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Thank you 

You have to add the three scores up and then divide by 3     :)

I think that the second one is good as well except that you forgot the minus sign near the end.  :))

The first one looks really good.  I did it exactly the same way :)

Trigonometry would be used heavily in surveying and building.  Actually it would be used for a great many things, launching rockets into space, navigating, calculating the size of planets etc etc.    

x+7=10

subtract 7 off both sides

x+7-7=10-7

       x=3

X + 7 = 10

x = 10 - 7

x = 3

@@ End of Day Wrap       Wed 19/11/14       Sydney,   Australia     Time 9:40 pm          ♬

Hello everyone,

Another busy day with a great many members offering great solutions.  These members were  Alan, sasflower, happy7, CPhill, relic, dancegirl101, geno3141,irmjj, BrittanyJ, Tiddle, JonesDaBoi, dogeminer, Rom, Pyramid and Heureka.  You are all wonderful.  

Now for some interest posts:

1) A look at imaginary numbers - powers of i

20/11/14

1) The children had a 'poetry fight' this morning

Thanks heureka,

This post is not just for heureka   

I am still a little confused. Is there a glitch in the calculator?  Why wasn't happy's answer the same?

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{400}}^\circ\right)} = {\mathtt{0.642\: \!787\: \!609\: \!687}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{400}}{\mathtt{\,-\,}}{\mathtt{360}}\right)} = {\mathtt{0.642\: \!787\: \!609\: \!687}}$$

Okay so why was mod function necessary - was it just that the sine function could not handle an angle that  was so huge?

9x-x=9x-1x=8x

I think that you are asking what percenage of the payment goes towards paying off the principal.

it will be

700/11000*100       percent

$${\frac{{\mathtt{700}}}{{\mathtt{11\,000}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{70}}}{{\mathtt{11}}}} = {\mathtt{6.363\: \!636\: \!363\: \!636\: \!363\: \!6}}$$

6.36%

Hi Rom,  it is really great to see you here !!!     

4.5*10^12=4500000000000

I do not understand this question  

this is the only bit of your question that I understand 

$$\\|x^2 - 7| <0.5\\\\
-0.5 -0.5+7 6.5 6.5 x^2>6.5\qquad or\quad x^2<7.5\\\\$$

$$[x<-\sqrt{6.5}\quad\cup\quad x>\sqrt{6.5}\quad ]\quad \cap \quad[ -\sqrt{7.5}

this is easiest to see in a graph

How to find integral of logarithmic functions:

$$\boxed{\int{log_a(x) \ dx} = x * log_a(x) - \dfrac{x}{\ln{(a)}} + c\ }$$

$$\begin{array}{lcrclcrccccl}
(u & * & v)' & = & u' &*& v & + & u &*& v' &\\
(x & * & log_a{(x)})' & = & 1 & *& log_a{(x)} & + & x & * & \dfrac{1}{x*\ln{(a)}} & \quad | \quad \textcolor[rgb]{1,0,0}
{
( log_a{(x)} )' = \dfrac{1}{x*\ln{(a)}}
}\\ \\
(x & * & log_a{(x)})' & = &&& log_a{(x)} & + &&& \dfrac{1}{\ln{(a)}} & \quad | \quad \int{}\ dx \\ \\
x & * & log_a{(x)} & = &&& \int{ log_a{(x)} \ dx} & + &&& \dfrac{1}{\ln{(a)}} \int{\ dx} & \\ \\
x & * & log_a{(x)} & = &&& \int{ log_a{(x)} \ dx} & + &&& \dfrac{x}{\ln{(a)}} & \\ \\
\int{ log_a{(x)} \ dx} & & & = &&& x * log_a{(x)} & - &&& \dfrac{x}{\ln{(a)}} &
\end{array}$$

Example:

$$basic \ a = e: \\
\int{ log_e{(x)} \ dx} =x * log_e{(x)} - \dfrac{x}{\ln{(e)}} \\
\int{ \ln{(x)} \ dx} =x * ln{(x)} - \dfrac{x} {1} \\
\int{ \ln{(x)} \ dx} =x * ln{(x)} - x\\$$

$$basic \ a = 10: \\
\int{ log_{10}{(x)} \ dx} =x * log_{10}{(x)} - \dfrac{x}{\ln{(10)}} \\
\int{ \log{(x)} \ dx} =x * log{(x)} - \dfrac{x}{\ln{(10)}}$$

inverse sine is the same as arc sine so on the calc on the home page just type in

asin(14/16) and press equals  

BTW i don't know how fast this goes, like 1 people has ebola, he infects another 3 person, they also infect another 9 persons so i goes faster and faster

Sasflower, you forget the negative sign.  But otherwise it was a great answer :))

I am really impressed by your logic JonesDaBoi  

I thought I might just try to do it by conventional algebra.

$$\\Find\;\; 2C+3T\\
6C+3T=4800 \rightarrow \;2C+1T=1600 \rightarrow \;2C=1600-1T \;\;(1)\\
8C+1T=4600 \rightarrow 1T=4600-8C \;\;(2)\\
$sub $ (2)\;\; into\;\;(1)\\
2C=1600-(4600-8C)\\
2C=1600-4600+8C\\
-6C=-3000\\
C=500\\
2C=1000\\
$sub back into (1)$\\
1000=1600-1T\\
1T=600\\
3T=1800\\
2C+3T=1000+1800=2800$$

so 2 cars and 3 Trucks are $2800

you know JonesDaBoi I like your solution better.   If I could give you more points I would  

(2222^5555+5555^2222)(mod7)=0

sin(12^12^14)

Hi Melody,

here is the solution from WolframAlpha:

I think, the argument (12^12)^14 is to big for our calculator. But the mod - function is correct and departs from the argument multiple from 360 degrees.

The formula is  $$\sin(\alpha) = \sin(\alpha \pm n*360\ensurement{^{\circ}} )$$

-2x+17 cannot be simplified  

((1 +3/20)*2)+(1+ 7/20)

just add the red bits and do it straight on the calc on the home pages