# Tagged Questions

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### rounding up to nearest square

Say I have x and want to round it up to the nearest square. How might I do that in a constant time manner? ie. $2^2$ is 4 and $3^2$ is 9. So I want a formula whereby f(x) = 9 when x is 5, 6, 7 or 8. ...
875 views

### 10 to the power of 3.5 [closed]

So $10^3 = 10\times 10\times 10 = 1000$, this is really easy to understand. But what about: $10^{3.5}$ My logic would suggest this was $10\times 10 \times 10\times 5 = 5000$ but the calculator ...
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### taking the log of $a^b$ (Project Euler problem 29)

I've been stuck on Project Euler problem 29 and thus asked a friend who solved it how to do it. What he basically did was for each power was: $\left(\frac{\log_{10}(a)}{\log_{10}(2)}\right)\cdot b$ ...
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### Solving an equation with $x$ as powers

How would I go about solving $$2^x -2^{x-2}=3 *2^{13}$$Hints please. Thank you.
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### Why is $\;n^2-\frac{n^2}{2} =\frac{n^2}{2}\;$? [closed]

Could someone please expand on how to get from $\;\displaystyle\left( n^2-\frac{n^2}{2}\right)\;$ to $\;\left(\dfrac{n^2}{2}\right)\;?\;$ I can't seem to wrap my head around that.
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### why if x in 1/n power >(<) y in 1/m power then x in c/n power >(<) y in c/m power?

As you might guess this is one more stupid question from non-matematician, and you are right. I found this exercise in "Algebra and trigonometry book": $7^{1/2}$ or $4^{1/4}$. After some googling I ...
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### How is this proof flawed?

$\sqrt{x}=-1$ $\sqrt{x}^2=(-1)^2$ $x=1$ Now substitute it into the original equation $\sqrt{1}=-1$ $1=-1$
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### Why when indices cancelled out leave 1 at top?

This is a really basic question, but I have just got interested in math and learning rules about powers/indices and this confused me a little. $\dfrac{a^3}{a^7}$ after they cancel out we get ...
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### Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
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### 1 to the power of infinity, why is it indeterminate? [duplicate]

I've been taught that $1^\infty$ is undetermined case. Why is it so? Isn't $1*1*1...=1$ whatever times you would multiply it? So if you take a limit, say $\lim_{n\to\infty} 1^n$, doesn't it converge ...
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### Proof for power functions

Which is greater? $\sqrt{n}^{\sqrt{n+1}}$ or $\sqrt{n+1}^\sqrt{n}$ I know that $\sqrt{n}^{\sqrt{n+1}}$ is greater but I tried using induction and I couldn't figure it out. Thanks for the help.
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### Units in exponent - e.g. solve: $2^{3 years}$

What happens to units in an exponent? My math textbook just introduced the exponential equation: $$A_t = Pe^{rt}$$ I've always made it a point in solving math problems to include the units in every ...
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### Simplifying $\;x({y^{3}}/{x^{4}})^{1/4}$

Iâ€™m a little unsure how to simplify the following expression: $$x\left(\frac{y^{3}}{x^{4}}\right)^{1/4}$$ According to the answer, this should get you $\;\; x y^{3/4} x^{-1} = y^{3/4}$. My ...
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### How to efficiently compute the coefficients in a bi-binomial expansion?

Is there a computationally efficient way of calculating the coefficients of the polynomial expansion of expressions like $(1+x^a)^m(1+x^b)^n$ for arbitrary positive integers $m,n,a,b$ (and especially ...
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### pow$(X,Y)$ $>$ pow$(Y,X)$, if $X<Y$.

How can we proof following? if $X < Y$, then: $X^{Y} > Y^{X}$ , Where X, and Y are integers. Also $X,Y > 1$. Except a special case $2^{3} < 3^{2}$. I think for other ...
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### What is the relationship between these expression?

Moderator Note: This is a Project Euler question If ...
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### Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime

My math teacher gave us problems to work on proofs, but this problem has been driving me crazy. I tried to factor or find patterns in the numbers and all I can come up with is that for $n > 0$, the ...
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### What's the intuition behind non-integer exponents/powers

Consider some $a \in \mathbb{R}$ and $x \in \mathbb{R}\backslash \mathbb{N}$. Is there some intuition to be had for the number $a^x$? For example the intuition of $a^2$ is obvious; it's $a*a$ which ...