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We have....

19 =  (1/2)(17)t  + (1/2)(-1.5)t^2   simplify  by multiplying through by 2

38 = 17t - (1.5)t^2      rearrange

1.5t^2 - 17t + 38 = 0    multiply through by 2 again

3t^2 - 34t + 76  = 0      this won't factor.....using the quadratic formula and the onsite solve, we have

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{76}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{17}}\right)}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{3.063\: \!250\: \!108\: \!031\: \!115\: \!2}}\\
{\mathtt{t}} = {\mathtt{8.270\: \!083\: \!225\: \!302\: \!218\: \!1}}\\
\end{array} \right\}$$

Bala is setting up a factory to manufacture tennis b***s. If he buys a machine that costs Rs. 59728, then he can manufacture a tennis ball for Rs. 3.7. On the other hand, if he buys a machine that costs Rs. 44500, he can manufacture a tennis ball for Rs. 8.4.
How many tennis ball should he make so that his total cost is the same no matter which machine he buys?

Let x  be the number of teniis b***s to make.....then, equalizing the total costs, we have

59728 + 3.7x   =  44500 + 8.4x       simplify

4.7x  =  15228      divide both sides by 4.7

x = 3240  b***s should be manufactured to equalize the cost

The corners of a square with side 12 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so formed?

Let S be the side of the octagon......then.....before the corners are to be cut from the square, an isosceles right triangle is formed at each of these vertexes. The hypotenuse of this triangle = S.....and  the other two sides are S/√2 each. 

Then, before we make the cuts, the side of the square is composed of lengths of S/√2,  S and S/√2 ...or,  put another way.....

S + 2S/√2  = 12   simplify

S + √2S  = 12      factor

S(1 + √2)  = 12

S = 12/ [ 1 + √2 ]

See the following illustration :

 GE, EF = S =  12 / [1 + √2]   ....     CE and FD  = S/√2

Because Carl and Megan are butterflies and thay are saving the apples for their babies.

And you thought human babies were demanding. You should try feeding a family of caterpillars!

I assume you want to solve this for "b"  .....we have.....

1/x = 1/a +1/b       subtract 1/a from both sides

1/x - 1a =  1/b       get a common denominator on the left

[a - x] / ax  =  1/b        invert both sdies

[ax] / [ a - x] = b/1  

[ax]/ [a - x]   = b

Vcone = (1/3)pi(2cm)^2(3cm) = 12.566cm^3

Vsphere= (4/3)pi(1.5)^3   = 14.137cm^3

(14.137 - 12.566)cm^3  ≈ 1.571 cm^3

hello, I'm your "friendly" professor, Professor Geraldo

wow TR, another attempt to take over the world. looks like germanys checked on the list.

ive done some research, and it looks like England is using a weapon to defeat you.

time to create the Fiction-To-Reality Spell, a new spell that can turn fiction things from fictional books/movies into a reality

lets go back to The Only Thing To Fear book, and bring the Anomalies and Dual Anomalies, especially the Corps of Five, to live, and destroy England's secret weapon, invade England, and rule the world!

*pays 1,000 gold to attack Germany, 1945

*deploys a bunch of golems, lava hounds, pekkas, giants, balloons, dragons, and pretty much everything else just to distract the soviet union

me: alex, matt, and dawn, youre coming with me to hitlrs bunker

*we invade hitlrs secure bunker from the back, highly guarded by a bunch of soldiers

*releases the stolen arabian shock launcher to shock the troops, and 2 flamethrowers to burn them to death

*grabs a bag, stuffs hitlr in it, and runs out of here

*royal army changes army target and changes task from distracting the soviets and reds to capturing the n**i army

*hitlr, the royals, the magical army, and everything else, magically disappears with the Smoke Infect-Your-Enemy's-Eyes Spell

*steals the n**i's loot with some artilery

Battle OutCome:

Soldiers Deployed: 77

Soldiers Lost: 0

Soldiers Missing: 0

Powder Used For Spells/Artilery: 50

Powder On Artilery: 15

Powder On Heal Spells: 4

Powder On Smoke (Your Eyes) Spell: 20

Powder On Missle Artilery: 11

Gold Stolen: 17, 639, 028

Powder Stolen: 87

Tanks Hijacked: 63

Supply Cargos Stolen: 64, 823, 085

Soldiers Captured: 89, 547, 028

Medics Captured: 364

Battle Results: Victory

Rare Victory Quote For Battle: Love Capturing Evil MasterMinds (Better Than Me) Every Minute Cuz it Makes Me So Alive!!!

okay, weve already captured Vietnam and Russia! Viva! Now Asia is ours!

we also stole all the sweet gadgets, guns, and tanks from the Sweedish, and the Finnish have inspired us to rise up fine prices for being bad and drunk drivers.

alright, lets go back to 1945, on April, to make another evil move

lets get Adolf H****r out of the bunker where he "commited suicide", bring him to the future, and we will use him (yea, we're fooling h****r) so we can conquer more forces of Europe, theres a few twists though:

-all jews, communists, and any other group of race or religion that has been tortured by h****r's nazis will not be tortured this time (im also a considerate villain), but thats becuz im a Royal, not a n**i

-he will be high in my ranks, but low enough so he cant try to ruin the operation

-we will capture hitlrs n**i army and political army, and the other nazis, train them in the ways of RoyShowGaun, aka The Royal's Way (Roayl version of Bushido), and attack FRANCE AND THE UK!!!

-bury the n**i religion to the graves of Hades of Greece so that way no one will ever re discover n**i and try to rebel or ruin

but first, we must block the Soviet Union's army, delay them from pushing boundarys to Berlin

time to raid, Royals, we got some Nazis to convert

Two bears every hour and there are 23 hours. 2 * 23 = 46

Your total is 46 bears.

(How large is the guy? He has a serious appetite.)

deleted deleted

There is no graph 

You need to be a member to post pics.

Thanks Alan I didn't notice that.

I wasn't trying to be smart.  I was just answering the question in an attempt to learn from it. I am new to modulo arithmetic.

Kes,

Could you please put just one question per post.

Thanks :)

For this type of investment, the “Annuity Due” formula returns the correct future value for standard depository account interest payments, correlating to the beginning of the month deposit and end of the month interest payment.  This returns the same value as Alan’s result.

$$\\
\noindent \text {Annuity Due: }{FV = D \dfrac{(1 + r)^{n} - 1} {r}(1 + r)}\hspace{20pt} |\hspace{10pt} \text {\small D=Deposit per interval}\\

\\ 200*\dfrac{(1.0025^{360}-1)}{0.0025}*(1.0025)\;=\;116838.75$$

In practice, financial institutions use the “average daily balance” to calculate the interest on deposits. The result returns a value with limits between the two formulas.

$$\text {FV(annuity ordinary) \leq $ Total Interest $ \leq $ FV(annuity due)}$$

It seems to me that there must be an infinite number of inverses of 35 ...

True, but the question specifies that the answer to be supplied must be a nonnegative integer that is less than 83.

. 

The small difference between my result and Melody's is that I've assumed the the total includes the interest paid at the end of the last month; whereas Melody's assumes that in the last month only the $200 deposited at the beginning of the month is added in.

.

I think you mean this:

 @@ End of Day Wrap   Fri 31/7/15     Sydney, Australia Time   2:12am   (really Sat)  ♪ ♫

Hi everyone,

Our wonderful answerers have been Alan, CPhill, TitaniumRome, Heureka, Headingnorth, Biotomic121, Radix and Geno3141.  Thank you.  

Hi Kes 1968:)

Let Neha travel at N km/hr  for T hours.   So she will travel a total distance of N*T km

Sonia drives at (N+4) km/hour for (T+1) hour.   So she will travel a total of  (N+4)(T+1) km

Sonia drives 60km more than Neha so

(N+4)(T+1) - NT = 60

NT+N+4T+4-NT=60

N+4T+4=60

N+4T=56    (1)

Archana drives at (N+8)km/hr  for (T+2) hours.  So she travels a total of (N+8)(T+2) km

she will drive (N+8)(T+2) - NT    further than Neha

(N+8)(T+2) - NT

=NT+2N+8T+16-NT

=2N+8T+16

=2(N+4T)+16

sub in  (1)

=2*56+16

=112+16

=128km

Archan will drive 128km further than Neha      

$${\frac{{\mathtt{30}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\frac{{\mathtt{18}}}{{\mathtt{5}}}} = {\mathtt{3.6}}$$

$3.60