In an isosceles triangle PQR where PQ = PR, and M is a midpoint of QR, how do you prove that line segment PM bisects angle QPR?
PQ=PR is givenQM=MR by definition of midpointPM=PM by reflexive propertyTriangle PQM is congruent to triangle PRM by SSS congruence.Angles MPQ and MPR are congruent because they're corresponding angles of two congruent triangles.PM bisects angle PQR by definition of angle bisector.
Is that possible to break the while(1); loop?
Since while is a keyword in almost all programming languages unfortunately it is not possible to break a while(1); loop and continue to next statement execution unless you write your own compiler with a new while definition and rules. But, if it is the last statement in a program then easily you can kill the process:Linux:How To Use ps, kill, and nice to Manage Processes in LinuxWindows:TaskkillLast but not least:Remove RAM or shutdown your system
Two spherical balls of 2kg & 3 kg masses are moving towards each other with velocities of 6m/s & 4m/s respectively. What will be the velocity of smaller ball after collision if velocity of 3kg mass is 3m/s?
Edit:Since the direction of the the balls aren't mentioned, let's assume they move in a straight line and against each other (opposite directions)And also, lest assume there are no losses involved. In reality, when two balls collide, there are energy losses in the form of friction, sound, deformation of the balls, etc. But for simplicity, let's assume, it's a perfect elastic collision.According to law of conservation of momentum, the total momentum of the system is always conserved, i.e., the sum of momentums of the balls before collision is equal to the sum of momentums of the balls after collision.Momentum is the product of mass of the ball and the velocity of the balls. Let m denote the mass of the balls. Let u and v be the initial and final velocities of the balls. Let subscripts 1 and 2 denote the first and the second ball.According to the law of conservation of momentum,[math]m_1u_1 - m_2u_2 = m_1v_1 - m_2v_2[/math][math]2 × 6 - 3 × 4 = 2 × v_1 - 3 × 3[/math][math]12 - 12 = 2v_1 - 9[/math][math]2v_1 = 9[/math][math]v_1 = 4.5[/math]The velocity of the smaller ball after collision will me 4.5 m/s. But in the opposite direction of the first body.
In triangle PQR angle PQR =90 degree and PR = 10 cm if S is the midpoint of PR then the length of QS is?
[math]S[/math] is the midpoint of the hypotenuse [math]PR.[/math]With [math]S[/math] as centre, draw a circle with radius equal to [math]PS.[/math] Obviously, this circle will pass through points [math]P[/math] and [math]R.[/math][math]\angle PQR = 90^o.[/math][math]\Rightarrow \quad[/math] The circle will also pass through point [math]Q[/math] since [math]PR[/math] is a diameter of the circle and the measure of the angle subtended by the diameter on the circle is equal to [math]90^o.[/math][math]\Rightarrow \qquad SQ[/math] is a radius of the circle.[math]\Rightarrow \qquad QS = PS = 5[/math] cm.
I have an exam in 3 hours but havent slept, should I sleep or keep studying?
It depends on syllabi that you have left for exam.During my JEE days I used to follow a technique called sleep management which helps you to cover 3 hour sleep in 15 minutes.Sit in a comfortable position on a chairClose your eyes and focus on your breathe(breath in and out and focus on if )Now repeat it to yourself slowly that I am sleeping for 5 minutes (repeat till the mind is fully convinced that you are actually sleeping )Gradually increase your time duration to 8 minutes,15 minutes,25 minutes ,45 minutes,1 hour ,2 hour and 3 hour respectivelySo when you wake up you will wake up with the same energy as if you really slept for 3 hoursP.s it is a scientifically proven technique.but don't use it regularly. It all depends on your subconscious ,whatever you repeat to your mind when it is in alpha state it tends to accept it.
Gate 2017: Should I prepare all subjects simultaneously or complete one subject then move to another subject?
A2AIt’s better to prepare all or at least some subjects simultaneously. You can divide all the subjects into certain number of blocks and prepare all the subjects in 1 such block simultaneously. Then move on to the next such block. Do not isolate any subject for a long time. If you are studying the subjects from one block, you can solve 1–2 questions daily from any subject from a different previously read block. In this way, you can keep in touch with most of the subjects simultaneously.
How is PNAS one of the top three journals? There are many journals with impact factors much higher than that of PNAS, so how is it considered one of the "big three" (along with Science and Nature) journals?
PNAS has always occupied a weird place in the scientific publishing landscape because of its relationship with the National Academy of Sciences of the United States. I'd hesitate to call it a top three journal (in my field, Cell definitely occupies that spot); it's probably more appropriately slotted with the second-tier generalist journals (like Genes and Development and EMBO J) because nobody quite knows what to think about it. PNAS has a weird publication process because it is one of the few journals that allows multiple forms of direct communication. National Academy members have the right to submit a paper directly and bypass a few of the early layers of the review process (in the past, they also got to pick their managing editor and have a lot of influence on who reviewed their papers), which means that PNAS has a reputation for considering reputation just as much as substance (whether or not it's entirely deserved is another matter.) A lot of big names publish in PNAS because of this privilege, which probably lends it some of its perceived prestige. PNAS has reformed their publication process for standard submissions, and it's now one of the most onerous in scientific publishing. A manuscript now has to get through three layers of review before being accepted: an editorial board member has to be interested in it, one or more NAS members have to think the paper describes a finding of "significant importance", and then the manuscript has to go through the standard anonymous peer-review process. Papers that make it through this route have definitely cleared more scientific hurdles than most, which might mean they're more solid science or describe more interesting findings (maybe). P.S. Impact factors are garbage. Want to know if a paper is good? Read it yourself and decide. Want to know if a journal is "good"? Read the articles it publishes and decide. If you're not equipped to evaluate primary literature, you're probably not the intended audience for it.
How powerful is Russia?
Apart from their soviet era, let us see the recent war strategy of Russia in Syria.After a thorough war plan & taking the permission from all intermediate countries’ ATC (except Turkey), He did this :He placed the warship in the Caspian sea equipped with Cruise missile whose specification was unknown to the world. Now, most of the country cant ever imagine of air strike done far from 1400 km! and that too with so much accuracy and consistency. This left the neighboring NATO countries of Russia in worry.Footage released by Russian army, RT news & CNN :This was the most lethal bunker buster ‘thermobaric’ bomb: (looks like nuke)You can see more of such photos on many sites. But, its really a devastating & disturbing too as many civilians causalities were also there. Terrorists now realizes what a grave warning from Putin really meant.So what makes it powerful?Firstly, no country in the world has enough spine to execute this type of air strike when someone like USA is against you.Secondly, you need a rock sediment ed confidence when a guided cruise missile fly above the most conflicted area in the world, i.e, middle east!Thirdly, it needs a proper backup to attack an area, which is surrounded by the powerful NATO military bases.Indirectly, Putin showed to world, that Soviet super power is still alive or coming soon. For more, see: https://www.rt.com/news/317864-r...Weakness of being powerfulWar needs money and lives. Sure, this show off of power needed huge of them.After those strikes, Russia’s Ruble and Oils are not favoring the country’s economy. Businesses are at all time low.PS: USA are much superior in military exercises and equipment than Russia in many attributes. They are #1 and #2. And we get to know only those things, what they want us to know. Much of the things are classified. But you should never tease a country who have enough superiority in Chess, Space & Hacks!