All Answers 359334 Answers

I believe this young person was thinking of: 7 X 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7=49, but NOT 7^7.

7^{4n + 1}  →  ending digit = 7

7^{4n + 2}  → ending digit = 9

7^{4n + 3} →  ending digit =  3

7⁴ⁿ⁺⁴ →   ending digit  = 1

For n  > 0

if you do 7 times seven it equals 49 but if you do 7 times 7 times 7 times 7 times 7 times 7 times 7 it equals 5,764,801. why does that happen?

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

It is thoughts like these that make the difference between someone with a mathematical mind and someone without a mathermatical mind.  You obviously have a good analytical brain.  :)

I cannot tell you why more than what you can see for yourself.  It is something that you will need to ponder on.

When you increase things exponentially then numbers change very dramatically, that is what you have done here.

\(7^7=823543\)

The exponent is the little 7

It is this fact that makes such a huge amount of difference to the total when money is compounded.  

Anyway keep thinking about concepts like this.  It will enhance your understanding of the mathematical world enormously. 

Why don't you become a member.  We need people like you here :)

EDIT

I didn't see the first answer when I posted mine.  YES EXACTLY .      Thanks answering guest!

7*2  and 7*7     is totally different from  7^7.

Many students confuse powers (exponents) with multiply.  

The sooner you sort that one out the better.

    5300{[1-(1/1.07)^9]/0.07}=34,530.73091862...etc.

Because: 7^2 is very DIFFERENT from 7^7, that's WHY!!!!!!.

BECAUSE YOU EAT TOO MUCH JUNK FOOD!!!!!.

calculate the wavelength and energy of light that has a frequency of 1.5e15 hz

Wavelength=c/v, where c=speed of light and v=frequency

W=3 X 10^8/1.5 X 10^15

W=2 X 10^-7m-wavelength of light.

E=vh, where v=frequency, h=Planck's constant

E=1.5 X 10^15 X 6.63 X 10^-34

E=9.945 X 10^-19 J-energy of light

Could you post  a specific example that is giving you trouble???  This is rather a broad quesrion to provide a definite answer.

Have a look at the graph, here........https://www.desmos.com/calculator/wslbve0v6i

It does appear that this approaches -1/4 as x→ infinity

LambLamb is correct.......here's the graph.......https://www.desmos.com/calculator/s6jkhwavah

Maybe 24²   ????  →  576

2/7 x 9 than divided by 2/7

\(\frac{2}{7}\times 9\div \frac{2}{7}\\\\ =\frac{2*9}{7}\div \frac{2}{7}\\\\ =\frac{2*9}{7}\times \frac{7}{2}\\\\ =\frac{\not{2}*9}{\not{7}}\times \frac{\not{7}}{\not{2}}\\\\ =9\)

3/8 x -4 x 3.5 x 8/3?= -14

All calculators differ of course, assuming your calculator is scientific, there should be a +/- button? 

Evaluate just means find the number answer. 

eg

evaluate 6+2

answer is 8

\(\displaystyle{\lim_{x \to \infty}}\dfrac{x^2+4x+3}{x+1}-(\alpha x + \beta)=3\)

\(\displaystyle{\lim_{x\to \infty}}\dfrac{(x+3)(x+1)}{x+1}-(\alpha x+\beta)\)

\(\displaystyle{\lim_{x\to \infty}}(x+3)-(\alpha x+\beta)=3\)

\(\displaystyle{\lim_{x\to \infty}}(1-\alpha)x+(3-\beta)=3\\ \\ \alpha = 1 \\ \beta = 0\)

lim(sqrt(4x^2-x)-sqrt(9x^2+1)+x),x->infinity 

lim_(x->infinity) (sqrt(4 x^2-x)-sqrt(9 x^2+1)+x) = -1/4

Find the following limit:
lim_(x->infinity) (x+sqrt(4 x^2-x)-sqrt(9 x^2+1))

x+sqrt(4 x^2-x)-sqrt(9 x^2+1)  =  x+sqrt(x (4 x-1))-sqrt(9 x^2+1):
lim_(x->infinity) x+sqrt(x (4 x-1))-sqrt(9 x^2+1)

The limit of x+sqrt(x (4 x-1))-sqrt(9 x^2+1) as x approaches infinity is -1/4:
-1/4

-1/4 = -1/4:
Answer: | 
| -1/4

\(\displaystyle{\lim_{x\to \infty}}\sqrt{4x^2-x}-\sqrt{9x^2+1}+x\)

\(\displaystyle{\lim_{x\to \infty}}x\left(\sqrt{4-\frac 1 x}-\sqrt{3+\frac 1 x}+1\right)\)

\(\mbox{In the limit we can ignore the }\dfrac 1 x \mbox{ terms}\)

\(\displaystyle{\lim_{x\to \infty}}x\left(\sqrt{4}-\sqrt{3}+1\right)=\displaystyle{\lim_{x\to \infty}}x\left(3-\sqrt{3}\right)\)

\(3 > \sqrt{3} \mbox{ so } \\ \displaystyle{\lim_{x\to \infty}}x\left(3-\sqrt{3}\right)=+\infty \\ \mbox{and so } \\ \displaystyle{\lim_{x\to \infty}}\sqrt{4x^2-x}-\sqrt{9x^2+1}+x=+\infty\)

\(x^2 + 2x\)

\(\mbox{note that }(x+a)^2 = x^2 + 2a x + a^2\)

\(\mbox{so we must have that }2a=2 \Rightarrow a=1\)

\(\mbox{and so we get } \\ x^2+2x = x^2+2x + 1 -1 = (x+1)^2 - 1\)

Now, if you only knew HOW it was calculated!!.

Now the question becomes.

Does any squared number contain the digit 7 ?

If so what is the first squared number that contains the digit 7 ?

Same suggestion as in the previous two.

Same suggestion as in the previous one.

You can go to this link and look up the "Formula Table", which has ALL the common financial formulas used in your calculations. https://en.wikipedia.org/wiki/Time_value_of_money