All Answers 355938 Answers

4 x 4   =  16  outfits

There is a well-known shortcut to this, and it is:

The sum of consecutive cubes =The sum of the consecutive numbers squared!. That is:

1^3 +2^3 + 3^3 + 4^3 + 5^3............100^3 =[1+2+3+4+5.......+100]^2

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, =[(100 x 101/2)]^2 =5050^2 =25,502,500.

amnesia:

No, it is the same basic percentage of 16 2/3%. The reason is very simple. On the outgoing flight, you have: 72 - 60 =12 minutes, or a reduction in time of 16 2/3%. On the returning flight, you have:90 - 72 =18 minutes delay, which is 50% greater(18/12 =1.5) than the reduction time of 16 2/3%. In other words, 16 2/3% x 1.5 =25% of 72 minutes =18 minutes.

Asinus is right, this is debated quite often in academic circles –at least among the science and math majors.

I’ll add another two cents worth.

A fraction is ostensibly the same as division.  Most will agree that all of these are the same thing the same as  

\(3 \div 5 \\ \dfrac {3}{5}\\ 3/5 \\\)

Most will also know that order of operations (PEMDAS) says division take precedence over addition. Meaning 5+20/4+1 = 11 (not 5)

But

\(\dfrac {5+20}{4+1} = 5\)

There are no parentheses here, and addition now appears to takes precedence over division --both before and after the division  to give the "correct" answer of 5.

(Take note, guest #7, you listed several calculators but left out this site’s calculator)

These are comments from my favorite troll:

If you paste this  48/(2)(9+3)  into the site calculator, it returns 2 as the solution.

This is isn’t a bug. The parentheses cause the value to be treated as a variable. Implicit multiplication of variables takes precedents over division – a noted exception, dating back to the late 1960s, to the normal convention of mathematical hierarchy . Herr Massow’s calculator is the only one I know of that that does this, and it’s probably because it allows the use of variables.

Of course, if you put the explicit multiplication operator in: 48/(2)*(9+3) or leave the parentheses off the 2 then it returns 288,  the normal solution for numeric values.

This calc does have one hierarchal fault. “Stacked powers” are right-associated. The calc resolves them from the left.

4^3^2 returns (4^3)^2 = 4096 (It shows the order at the top).

With the correct hierarchy, it is 262144.

It’s always a good idea to know the quirks and faults of the tools you might use.  I drove an old car once that ran great, but the breaks didn’t work so well –I had to drag my foot to help it stop. It sure wore out my shoes faster than normal. :)

I appreciate ur try to explain me the math, but im stuck at the logic part :D 

I just dont get the difference in the wind. I mean it has a different % of influence on the second flight then it has on the first,

even thought it doesnt changes its strength. Just -/+

First flight was 1/6 = 16.6% faster then normal. 12/72. And the second flight was 25% slower then average. 18/72.

But nevermind, I will just let that hole stay in my head.

Beatng a dead horse .....but....I'm not "conceding" anything here

48/2(9+3)   means  [ using the order of operations ]

48/ 2 * (9 + 3)   =   

24 * 12  =

288

For this to equal 2....we would have to have

48 / [ 2 (9 + 3) ]  =

48 / [ 24  ]  =  2

So this........ 48/2(9+3) ....... is clearly  different from this.......  48 / [ 2 (9 + 3) ]

how do i use fractions

Let the original cost  = x    and the  profit is 15% of this= .15x  = 1350

So...original cost + .15x  = 1.15x  = selling price 

Then......

x   + 1350  = 1.15x    subtract x from both sides

1350  = .15x     divide both sides by .15

9000  = x

So.....the selling price  = $[ 9000 + 1350 ]  =  $10,350

Do not know what you are asking but

36kg / 30wk = 1.2 kg per week  = 2.65 pounds per week

Just use the division symbol for the numerator-denominator seperator.

1  Is there a decimal point in this 171 2 %   somewhere?  I will assume 17.12%

  17.12/100%  x £16.00  = £ 2.74 tax

2  100(1.1)(.9) =£ 99.00

What is your VAT rate? Is it 17.50%, or 17.12%?????

At any rate, I shall take it as 17.50%. You can change it, if I didn't get it right.

17.50% means =17.50/100 =0.1750, then:

.175 x 16 =2.8 pounds - the amount of VAT. So,

16 + 2.80 =18.80 pounds - the cost of the computer game PLUS 17.50% VAT.

amnesia:

             Remember that the ABSOLUTE speed of the plane, going and coming, is 5/6 of the distance between the two cities, which worked out to be 6/5 hours, or 72 minutes.  But the ougoing plane took 60 minutes, thereby shaving off 12 minutes, or 1 - (60/72) x 100 =16 2/3% off the 72 minutes(72 x 16 2/3%) =12 minutes.
Similarly, the incoming plane was supposed to take 72 minutes, but it took 90 minutes. Or 90/72 - 1 x 100 =25% longer. And 25% of 72 =18  minutes longer.
You are taking the AVERAGE time due to the wind, by basically adding the times up and dividing by 2, or 12+18 =30/2 =15 minutes. But you can't do that in figuring out the outgoing and incoming times, which worked out to be 12 and 18 minutes respectively.

Ok so I kinda understand the proof , but jea also still a bit stuck on the indeph part :D 

Thanks Tiggsy, 

This will give me lots to think about :))

\(\displaystyle \frac{d}{dx}\sin \left( \frac{1}{x}\right)=\lim_{h \rightarrow 0}\left(\frac{1}{h}\right)\left[\sin\left(\frac{1}{x+h}\right)-\sin\left(\frac{1}{x}\right)\right]\),

\(\displaystyle =\lim_{h \rightarrow 0}\left(\frac{1}{h}\right)\left[2\cos\left( \frac {2x+h}{2x(x + h)}\right)\sin\left(\frac{-h}{2x(x + h)}\right)\right]\),

(using the identity for sine minus sine).

The cosine term will tend to cos(1/x) as h tends to zero, so ignoring that for the moment, the rest of it can be written

\(\displaystyle - \lim_{h \rightarrow 0} \frac{1}{x(x+h)}\sin\left(\frac{h/2}{x(x+h)}\right)/\left(\frac{h/2}{x(x+h)}\right)\)

the x(x + h) being introduced so that we have a sin(theta)/theta ratio. (It cancels out).

and that will equal \(-1/x^{2}\) since the sin(theta)/theta part of it tends to 1 as h tends to zero.

Put that with the earlier cosine term and we have the final result \(-\frac{1}{x^{2}}\cos(\frac{1}{x})\).

Still not sure what to do about (1/x)sin(1/x) though.

Tiggsy

(b) A visitor to this country buys a souvenir costing £27.50 including VAT at 171 2
%. How much
VAT can be reclaimed?
(c) At the end of 1999 you bought shares in a company for £100. During 2000 the shares increased in value by 10%. During 2001 the shares decreased in value by 10%. How much were the shares worth at the end of 2001?
(Give your answers to the nearest penny.)

If the computer is sold at a profit of 15%,the profit will be $1350 find the selling price of the computer

let the original price be x

15% of x = 1350

0.15x=1350

x=1350/0.15

Sale price will be x+1350

Thanks very much Tiggsy.

I shall look at what you have presented so far :))

THAT is a BIG increase:

6,000,000 / 120,000 x 100% = 5000 %  increase

The Quadratic FORMULA is used to find the solutions (A.K.A the 'roots' or the 'zeroes') of a Quadratic EQUATION of the form

ax^2 + bx +c = 0

The formula is

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)   

Hi Melody

The trig formula for sinA - sinB is one of a group of four identities, the others being for sinA + sinB,

cosA + cosB and cosA - cosB. It helps if you can remember all four of them.

The identity for sinA + sinB is

sinA + sinB = 2sin{(A + B)/2}cos{(A - B)/2}

It's derived by adding the identities for sin(C + D) and sin(C - D) and then writing C + D = A and C - D = B.

I remember it as sin + sin = 2 sin semi sum cos semi diff. (if that makes sense !)

The others are

sin - sin = 2 cos semi sum sin semi diff

cos + cos = 2 cos semi sum cos semi diff

and

cos - cos = -2 sin semi sum sin semi diff.

(They are not difficult to remember if you look at the form of the identities for sin(A + B), sin(A - B) and so on.)

The mistake in #5 is that the negative sign in front of the first 2 should be an equals sign.

As to the calculus, I think that the original question is not well defined, are we supposed (to try) to diferentiate (1/x)sin(1/x) from first principles or are we allowed to derive the product and foaf rules and simply differentiate sin(x) from first principles, or do we derive just the product rule and differentiate sin(1/x) from first principles ?

(Can we assume the product and foaf rules ?)

If I have time, I'll post a derivation for sin(1/x) after lunch (UK).

Tiggsy

x2+8x+16=0

x^2+8x+16=0

I just pasted it into the calc :)

x^2+8x+16=0 = x=-4