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Problem on Apparent Height of Postage Stamp Underneath Paperweight

I believe you made a mistake at \$tan angle NGI fracINd Rightarrow IN d tan 60\$. It should be \$angle NGI 30\$ and not \$angle NGI 60\$.

If you use \$angle NGI 30\$, you get \$d - 1.5 fracd tan 30tan(arcsinfrac 3sin 302)approx 0.5 d \$ and \$dapprox 3.1 cm\$.

â€¢ Related Questions

I have done that before vs I have done that

All of these are correct. They can replace each other easily, and in the same conversation. If you want to stress that fact that you only did something once then throw 'once' in there.

"Yes, I have done that once before." or "Yes, I've lived there once before."

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Creating a new cipher! closed

Issues:So, this scheme has some pretty major weaknesses. I would say it's fatally flawed, and is easily breakable. There might be some really, really specific letter->number mappings that make the simple attacks not work right, but I strongly suspect that even those are easy to break.

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Assuming that \$gcd(a,b)1\$, show that \$gcd(ab,a^2b^2)1\$ or \$2\$.

Let \$p\$ be a prime divisor of \$d\$. If \$p mid a\$ then as it divides \$ab\$ we have that it divides \$ab-ab\$. But this means that \$p1\$, as \$gcd(a,b) 1\$Now similarly we can consider the cases \$p mid b\$ or \$p mid 2\$

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Differential Equation involving Polynomial Discriminants

I would suggest computing \$f(xc) -f(x) 0\$ as a Taylor series, so that the first coefficient, linear in \$c\$ will contain only first derivatives, and vanish. You might want to use the definition of the discriminant in terms of roots, or otherwise, also. Hope it helps

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can vs be able to in present

Long hours and unsociable shifts are not able to act on their own in taking their toll on health, relationships and family life.They require a person subject to health, relationships and family life. Therefore the most logical answer is C. A and D are non-relevant or opinionated

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Prove that \$U-f(U)\$ is an open set.

Set \$\$overlineUx|d(x,x_0)leq1.\$\$Then \$overlineU\$ is closed in \$X\$ and hence compact. Since \$f\$ is continuous, \$f(overlineU)\$ is again compact, and in particular closed. By assumption we have\$\$Usetminus f(U)Usetminus f(overlineU),\$\$and we're done.

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Interfacing microSD with LPC1769 Board

Check - it's a software stack for LPC1343, but is has a nice FAT / SD card library that is abstract enough, you shuld be able to copy and use it quite easily, all you have to do is to rewrite SPI calls

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How to properly simplify and trig substitute this integral?

If \$x 5sintheta\$ then \$dx 5costheta, dtheta.\$ That was neglected.You also replaced \$sqrt25 - (5sintheta)^2\$ with \$5 - 5sintheta.\$ That is also not correct. Notice that, for example,

\$\$

sqrt5^2 - 3^3 sqrt25-9 sqrt16 4 ne 5-3, text so sqrt5^2-3^2 text differs from 5-3.

\$\$

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Product of Divisors of some \$n\$ proof

Let the set of divisors of \$n\$ be \$s(n)x_1,...,x_d(n).\$ Then \$\$s(n)n/x_1,...,n/x_d(n).\$\$ \$\$text Thereforequad prod_xin s(n)xprod_xin s(n)n/xn^d(n)/prod_xin s(n)x.\$\$

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Does reply use the same path from which the ping has been sent?

The ping echo request and its reply follow the current routes on the hosts and routers they cross. So, it's definitely possible that each follows a different route - depending on what exactly you're trying to achieve, using asymmetric routing may be seen as bad practice by some

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Choosing between two programmers: experience vs. passion closed

I would say it depends on the rest of the team:if you have a lot of experienced programmers already, then pick the passionateif, on the other hand, you have only one or two experienced programmers plus many students/cheap-labor-with-little-experience-but-that-don't-cost-much, then the experienced one will be more useful

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Effective Mass structure outside first band minimum

The term as you describe it is the effective mass of a carrier in that band and at that k-point. A constant effective mass resulting in a parabolic dispersion is just an approximation. If it's a good or good enough approximation depends on what you need to do.

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Invertibility of Time-Dependent Fourier Transform

I have the 2nd edition, and there the case \$m0\$ is considered, so the equation reads (Eq. \$(10.21)\$ on p. 716)\$\$xn frac12pi w0int_0^2pi Xn, lambda)dlambda\$\$(which of course assumes \$w0neq 0\$). This makes sense because \$e^jlambda m\$ equals \$1\$ for \$m0\$.

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Let (X, d) be a metric space and let A be a subset of X. Prove that A is closed if and only if Fr(A) \$subseteq\$ A.

Suppose that \$Fr(A) subseteq A\$ and let \$(a_n)\$ be a convergent sequence in \$A\$ with limit \$a\$. We have to show that \$a in A\$.Case 1: \$a in A\$. Then we are done.Case 2: \$a notin A\$. Then \$a in Fr(A)\$. Hence \$a in A\$.

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Are there long arithmetic progressions non-coprime with the given number?

Well take

\$\$qkdnq(d-1)nkdn(d-1)ndnkdd(kn)\$\$

Note \$n notmid kd\$,I guess this is the solution you could try replacing those numbers and checking if it adds up(I currently got no time to do so)

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How to mount a windows administrative share on linux via SMB

I would add a line for that purpose to /etc/fstab file:After saving changes to this file, mount the file system by means of the command mount -a.In this case the option rw allows the directory to be read-write, otherwise it should have the option ro

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Polar coordinates in simple integral

It's just a matter of simply checking that we get the desired result:\$\$intint_D dx,dystackrel?int_0^1int_0^2pir,dtheta,dr2piint_0^1r,drpi\$\$The reason why we get the correct result was already stated by Cocopuffs in his comment above

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Keyboard shortcut to location bar without selecting all text

There is no shortcut for this yet if I know correctly but you can do it by using AutoHotKey script very easily. First download the AHK for Windows and install it then run the following script.Here CtrlM will focus to the address bar without selecting url.

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UML Sequence Diagram with PGF and Tikz produces No shape named inst1 is known

I think you're using a somewhat old version from pgf-umlsd.sty which does not support empty diagrams. Version 0.6 should fix this (and does that in my case) and TeX Live 2011 uses 0.

5 as far as I could see.

com/p/pgf-umlsd.

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Using Rsync to backup to an external drive

It really depends on whether you're running databases or not. Rsync will grab a snapshot of every file, and ignore any intervening writes. If you want to back up a database, you should look at setting up an ignore filter and running DB dump tools before the rsync.

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conitional probability-probability this given this

\$\$Pleft(Dmid Fright)Pleft(Fmid Dright)timesfracPleft(Dright)Pleft(Fright)\$\$ and:\$\$Pleft(Fright)Pleft(Fmid Dright)Pleft(Dright)dotsPleft(Fmid Svcright)Pleft(Svcright)\$\$

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How to interpret this output from MegaCli? duplicate

Your answer appears to start at page 13 of this SNIA specification "Mirrored array"Secondary-3 "Spanned 0x03 A combination of stripping and concatenations involving Basic VDs of different sizes."RAID Level Qualifier-0 "Mirroring across two extents"

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A small doubt on calculation

You get two equations in two unknowns \$a,d\$; solve them to find \$d\$. Since we only want to find \$d\$, we can equate the coefficient of \$a\$ by multiplying the first equation by \$q\$, the second by \$p\$, and subtracting to get a linear equation for \$d\$

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derivative of limited summation

HINT You can do termwise differentiation which is valid within the annulus of convergence or if you do not want a sum as an answer you can for example use the factorization \$\$(1xcdots x^n)(x-1) x^n1-1\$\$ followed by differentiating the function this gives you

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Is this gradient an isomorphism on its range?

Summarizing the hints by @5pm, we can state:Since the norm in \$H^1(Omega)/mathbbR\$ is equivalent to the \$L^2\$-norm of the gradient, one has that the \$nabla\$ as defined above is bounded from below. Thus, \$nabla\$ is injective and, as it is linear, also closed.

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Format Date (25 Jul) using Javascript Object Model

If the format does not vary from what you presented, you could use split, and access the desired elements in array notation.You lose any date properties by doing this, so if the other elements of the date object are important you're probably better off with moment.js

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Strange 'My Documents' Folder behavior after aborted upgrade to Windows Vista

From my understanding, when Windows is looking for a user's folder, it goes under 'Document and Settings' and then looks for the logged in computer user's directory. It seems that your installation of Windows is looking directly at the folder rather than thinking it's under 'Document and Settings'

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Appium: Same code is working Sometimes and failing Sometimes

Agree - wait should be introduce before any action. Best practices will be to use implicit wait Each time it wont happen that element will be ClickableI'll suggest to use "ExpectedConditions.visibility" instead of "ExpectedConditions.

elementToBeClickable"This solution will work for each and every scenario irrespective of action

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Complex integration - How to calculate this one?

Draw a multi-keyhole contour \$Gamma\$ around each of the zeroes of \$f\$ so that \$Gamma\$ circles \$D(0,1)\$ once. \$f'(z)g(z)/f(z)\$ is holomorphic inside \$Gamma\$, so the integral is zero. Then calculate the residue of \$f' g/f\$ at each of the zeroes of \$f\$.

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Converting polar equation into cartesian equation to obtain derivatives

\$\$x r costheta Rightarrow fracdxd theta frac partial xpartial r fracdrdtheta frac partial xpartial theta

costheta (2 sintheta) -r sintheta

2costheta sintheta - (1-2 costheta) sintheta\$\$Do the same for \$y\$.

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Help with the proof of Max Noether's Residue Theorem from Fulton's book

The equality holds because the divisors are defined in terms of the local rings of the curve \$C\$. Since \$F\$ is the form defining \$C\$, its residue is zero in the coordinate ring and the local rings of the curve. Hence,\$\$

textdiv(F'F G'H') textdiv(G'H')

\$\$

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Problem with 2nd degree in minor scale

Literal transposition from major to minor doesn't work very well. You have discovered one of the reasons.You seem to think minor' just means 'natural minor'. There's the Harmonic and Melodic minor scales as well. Those non-flattened 6ths and 7ths are very useful options when attempting functional harmony

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Remote Power On and IPMI Poweredge 2950

If you're running vSphere 5 then this will probably help. Installing DOMSA using VUM (VMware Update Manager) is by far the easiest, but if you don't have VUM then one of the other methods should work. pdf.

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Given sequence of harmonic functions converges uniformly on compact subsets

Consider first the case of a disk \$B\$ containing \$z_0\$. Then \$u_n textRe(f_n)\$ where \$f_n\$ is analytic on \$B\$. By Montel's theorem the \$f_n\$ form a normal family. What can you say about the limit of a subsequence that converges on \$B\$?

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One has

\$\$r_a(A)leq left(left|sum_fin mathbfF(n,d) mathbfA_f^*mathbfA_fright|^frac12n right),\$\$

for all \$nin mathbbN^*\$.If \$n1\$, then

\$\$r_a(A)leq left|displaystylesum_k1^dA_k^* A_k right|^1/2||A||.\$\$

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Fermat's Little Theorem: Proving an integer exists which satisfies the following criteria mod \$5\$ duplicate

\$mnotequiv0bmod5\$, since otherwise \$dequiv0bmod5\$, contradicting the given facts. Hence, since \$5\$ is a prime number, \$m\$ has an inverse modulo \$5\$ let \$n\$ be this inverse. Multiplying \$am^3bm^2cmdequiv0bmod5\$ by \$n^3\$, we can easily verify that \$n\$ satisfies the final congruence.

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PHP phantom cron job

Debian's cron, like many other modern variants, read jobs in files under directories called /etc/cron.d, /etc/cron.hourly, etc., in addition to the traditional /etc/crontab. In particular, the job you see comes from /etc/cron.

d/php5 which is installed by the php5-common package

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Proving that a unit disc is open in \$mathbfR^2\$.

Yes, it is correct. And, since you always have \$R_(a,b)subset D\$, then\$\$Dbigcup_(a,b)in Dbigl(a,b)bigrsubsetbigcup_(a,b)in DR_(a,b)subset D\$\$and therefore \$bigcup_(a,b)in DR_(a,b)D\$ indeed

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Invariant Subspaces of a representation

Your own characterization for an invariant subspace is more correct than the one you quoted. Such a projection \$P\$ only exists if there is another invariant subspace \$W'\$ which is complementary to \$W\$ (where \$W' ker P\$).In characteristic zero for finite groups, such a \$W'\$ always exists.

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Do I need a comma before particularly?

This sentence had raised a question in my mind. Vitamin D has what property against metabolic, neoplastic and immune disorders..... I think it is better to be specific and clear. May be this sentence can be better rephrased as "Vitamin D has prophylactic/preventive/therapeuti effect against metabolic......"

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