All Answers 358087 Answers

We will stomp on your army like they are ants.  

I assume that you mean the 20th term is -30

Sn=n/2(a+L)

160=20/2(a+-30)

160=10(a-30)

16=a-30

46=a

a=46

The first term is 46

I have no checked you should though

Tn=a+(n-1)d

-30=46+19d

-76=19d

d=-4

Maia, have a look at your private messages for a clarification.

"So the process is, calculate the third unknown side using pythagoras and then tan a = opposite side / closest side. "

This is correct.  

The "closest" side is called the "adjacent" side.

The "opposite" side is just that.

The longest side is called the "hypotenuse".

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Thanks Alan, it was pi/2 < a < pi so -sqrt(11)/5 should be correct.


So the process is, calculate the third unknown side using pythagoras and then tan a = opposite side / closest side. Correct me if I'm wrong.

English is not my native language, dont know the correct term for the sides in a triangle.

That is good :))

If N = total number, then 420 represents (100 - 35 - 45)% (=20%) of the total, so 20%N = 420 or 0.2N = 420

N = 420/0.2 or N = 2100

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What question?

With what ?

There are two possibilities:

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melody thanks i think i've got it:)

"For the last bit you just have to show that 9m/19 is not an integer for  0<m<19 can't you just say that 9 and 19 are relatively prime so 9m/19 will only be an integer if m is a multiple of 19.  Since m cannot be a multiple of 19, 9m/19 is not an integer. That is, 9m is not divisable by 19"

Yes.  Much neater Melody.

Thanks Alan,

Sorry, I screwed up again  

Hi Sabi,  

There are a couple of ways to do this but I will show you the way that I think is usually easiest.

You want to get rid of the fraction.  If this was an equal sign then you would note that x cannot be 2 and then you would multiply both sides by x-2.

It is a little different with an inequality because you would have to have 2 different scenarios, one for when x-2 is positive and one for when x-2 is negative.   SO

it is much better to multiply both sides by something that you KNOW is positive.

Multiply both sides by (x-2)^2   that HAS to be positive

$$\\\frac{1-x}{x-2}>0\\\\
\frac{1-x}{x-2}\times \frac{(x-2)^2}{1}>0\times \frac{(x-2)^2}{1}\\\\
\frac{1-x}{1}\times \frac{(x-2)}{1}>0\\\\
(1-x)(x-2)>0\\\\\\
--------------\\
$The only way 2 expressions multiply to be positive is if they are both positive or they are both negative.$\\\\
1-x>0\quad and \quad x-2>0 \qquad OR \qquad 1-x<0 \quad and \quad x-2<0\\\\
$ I can continue this if you want but there is a better way.$\\\\
------------------\\\\$$

$$\\(1-x)(x-2)>0\\
$If you let $ y=(1-x)(x-2)\\
$then the statement will be true when $y>0\\
y=(1-x)(x-2)\\
y=-1x^2+3x-2\\
$this is a parabola- the coefficient of $ x^2$ is -1$\\
$So it is concave down.$\\
$The middle bit will be above the x axis where y is positive.$\\
$The roots are x=1 and x=2$\\
SO\\
(1-x)(x-2)>0\quad when\;\;1

This is not as hard as it may at first look.

If you need me to explain anything please ask :)

There isn't one, this is not a GP

if it were a GP then

1/-2 would equal -12/1   and this would  be the common ratio

Yes, sorry Alan I did not realize that our answers were different. 

Alan is totally corect.

This is the formula for the the future value of an ordinary annuity.  This is where the money is put into the account at the END of the time period instead of at the beginning.

It is easy to adjust it for this question.  

Here we have $200 invested at the very beginning so we must ADD 200 plus the interest it will accrue for the whole 30 years  that will be    C(1+i)^n = 200*(1.0025^360)

but NO $200 is  invested at the very end SO we must subtract C = $200 at the end

so we get 

$$\\FV=\left[\frac{(1+i)^n-1}{i}\right]+C(1+i)^n-C\\\\
$If you rearrange this you will find that it is identical to Nauseated's formula.$\\\
FV=$my original answer$+C(1+i)^n-C\\\\
FV=116547.38+200(1.0025)^{360}-200\\\\$$

$${\mathtt{116\,547.38}}{\mathtt{\,\small\textbf+\,}}{\mathtt{200}}{\mathtt{\,\times\,}}{\left({\mathtt{1.002\: \!5}}\right)}^{\left({\mathtt{360}}\right)}{\mathtt{\,-\,}}{\mathtt{200}} = {\mathtt{116\,838.748\: \!442\: \!299\: \!145\: \!509\: \!1}}$$

FV = $ 116838.75  

This is identical to Alan's answer.  And Nauseated also agreed that it is correct.

 ------------------------------------------

Nauseated has gone one more step with this.

He has said:

"In practice, financial institutions use the “average daily balance” to calculate the interest on deposits."

Yes  this is correct  

Nauseated has then stated that:

"The result returns a value with limits between the two formulas. "

Yes I can see how this could possibly be justified..   but I would like Nauseated to justify/discuss this statement. :)

How many significant figures?

what is 3.1536e16 in sigfigs?

Also, if this is a calc read it probably means    $${\mathtt{3.153\: \!6}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{16}}}$$

otherwise it may mean         $${\mathtt{3.153\: \!6}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{16}}} = {\mathtt{28\,023\,238.137\: \!473\: \!627\: \!147\: \!295\: \!9}}$$  

If you really mean 5.0909 then you just get 50909/10000 as a fraction.  However, if you mean 5.0909.... where the 09s go on forever, then, because 1/11 = 0.09090909.... it can be written as 5+(1/11) or 56/11

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If the complex number is in rectangular form:   z = a + i*b then the polar form is:

z = r*e^iθ, where r = √(a² + b²)  and  θ = tan^-1(b/a)

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its like hes been watching too much Man V Food and Bizarre Foods

*pays 1,000 gold for the journey and attack at England

Location: London, England, 1945

lets start off with a few things I like to call Poison Spells

*drops 20 poison spells around the city, causing 2/5 of londons population to die from the poison spells, 1/3 of the 2/5 population being of the british Military, and the rest to the public

BOMBS AWAY!!!

*shoots 3 artilery at giant bombs so they go off and explode before sending in hog riders and risking them killed by the giant bombs

alright, lets send in the Anomaly Hog Riders And The WitchArd!

*sends 24 hog riders to attack the defenses on front, while sending in 12 wizards and 6 witches on the back doing the actual damage

*deploys Castle Rienforcements containing 2 more witches, 2 more wizards, and the Twin barbarians and pretty Archer

*fires 1 more artilery at 2 more giant bombs next to each other to not face risk of losing troops

*places Heal Spell on the Hog Riders so they can heal

*freezes inferno towers and wizard towers, one of the hog riders weaknesses

all wizard towers get destroyed and 1 inferno tower is down

*heals and rages hog riders to defeat the final inferno tower guarding the "Royal" Castle of London, where Churchill will be waiting

*british military tries to fight back, but the witch's and wizard's love is too strong to ever be destroyed

*advances to the castle

*sends in the Royal Heroes: Barbarian King and Archer Queen

*freezes Churchill, slays him, and then, the royals destroy the Castle, them

BOOM!!! all of england is destroyed, now under real Royal Control

*scottish army comes to invade us, this time with GoWiPe Your Eyes (Golems+Wizards+Pekkas)

*releases the stolen Shock launchers and Rocket Launchers, Boom Cannons, and Inferno Towers quickly kills all Golems

*all wizards deployed right away encounter a giant bomb, forgot to set it off before it explodes, giant bomb explodes and kills all wizards

*Spainish Army arrives with a LavaLoonIon Attack

*Pekkas from scottish military destroy the junk on the outside, allowing a Hidden tesla to pop up, zap the pekkas constantly and with damage, kills all 3 pekkas all of a sudden, tries to deploy royals and rienforcements, but fails by the inferno towers

*scottish army surrenders and now Scotland is Ours!

*Lava Hounds  quickly die and heroes right away die by the air defenses and the stolen Ottoman Empire Cannons

*Balloons and Minions slowly go down by the air sweeper and air defenses, air bomb triggers, kills all minions, does most damage to balloons, right away shot down from the Archer Towers stolen from Finland

*does not deploy rienforcements, spain surrenders

NOW ALL OF EURASIA IS OURS! NOW LETS GO AND INVADE THE ReST OF THE AMERICAS

*after many more successful attacks, only africa and australlia remain free from royal control

Operation Eurasia Over

Result: Success

Next Operation: Operation Africa

Next Continent Target: Africa (6th continent to attack)

Last Operation: Operation Australi-DOOM

Last Operation Target: Sydney, Australlia (your hometown, Melody)

Saina is deciding to buy a car. She can choose between a diesel car and a petrol car. 
The diesel car costs Rs. 7310 than the petrol car. However, it can travel 15.9 kilometres per litre, whereas the petrol car can only travel 11.3 kilometres per litre.
Also diesel costs Rs. 55.65 per litre, and petrol costs Rs. 58.76 per litre.
If she buys a diesel car, how many kilometres must she drive before the savings in fuel covers the extra price of the diesel car?

.................................................................................................................................................

The diesel car costs  55.65/15.9 = 3.5R/km to operate ..... and the petrol car costs  58.76/ 11.3 = 5.2R/km to operate

So  (5.2 - 3.5)x  = 7310    where x is the answer we're looking for

1.7x = 7310    divide both sides by 1.7

x =  4300km

I tried feeding a pack of Hog Riders with ProtoType RadioActive Juice, and instead of them dying, they grew together, strong, strong enouygh already to defeat Winston Churchill of England, he shall surrender when I attack England!

good idea, professor!

hmm, lets see what should we experiment the anomalies with? hmmm, lets use it on the Hog Riders, or as some of you better known him as, Mr. T riding a Hog

now, to be honest here, back in 1945, the hog riders used to suck. in fact they were the worst troops in the game,too expensive, took long time to train, attacked anything, and got shot down easily.

now lets test them with n**i DNA

mwahahahaha! its been complete! the Anomaly Hog Rider, new ability: shorter train time, price dropped, more health, more power from changing from a normal hammer to a Thor's Hammer, and the best part: THEY NOW ATTACK DEFENSES!!!! this will be worthy, now lets upgrade our heal spells....wonder what they will do

YES!!! THE HEAL SPELL DOES 50% MORE HEALING TO HOG RIDERS THAN OTHER TROOPS!

now lets test on some other troops

mwahahaha, more combinations!

LavaLoonIon

BalloonIon

GIzEaler

GoWiPe (Your Eyes)

GoWiWi (Your thingy)

WiGoWiPe (Your Laughter)

LaGon

(I Just) BaRch (Your Village)

GoWiPe (Your Eyes Cuz You're About To Be Destroyed By) Hog

WitchArd (Your Crush aka Witch+Wizard make a perfect deadly couple)

and, we have the ultimate one:

Royal Destruction (Every Troop United)

the ProtoTypes for the nazis were perfect! although nazis may be stupid in society, they are some evil geniuses, and that was exactly what I was looking for

now, its time to call:

LETS ATTACK ENGLAND!!!