CPhill

We can use the sine inverse to find x

So

sine^-1(6/7) = 58.997280866126°  = x

So.... sine (58.997280866126 / 2) = 0.492402907365

Also, x could be 121.002719133874°

And the sine of (121.002719133874 / 2) = about .870

We can use the Law of Cosines to find  DE...so we have

DE^2 = 720^2 + 940^2 - 2(720)(940)cos47

DE^2 = 478847.0198200768

DE = about 692                                                                        

And using the Law of Sines, we can find angle EDF                 

So we have

sin EDF / 940 = sin 47 / 692

sin EDF  = 940sin47/692 = .9934573403495087

And using the sin inverse

sin-1 (.9934573403495087) = EDF= 83.44°

And the remaining angle, DEF = (180 - 47 - 83.44) = 49.56°

Have a look at the graph of the function, here.....

Notice that we can write

16 sin36 / sin(36 + 36) =

16 sin 36 / (sin36cos36 + sin36cos36) =

16 (sin 36) / [(sin36) [cos 36 + cos36] =

16 / (2 cos 36) =

8/cos 36 = 8(1/cos36) =

8sec36 =  about 9.89

(36^2+25^2-23^2)/(2x36x23)

Just copy and paste the above into the onsite calculator.....it gives

$${\frac{\left({{\mathtt{36}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{25}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{23}}}^{{\mathtt{2}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{36}}{\mathtt{\,\times\,}}{\mathtt{23}}\right)}} = {\frac{{\mathtt{58}}}{{\mathtt{69}}}} = {\mathtt{0.840\: \!579\: \!710\: \!144\: \!927\: \!5}}$$

as the answer....!!!!

400,000(1.05^x)=1,000,000     divide both sides by 400,000

1.05^x = 1000000/40000

1.05^x = 2.5     take the log of both sides

log 1.05^x = log 2.5      and we can write

x log 1.05 = log 2.5        divide both sides by log 1.05

x = log 2.5 / log 1.05  = about 18.78

That's quite creative, jillybean...!!!

Well presented,  Anonymous.....why don't you become a member???....then, you wouldn't be "Anonymous" anymore !!!

Cos B= (36^2+25^2-23^2)/(2x36x23)

This is solving a Law of Cosines problem for an angle

So, using the cosine inverse, we have

cos^-1 (36^2+25^2-23^2)/(2x36x23) = about 32.8°

Lea just emptied her piggy bank and found that she had $2.85 in nickels and dimes. If the number of nickels is 1 more than twice the number of dimes, how many nickels did she have in her piggy bank?

Call the number of dimes , x

Call the number of nickels 2x + 1

So we have, the number of nickels times their value plus the number of dimes times their value = the total value....algebraically, this is....

.05(2x + 1)  + .10x  = 2.85     multiply through by 100 to clear the decimals

5(2x + 1) + 10x = 285             simplify

10x + 5 + 10x = 285   

20x + 5 = 285                        subtract 5 from both sides

20x = 280                              divide by 20 on each side

x = 14    = number of dimes

2(14) + 1  = 29 = number of nickels