All Answers 356721 Answers

Hmm!!

0^0 is undefined.

Oh... I meant the computer keyboard.

Can you prove that the LHS converges to 2.38423 ?

Anything to the power of 0 is 1.

[Edited]

And here's why.

Let's start with powers of 3s because they are easy.

Let's first assume 3^0 is 1.

So...

3^0 =1.

3^1=3.

3^2=9.

3^3=27.

3^4=81.

Now as you can see, a number is 3 times greater than the number before it. Here's what I'm talking about.

3^2 is 9 and 3^3 is 27. It is obvious that 27 is 3 times greater than 9. This is the same with other numbers that is in the

"3-to-the-what power" form. 

So if you think about it, shouldn't 3^0 be 1?

Because we know that a number is 3 times greater than the number before it. 

And 3^1 is 3. So we have to divide that by 3 to get "3^0."

3/3 is 1. 

So 3^0 is 1. 

This concept can be hard to understand with one example. 

But think about it. A similar rule applies to any other set of exponents with the same base. 

2^1 (That 's 2) divided by 2 would get us 2^0.  And 2^0=1. See a pattern?

So you see that you can divide a number with an exponent by its base to get the number that has an exponent 1 less than the original number's exponent. (example: 2^2 and 2^1.  2^1 has an exponent 1 less than 2^2. )

And that's my explanation.

There are probably many simpler and better-to-understand explanations out there...

Correct me if my explanation is wrong. I often get things mixed up in explaining things.

Yes I can now see I am wrong.

I took a and b to be pronumerals when they are cleaarly marked as directional vectors.

If a and b were ordinary pronumerals then the question would be nonsense but as directional vectors (as is stated in the question) it is my answer that is nonsense.  Sorry all.

Thanks Tiggsy and Heureka. 

Also CPhill found the answer as a video clip on a seperate site.

This is the site

Use this formula to get the FV of the investment:

FV =P x {[1 + R]^N - 1 / R}

FV =$100 x {[1 + 0.45/12]^(20*12) - 1 / (0.045/12)}

FV =$38,812.44 - This is what you should have after 20 years.

Who said, "it wasn't right"??

If you purchased 50 shares for $70 per share, then sold it 6 years later for $5,600, then the stock must have appreciated: $5,600 / 50=$112 per share in 6 years. So, your total profit would be:$5,600 - (50 x $70) =$2,100.

Your annual return on your stock would be:($112/$70)=1.6 - 1 x 100 =60% over 6 years. Or 60% / 6=10% per year-simple return.

please explain q.22

\(\text{CAYB is a quadrilateral. } \\ \vec{CA} = 3\vec{a} \\ \vec{CB} = 6\vec{b} \\ \vec{BY} = 5\vec{a}-\vec{b} \)

\(\begin{array}{|rcll|} \hline && \mathbf{\dfrac{\vec{CY}} {\vec{CX}}} \\\\ &=& \dfrac{\vec{BC}+\vec{YB}} {\vec{AC}+\vec{XA}} \\\\ &=& \dfrac{6\vec{b}+5\vec{a}-\vec{b}} {3\vec{a}+\frac13\vec{AB}} \\\\ &=& \dfrac{5\cdot(\vec{a}+\vec{b})} {3\vec{a}+\frac13(\vec{CB}-\vec{CA})} \\\\ &=& \dfrac{5\cdot(\vec{a}+\vec{b})} {3\vec{a}+\frac13(6\vec{b}-3\vec{a})} \\\\ &=& \dfrac{5\cdot(\vec{a}+\vec{b})} {3\vec{a}+2\vec{b}-\vec{a}} \\\\ &=& \dfrac{5\cdot(\vec{a}+\vec{b})} {2\cdot(\vec{a}+\vec{b})} \\\\ &=& \mathbf{\dfrac{5}{2}} \\ \hline \end{array}\)

said it wasnt right :(

What you are thinking about is something called "Perpetual Annuity". You can get it as follows:

$50,000 / 7% =$714,285.71. This is how much you must save in 35 years from age 25 to 60. So, the question becomes how much must you deposit each month OR each year to get the above amount at age 6o?.

This is the formula you will use to attain your goal. Will assume annual deposits.

FV =P x {[1 + R]^N - 1 / R}

$714,285.71 =P x {[1 + 0.07]^35 - 1 / 0.07}, solve for P, or annual payment.

P =$5,167.11 - This is what you must deposit each year in your fund to get $714,285.71 at 60, which will allow you to withdraw $50,000 @ 7% FOREVER !!.

P.S. Try and do the math in the above formula and let us see if you can get the same answer that I did.

Sorry Melody, but that is wrong.

It's a perfectly acceptable exercise in vector addition.

a and b are vectors, they each have an magnitude, (unknown), and a direction. The direction of a is parallel to CA, in that direction and b is parallel to and in the direction of CB.

Vectors obey a triangle law of addition.

In the original diagram, put a line between C and X, then the vector CX will equal the sum of the vectors CA and AX.

\(\displaystyle \underline{CX}=\underline{CA}+\underline{AX}\)

Similarly,

\(\displaystyle \underline{CX}=\underline{CB}+\underline{BX}\) ,

so long as you start and end at the same points, you can visit any other point(s) on the way.

The law can be extended to more than one intermediate point.

For example, put a line between Y and X, and you can say that \(\displaystyle \underline{BX}=\underline{BY}+\underline{YX}\),

so \(\displaystyle \underline{CX}=\underline{CB}+\underline{BY}+\underline{YX}\).

So long as you start and end at the same points, ... .

Onto the actual question.

We are told that \(\displaystyle \underline{AX}:\underline{XB}=1:2 \text{ , so, }2\underline{AX}=\underline{XB}\).

Using the triangle law,

\(\displaystyle \underline{CX}=\underline{CA}+\underline{AX}=3\underline{a}+\underline{AX}\),

and

\(\displaystyle \underline{CX}=\underline{CB}+\underline{BX}=\underline{CB}-\underline{XB}=6\underline{b}-2\underline{AX}\).

Eliminate the \(\displaystyle \underline{AX}\) between the last two equations, (twice the first plus the second), and we have

\(\displaystyle 3\underline{CX}=6\underline{a}+6\underline{b}\), so \(\displaystyle \underline{CX}=2(\underline{a}+\underline{b})\).

Using the triangle law again,

\(\displaystyle \underline{CY}=\underline{CB}+ \underline{BY}= 6\underline{b}+(5\underline{a}-\underline{b})=5(\underline{a}+\underline{b})\).

So, \(\displaystyle \underline{CX}= 2(\underline{a}+\underline{b})=\frac{2}{5}.5(\underline{a}+\underline{b})=\frac{2}{5}\text{ .}\underline{CY}\),

as required.

Tiggsy

Yes, I did accept your website proof but it is good that you explained it in your own words :)

This is the formula you would use to find the FV of the IRA at 65.

FV=P{[1 + R]^N - 1/ R}

FV =$75 x {[1 + 0.05/12]^(40*12) - 1 / (0.05/12)}

FV =$114,451.51 - This is what you would have in your IRA at 65.

P.S. Do the math in the above formula and see if you can get the same answer that I did.

True what you say! Here is my take on it:

Suppose we ONLY had these Primes: 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19=9,699,690. Now, we add 1 to it and we have: 9,699,690 + 1=9,699,691. Now, this new number is either a prime or has Prime Factors that are NOT included in our list, because if you divide it by any of them, it will always leave a remainder of 1. It, therefore, must either be a Prime Number or has Prime Factors > 19 listed above.  And if we check it, we see that 9,699,691 = 347 * 27953, which are its Prime factors and both, in this case, are larger than our listed largest prime, or 19!. And that proves there are infinitely MANY PRIMES!!.

You 'assumed' all people interested in mathematics knew. 

As someone interested in mathematics you should know that assumptions usually lead to errors.

That is why in mathematics all things must be proven. :)

And proofs must be demonstrated :)

Good Point! I thought everybody interested in Math knew it! Here is a brief proof of it.

https://math.stackexchange.com/questions/1017218/euclids-proof-for-infinitely-many-prime-numbers

Why don't you demonstrate :)

what IS 10 TO THE 1000000000000 POWER

You could abbreviate it like this: 10^10^12

For your "Proof by Contradiction", you should have used the famous proof of Euclid of "Infinity of Primes!" That is one of the most elegant proofs in the history of Math.

Chill dude.

Thanks!

Thanks, Mathhemathh  !!!!!!

120  factors as    2^3 * 3 * 5  and the sum of these is

3(2)  + 3 + 5  =

6 + 8

14

144000  factors as  2^7 * 3^2 * 5^3  and the sum of these is

7(2) + 2(3) + 3(5)  =   

14 + 6 + 15  =

35