Say for example I take a 30 year mortgage and I make repayments fortnightly. How many repayments will I be making, will it be exactly 780? If so, how does one account for the extra days?
I just bought a house. Now I'm getting ads in the mail every day or two trying to get me to sign up to pay my mortgage bi-weekly (every two weeks) or weekly instead of monthly. In their words I could cut seven years and thousands of dollars off what I pay in long term. It seems like I would be paying the exact same amount of money, also.  I know "if something sounds too good to be true then probably it is". But I cannot figure out why in this case. What is the catch? Or is this something I should be signing up for ASAP?
Do gravitational lenses work on gravitational waves? Do gravitational lenses work on gravitational waves? Could we get an Einstein cross of gravity? How to evaluate the limit of this expression?  $$\lim_{x\to\infty} \frac{\sin^2\left( \sqrt{x+1}-\sqrt{x}\right)}{1-\cos^2\frac{1}{x}}$$  I managed to simplify the denominator into a sinus form by the Pythagorean formula, and also modified the argument of the sinus in the numerator by dividing with a conjugate which I think is necessary, into this final form:  $$\lim_{x\to\infty} \frac{\sin^2\left(\frac{1}{\sqrt{x+1}+\sqrt{x}}\right)}{\sin^2\frac{1}{x}}$$  And that's where I got stuck. So far I've tried to come up with some solution to eliminate the sinus from the denominator, without success. I'm sure the solution is pretty obvious but I don't quite know how to modify the trigonometric functions in this fashion, so any help would be most appreciated. The shellscript is very simple:  retroarch $* -c /tmp/retroarch/Data/retroarch/gambatte.cfg   ("retroarch" is another shellscript)  If the filename passed contains spaces it fails:  RetroArch [ERROR] :: Could not read ROM file. I'd like to install both Ubuntu 12.04 and Windows XP on a Dell laptop, and I was thinking about using a dual boot structure, and using the bulk of my hard drive as empty hard drive space to share files between the two operating systems (so choice of file system type is very important in this set-up).     The kind of partitioning structure I would like to use is  Partition 1 - Ubuntu 12.04 (root) (20GB)  Partition 2 - Ubuntu /home        (20GB)  Partition 3 : Free Space          (560GB)  Partition 4 : Windows XP          (35GB)  Partition 5 : SWAP                (3GB)  (Total Hardrive Capacity is ~640GB)    My question is; what is the best way to go about setting up this kind this system?   Should I install Windows XP first and setup the partitions, and then install Ubuntu which I believe will install the GRUB bootloader for OS booting choice   or   Do I install Ubuntu first, setting up the available partitions and then perform a WIndows install?  Please let me know if there is anything in this setup that I have left out and should know about, including things related to setting particular partitions as logical or primary, and whether the boot partition and the filesystem partition should actually be two separate partitions. Is a bivariate function that is a polynomial function with respect to each variable necessarily a bivariate polynomial? Lie algebra and tangent space at the identity are isomorphic Define the Lie algebra $\mathfrak{g}$ of a Lie group G to be the set of all left-invariant vector fields of $G$. I want to prove that   $$          f: \mathfrak{g} \rightarrow T_eG \\              X \mapsto X(e) $$ is a linear isomorphism.  The only thing that I have left to prove is surjectivity.Letting $v\in T_eG$, we set $X\in \mathcal{X}(G)$ such that $\forall x\in G,\,X(x)=L_{x_{*,e}}(v)$ (I still have to show that such an $X$ is indeed a vector field on $G$). We get that  $$ f(X)=X(e)=L_{e_{*,e}}(v)=v $$  where the last equality holds because  $$       L_{e_{*,e}}(v)f = v(f \circ L_e) = v(f \circ id_G) = v(f) $$ for any $f\in C^\infty(G)$. (I am thinking of the tangent vectors as derivations).  Now all we have left to do is prove that such an $X$ is left-invariant, and it is therefore an element of $\mathfrak{g}$, but I do not know how. I tried to prove that  $$            \forall f\in C^\infty(G),\, L_{{x}_*,y}(X(y))f=X(L_x(y))f $$ but with no success. Create Generic method constraining T to an Enum I'm building a function to extend the Enum.Parse concept that  Allows a default value to be parsed in case that an Enum value is not found Is case insensitive  So I wrote the following: public static T GetEnumFromString&lt;T&gt;(string value, T defaultValue) where T : Enum {     if (string.IsNullOrEmpty(value)) return defaultValue;     foreach (T item in Enum.GetValues(typeof(T)))     {         if (item.ToString().ToLower().Equals(value.Trim().ToLower())) return item;     }     return defaultValue; }  I am getting a Error Constraint cannot be special class System.Enum. Fair enough, but is there a workaround to allow a Generic Enum, or am I going to have to mimic the Parse function and pass a type as an attribute, which forces the ugly boxing requirement to your code. EDIT All suggestions below have been greatly appreciated, thanks. Have settled on (I've left the loop to maintain case insensitivity - I am using this when parsing XML) public static class EnumUtils {     public static T ParseEnum&lt;T&gt;(string value, T defaultValue) where T : struct, IConvertible     {         if (!typeof(T).IsEnum) throw new ArgumentException(&quot;T must be an enumerated type&quot;);         if (string.IsNullOrEmpty(value)) return defaultValue;          foreach (T item in Enum.GetValues(typeof(T)))         {             if (item.ToString().ToLower().Equals(value.Trim().ToLower())) return item;         }         return defaultValue;     } }  EDIT: (16th Feb 2015) Christopher Currens has posted  below, which is well worth a look, and an upvote. I will remove this edit if the solution bubbles further up the page. EDIT 2: (13th Apr 2021) As this has now been addressed, and supported, since C# 7.3, I have changed the accepted answer, though full perusal of the top answers is worth it for academic, and historical, interest :) Does time freeze at Absolute Zero? Time has many definitions per se, but the basic idea being it's "the measurement of change" so as we know, all matter looses it's ability of changing with the loss of kinetic energy. and the where it becomes zero is the absolute zero (−273.15°C). so my question would be, will time stop/freeze at Absolute zero? and does time get slow while reaching there? Concatenating two std::vectors JavaScript displaying a float to 2 decimal places "He acted strange(ly?)" E: The repository 'http//archive.canonical.com precise Release' is not signed When "Questions that may already have your answer" (similar questions) appear as a right column, it overflows and overlaps the footer.  (shown in the figure)        This happens on all SE network sites on which I have asked questions.  Also this happens to other columns also like "How to Format". I am trying to use the Alt+Right Click to select edge loops in Linux Mint but this shortcut doesn't work it is already used for Linux to reduce a window. I have checked the keyboard shortcut but it doesn't appear. What does "cpu MHz" field mean in the /proc/cpuinfo of a hyper-threading cpu? The CPU is a i7-3770@3.40GHz. It has 4 cores and each core has 2 threads. Here is the dmidecode output:  # dmidecode -t 4 # dmidecode 2.9 SMBIOS 2.7 present.  Handle 0x0042, DMI type 4, 42 bytes Processor Information     Socket Designation: SOCKET 0     Type: Central Processor     Family: &lt;OUT OF SPEC&gt;     Manufacturer: Intel(R) Corporation     ID: A9 06 03 00 FF FB EB BF     Version: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz     Voltage: 1.1 V     External Clock: 100 MHz     Max Speed: 3800 MHz     Current Speed: 3400 MHz     Status: Populated, Enabled     Upgrade: &lt;OUT OF SPEC&gt;     L1 Cache Handle: 0x003F     L2 Cache Handle: 0x003E     L3 Cache Handle: 0x0040     Serial Number: Not Specified     Asset Tag: Fill By OEM     Part Number: Fill By OEM     Core Count: 4     Core Enabled: 4     Thread Count: 8     Characteristics:         64-bit capable   It will be 8 logic core in a system, like what shows in /proc/cpuinfo. But can any one tell why the cpu MHz of a core is 1600MHz? I guess there is 2 threads in a core, so a hw thread freq may be about the half of the core's? How this number is calculated?  processor   : 7 vendor_id   : GenuineIntel cpu family  : 6 model       : 58 model name  : Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz stepping    : 9 cpu MHz     : 1600.000 cache size  : 8192 KB physical id : 0 siblings    : 8 core id     : 3 cpu cores   : 4 apicid      : 7 initial apicid  : 7 fpu     : yes fpu_exception   : yes cpuid level : 13 wp      : yes flags       : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx rdtscp lm constant_tsc arch_perfmon pebs bts rep_good xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat tpr_shadow vnmi flexpriority ept vpid bogomips    : 7013.49 clflush size    : 64 cache_alignment : 64 address sizes   : 36 bits physical, 48 bits virtual power management:   Also, here is the output of lshw and lscpu command. There are also 1600MHz mentioned.   lshw info:  #lshw -class processor   *-cpu                           description: CPU        product: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz        vendor: Intel Corp.        physical id: 42        bus info: cpu@0        version: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz        slot: SOCKET 0        size: 1600MHz        capacity: 3800MHz        width: 64 bits        clock: 100MHz        capabilities: fpu fpu_exception wp vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx rdtscp x86-64 constant_tsc arch_perfmon pebs bts rep_good xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat tpr_shadow vnmi flexpriority ept vpid cpufreq   lscpu info:  #lscpu Architecture:          x86_64 CPU op-mode(s):        32-bit, 64-bit CPU(s):                8 Thread(s) per core:    2 Core(s) per socket:    4 CPU socket(s):         1 NUMA node(s):          1 Vendor ID:             GenuineIntel CPU family:            6 Model:                 58 Stepping:              9 CPU MHz:               1600.000 Virtualization:        VT-x L1d cache:             32K L1i cache:             32K L2 cache:              256K L3 cache:              8192K What does "isomorphic" mean in linear algebra? Why do I get "warning longer object length is not a multiple of shorter object length"? Why am I getting no power when I pedal? Yesterday when I was biking my mountain bike on level paved path, I would pedal but get no power to the wheel.  To use a car analogy, it was as if I had the clutch in and was apply gas.  It seemed to happen most often after I coasted and then went back to pedalling.  I would pedal and realize that no power was going to the wheel.  The chain was definitely on the sprockets and moving. I could change gears no problem while I had no power.  Sometimes stopping the bike and starting again would work, or just trying again.  Needless to say, I'm taking it in as I'm not mechanically inclined, but I'm hoping to learn something.  Perhaps a link to a site that explains the problem?  So my questions.   What is going on?  I have heard of something called the "freehub".  I really don't know how bikes work though, so I'm hoping for an explanation of how one can pedal and give power to the wheel and then stop pedalling and the wheel just keeps moving (without the pedals moving).   If you are on a ride, is there any emergency adjustment to make?   For what it's worth, it's an old bike.  Circa 1993 Performance Mtn Bike.  So it's not too surprising that it's falling apart.  I haven't used it a whole lot, and have tried to wash and oil it, but I probably haven't taken the care that a biking aficionado would.  Also, besides losing power after coasting, one time I was pedaling and suddenly the pedals weren't powering the wheel.  I almost went over the handlebars!  So, I definitely want to get it fixed.  I'd just like to know a little bit about what is going on.  Thanks,  Dave.  Bonus question:  If there is enough info to make a diagnosis and you have ideas on costs to fix, perhaps you could comment on whether it's worth fixing.  Like I said, it's circa 1993 and cost about $450 then.  No shocks or anything.  Just 21 speed Mtn. Bike. Can Git hook scripts be managed along with the repository? We'd like to make a few basic hook scripts that we can all share -- for things like pre-formatting commit messages.  Git has hook scripts for that that are normally stored under &lt;project&gt;/.git/hooks/.  However, those scripts are not propagated when people do a clone and they are not version controlled.    Is there a good way to help everyone get the right hook scripts?  Can I just make those hook scripts point to version controlled scripts in my repo? Shipping Labels not received for round trip courier service for UK Visa using VFS Global I purchased the round-trip courier service through VFS Global. In the instructions, it states that you will receive in a separate email the shipping labels for this courier service. I receive Registration Details and Transaction Details only. No Shipping labels. I have called VFS Global in NY,NY and no human being access to ask questions, just an insane phone tree that does not answer my questions on how to get shipping labels that were never sent. I have called the British Consul in Atlanta and she could not answer my questions then transferred me to the same phone tree message that I receive through the British Consulate. I have sent emails to customercare@vfsglobal.com, info.vfsnewyork@vfsglobal.com, NYscanhub.escalate@vfsglobal.com, DLUKVInewyorksensitive@fco.gov.uk and I have received no response from anyone.  Frustrated. I do not know what to do. Please help me!!