Melody

Is our guest calling my solution an elephant ??    LOL     

Thanks guest      

Gee Chris, and I thought I was the expert in turning mole hills into mountains  LOL

Well I would say so because he wants to catch the train.....

rehi bought 150 oranges and 100 apples for her neighbors. she divided the oranges equally among them and had 17 oranges left. she also divided the apples equally among them and had 5 apples left. how many neighbors were there?

So the number of neigbours is a factor of 150-17 = 133

and also a factor of  100-5=95

now i will use the web2.0calc to tell me the factors.

factor(133) = 7*19

factor(95) = 5*19

The only common factor is 19 so there are 19 neighbours   

I really liked that question :)

If to a capital you earn 2% per month, How do you calculate the final amount after 12 months?

considering the compounding interest of each previous month added to the capital.'=

If you let the original amount by P then you will have

P(1+0.02)^12 = P*1.02^12 = P*1.26824     approximately

So 2 % per month is approximately the same as   26.824% per year

Let f(x) = 4x-5 and g(x) = 3x, find (f/g)(x)

\((f/g)(x)=\frac{4x-5}{3x}\)

Thanks Alan,

I could not resist graphing this too :)

My graph is a bit interactive.

17x40

Double 17=34

Double 34=68

Add a zero = 680

That is how I would do it :)

2sin(x)tan(x)=tan(x)+2sin(x)

\(2sin(x)tan(x)=tan(x)+2sin(x)\\ \frac{2sin^2(x)}{cos(x)}=\frac{sin(x)}{cos(x)}+\frac{2sin(x)cos(x)}{cos(x)}\\\ 2sin^2(x)=sin(x)+2sin(x)cos(x)\\ 2sin(x)-2cos(x)=1\\ 4(sin(x)-cos(x))^2=1\\ 4(sin^2(x)-2sinxcosx+cos^2(x))=1\\ sin^2(x)+cos^2(x)-2sinxcosx=0.25\\ 1-2sinxcosx=0.25\\ -2sinxcosx=\;-0.75\\ 2sinxcosx=\;0.75\\ sin(2x)=\frac{3}{4}\\ 2x\mbox{ must be in the 1st ot 2nd quadrant}\\ 2x=asin(\frac{3}{4})\\ 2x\approx 48.6^\circ,\quad 180-48.6^\circ, \quad (48.6+360)^\circ,\quad (180-48.6+360)^\circ, \quad \\ 2x\approx 48.6^\circ,\quad 131.4^\circ, \quad 408.6^\circ,\quad 491.4^\circ, \quad \\ x\approx 24.3^\circ,\quad 65.7^\circ, \quad 204.3^\circ,\quad 245.7^\circ, \quad \\ \)

I have checked these points from substitution.  Only the 2 middle ones work. It has probably got something to do with the squaring that I did as part of the working

\(x= 65.7^\circ \qquad or \qquad 204.3^\circ \qquad (\pm360n)\)

I suggest that you use Desmos for you graphs.  :)