72} \qquad L2=L3=\frac{h}{sin55}\\ ...\\ L1+L2+L3=\frac{h}{sin72}+2*\frac{h}{sin55}\\ total\;\; length=\frac{h}{sin72}+\frac{2h}{sin55}\\ total\;\; length=h[\frac{1}{sin72}+\frac{2}{sin55}]\\ total\;\; length\approx 3.493\;h\\\)

Thank you and you are very welcome :)

Could you explain please Alan ?

e^(2ipi)

\(e^{2i\pi}\\ =e^{2\pi i}\\ =cos2\pi\;\;+\;i\;sin2\pi\\ =1 + i * 0\\ =1 \)