What is the smallest value of n such that an algorithm running at 100*n^2 operates faster than 2^n ? [How to figure out without brute force]

Okay, so I needed to find the smallest value of n such that algorithm 100*n^2 is faster than 2^n.

[what I have tried]

So, I instantly thought ‘0’. But, I then realized it can’t be 0, 0 implies that there are no digits being entered in the algorithm, it also implies that the program does not run or terminate.

I typed in 2^32 and got a number over 4 billion. Okay, this is good, I’m finding numbers that have 100*n^2 being faster than 2^n.

I halved that, n = 20.

I kept inserting values counting down until I got to n = 15.

I also counted up from n = 10, the answer is undoubtedly n = 15, but I have a problem . . . .I solved this using brute force and that isn’t good. What if I was given a bigger number and a larger bredth of numbers?

[What I need]

I need a way of finding the value instantaneously by only doing the math, I tried using logarithms, but my answer was wrong, my knowledge of logs is a bit rusty and I need a little help.

Think of it as a student trying to solve a question on an SAT or having a timer for a test.

Number of ways painting graph in two colors, such that two nodes of same color are linked by edge

We are given undirected graph of $ N$ nodes and $ M$ edges, we want to count the number of possible ways to paint this graph in $ 2$ colors such that for each two nodes having the same color, there must be an edge between them.

I tried some examples on paper and I always got numbers of the form $ 2^x$ , however I couldn’t see a valid way to find such $ x$ or I couldn’t prove why this is the case.

Does this problem become easier if we are given directed acyclic graph instead of undirected one?

apt-get upgrade fails with “Fatal: open /boot/vmlinuz-4.18.0-20-generic: No such file or directory”

This happens on all apt-get install and apt-get upgrade. Anyone knows what’s going on?

biran0079@ubunduck:~$   sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Calculating upgrade... Done The following packages were automatically installed and are no longer required:   libllvm7 shim Use 'sudo apt autoremove' to remove them. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 5 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue? [Y/n] y Setting up initramfs-tools (0.130ubuntu3.8) ... update-initramfs: deferring update (trigger activated) Setting up linux-image-4.18.0-25-generic (4.18.0-25.26~18.04.1) ... Setting up linux-firmware (1.173.8) ... update-initramfs: Generating /boot/initrd.img-4.18.0-25-generic Warning: /dev/disk/by-id/ata-ST1000DM003-1CH162_S1DGBMYR is not on the first disk Fatal: open /boot/vmlinuz-4.18.0-20-generic: No such file or directory run-parts: /etc/initramfs/post-update.d//runlilo exited with return code 1 dpkg: error processing package linux-firmware (--configure):  installed linux-firmware package post-installation script subprocess returned error exit status 1 dpkg: dependency problems prevent configuration of linux-image-generic-hwe-18.04:  linux-image-generic-hwe-18.04 depends on linux-firmware; however:   Package linux-firmware is not configured yet.  dpkg: error processing package linux-image-generic-hwe-18.04 (--configure):  dependency problems - leaving unconfigured dpkg: dependency problems prevent configuration of linux-generic-hwe-18.04:  linux-generic-hwe-18.04 depends on linux-image-generic-hwe-18.04 (= 4.18.0.25.74); however:   Package linux-image-generic-hwe-18.04 is not configured yet.  dpkg: error processing package linux-generic-hwe-18.04 (--configure):  dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                                                                                                           No apport report written because the error message indicates its a followup error from a previous failure.                                                                                                                                                                                                                     Processing triggers for initramfs-tools (0.130ubuntu3.8) ... update-initramfs: Generating /boot/initrd.img-4.18.0-25-generic Warning: /dev/disk/by-id/ata-ST1000DM003-1CH162_S1DGBMYR is not on the first disk Fatal: open /boot/vmlinuz-4.18.0-20-generic: No such file or directory run-parts: /etc/initramfs/post-update.d//runlilo exited with return code 1 dpkg: error processing package initramfs-tools (--configure):  installed initramfs-tools package post-installation script subprocess returned error exit status 1 No apport report written because MaxReports is reached already                                                               Processing triggers for linux-image-4.18.0-25-generic (4.18.0-25.26~18.04.1) ... /etc/kernel/postinst.d/initramfs-tools: update-initramfs: Generating /boot/initrd.img-4.18.0-25-generic /etc/kernel/postinst.d/zz-runlilo: Warning: /dev/disk/by-id/ata-ST1000DM003-1CH162_S1DGBMYR is not on the first disk Fatal: open /boot/vmlinuz-4.18.0-20-generic: No such file or directory run-parts: /etc/kernel/postinst.d/zz-runlilo exited with return code 1 dpkg: error processing package linux-image-4.18.0-25-generic (--configure):  installed linux-image-4.18.0-25-generic package post-installation script subprocess returned error exit status 1 No apport report written because MaxReports is reached already                                                               Errors were encountered while processing:  linux-firmware  linux-image-generic-hwe-18.04  linux-generic-hwe-18.04  initramfs-tools  linux-image-4.18.0-25-generic E: Sub-process /usr/bin/dpkg returned an error code (1)  

Why getData() and toArray() on collection have a different behaviour for EAVs tables such as Product?

 $  collection = $  this->productCollectionFactory->create();  $  collection->addAttributeToSelect('*'); 
  • collection->getData() -> returns only a few data (most of the main table until explicitly provided in addAttributeToSelect('my_attr_code').
  • collection->toArray() -> returns complete data.

This behaviour is same on the Flat tables, but why different on EAV table such as product?

Grub error: no such partition

I was recently dual booting my acer netbook to run ubuntu and windows 7, I ended up deleting the partition for ubuntu and came with the no such partition error. the matter got worse when I decided to wipe the hard drive using gparted live, wich still came up with the grub rescue error. all the other questions that were asked required some sort of operating system. since there is none, I don’t know what to do.

Is a 10th level transmuter considered a shapechanger for the purpose of effects such as Moonbeam?

Spells such as Moonbeam specifically affect creatures with the “Shapechanger” tag, such as lycanthropes. As per this previous question, the ability to change one’s shape through class features is not sufficient to be considered a shapechanger.

However, upon reaching the 10th level, transmutation specialist wizards literally receive the “Shapechanger” class feature, granting them the ability the polymorph themselves with greater ease. This feature’s description is obviously adapted for player characters, but is otherwise similar to the “shapechanger” feature found in the stat blocks of creatures with the shapechanger tag.

In this context, would possessing the “Shapechanger” feature through the wizard class mark you as a “shapechanger” for the purpose of spells such as Moonbeam?

Why can Complex Forms be threaded at such high levels?

There are a great many equivalencies between Resonance and Magic; many of their abilities are very similar both in fluff and mechanics. One difference that stands out is the limit at which their respective abilities can be used at.

Spellcasting

You must declare the Force at which to cast the spell… You can cast a spell at a Force up to twice your Magic rating. (emphasis mine)

Threading

When you thread a complex form, you choose a Level for the effect… You can choose a Level up to three times your Resonance rating. (again, emphasis mine)

I am well aware of the fact that the sourcebook is laden with typos and lazy editing.
Is that all this is, a typo, or is there a stated reason for this difference?

How could I make a Character use a device such as a magic sword after a teleport or dash?

First and foremost if you didn’t get it from the question this is talking about Mutants and Masterminds. and its a question about character building. Im not sure how to tell but I think its second edition. all I know its it isnt the one that splits Dex into three separate stats

I would like to know the appropriate Powers to make a character both Dash a set distance and attack with his magic sword which is a 3 point device As a regular equipment point sword doesnt have powers. or teleport and Use the magic sword.

the character also needs to be able to use the magic sword for normal non-teleport attacks and the Dash or teleport needs to be expandable to allow for the addition of other powers later such as a Explosion or trip