What does (-2) ^x look like? How is this different from -(2) ^x?

If we are considering x in the set of real numbers, and want the expressions [math]f(x)=(-2)^x[/math] and [math]g(x)=-(2)^x[/math] to evaluate to a real number, then there is a great difference between these two expressions; specifically,

  • [math]f(x)=(-2)^x[/math] is defined for an infinite but relatively small subset of real numbers, while
  • [math]g(x)=-(2)^x[/math] is defined for all real numbers.

The reason for this difference is that when [math]a>0[/math], [math]a^x[/math] has domain [math]\mathbb{R}[/math]; [math]g(x)[/math] is just an ordinary exponential function (reflected across the x-axis). Meanwhile, when [math]a<0[/math], the expression [math]a^x[/math] only has a real (and unambig

How important is it for a newly-developed product to fit into a company's current portfolio of products and services?

My family has owned and operated a manufacturing business since 1963.

We started making chalk boards.

Then switched to making doors for tractor trailers in ‘73.

Then made the sides for above ground pools in ‘83

Then made commercial building materials in ‘89

Then added signage materials in ‘91

Then added a whole new way to make both sign and building materials in ‘96, which made the signage market rush our company – generating significant income, and radically changing that market. While introducing a “slow-to-gain-steam” motion in the building industry.

Today, we’re currently feeding off of that slow-to-boil building industry line (in it’s cash cow phase), and pivoting into something amazing, but I can’t share that information right now. Anyway, we primarily make Building and Signage materials today.

We’ve had to reinvent ourselves about once every 10 years. Each time we’ve re-invented ourselves, we’ve been forced to step away from our primary market, add new capabilities to our production systems, while gathering new knowledge to operate in that new industry.

Each time we change – is called a “pivot.”

Most pivots, at least for us, involved either a line addition (a branch off of our current production processes or products), a service addition (customers ask: Hey, can you do this for us too?), or an outright leap forward in technology.

Mostly, each of these changes has revolved around using the same equipment we have on our production floor – or adding new equipment to augment existing lines.

So – to answer your question, it is highly unlikely that a company will pivot from, say, making board games, to making something like, automobiles. Board Games and Cars are 2 separate companies, with two very different production lines, and have almost no overlap anywhere. But, a company that makes Board Games, might choose to slowly pivot into making electronic board games, simply by slowly introducing el

What should be my strategy for getting 250 in JEE Mains as well as 350 in BITSAT 2018? (I'm not preparing for JEE Advanced.)

JEE mains paper is given by central board. So you can answer the questions pretty well in case you are clear with the concepts. First of all make good hold on all the three subjects as only then you can cross 240 marks ( here good hold means you can atleast score 80 marks in each ). If you are having some what perfection in a subject then you can balance the marks with other subject.

According to me, if you will do ncert and some extra notes given by your coaching centre then you can easily score around 100 in chemistry. And prepare inorganic chemistry at your best level as they will give you instant marks without wasting time as they are just facts.

For maths all you need is practice, by only clearing concepts you cannot score good in maths but you should solve some questions and don't solve many questions but just repeat the questions that you have solved earlier. Also mark the conceptual mistakes that you made while solving them and make sure that you are cleared with that. For practice you can prefer book by S.K.Goyal ( solve section A for mains ) or can solve “Pearson guide to complete mathematics for Jee” by SL Loney. You can score around 80 in maths by clearing concepts and having a good practice for it.

For physics at mains level clear your concepts perfectly as physics is based fully on concepts and do not do a rigorous practice for physics ( here I doesn't mean to just work casually )work hard for physics but conceptually only. In physics you need to solve the variety of questions to gain marks, atleast you should know which type of questions can be framed from such concept and it is easy to predict that at mains level. For practice you can solve HCV or “complete physics for Jee main 2018” by Irodov.You can get around 80 in physics by putting a genuine effort.

First solve all your basic books i.e. textbook numericals. Also I recommend you to master your chemistry so you can balance it with physics or maths as chemistry is the easiest of all the three.

Same you can apply for bitsat as there is no need to do something extra except practice papers for bitsat.

Thank you..

My best wishes is with you..!!

Best of luck..!!

What are some great books to read on building a tough mindset?

There are many different aspects that go into achieving success. Talent will always play a part in it, however it is not as significant as you may think.

As the famous quote states “Hard work beats talent when talent doesn’t work hard.”

The human brain is the most powerful tool you can possibly possess. Are you training and using your brain to its full potential? These seven books will help you achieve the peak performance you’ll need to compete, today and in the future.

Newton declared, “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.”

In other words, if you are flying in the International Space Station and toss an apple out the window (come on, use your imagination), it will keep going in that same direction forever, unless something stops it (like a planet, gravity or alien life form).

Although Newton was talking about physics, little did he know he was also describing life.

People tend to move in the same direction as they always have unless some external force is applied. I don't know about you, but I don't want my life to be lived in a straight line. I want to change, to improve, to crush it.

A book is a powerful external force that can completely knock your life off its mundane straight line and change everything about who you are.

Mental toughness is staying strong in the face of struggle. It’s the ability to stay focused regardless of the hurdles that come your way. Now the question is how do we attain this so called mental toughness? This is where books on mental toughness comes into play. Like anything else in life, the more you work at something, the better you get at it. By reading books on developing mental toughness or mental strength you will be in a better position to reach new heights in whatever endeavours you are perusing.

Mindset: The New Psychology of Success

The book has a lot of great information that is as applicable to managers at high growth companies as it is to parents. The key takeaway for me is that highly capable people tend to be risk-avoiders because they are afraid of failure. They get so used to being praised for their achievements that they end up not pushing themselves to their full potential for fear of looking dumb. As a parent (or a manager), the book recommends praising effort, not accomplishment, and creating an environment that encourages risk-taking and celebrates failure.

The Art of Mental Training: A Guide to Performance Excellence

From the offset it is very clear that the author of this book is passionate about his writing. The Art of Mental Training shows us all the different methods and techniques we can use to eliminate the negative mentality that is constantly going through our minds, and push our mind into a state of focus. This book is packed with advice and tips that can be implemented. So if you need to know how to be mentally strong then you should definitely consider this book.

Unbeatable Mind: Forge Resiliency and Mental Toughness to Succeed at an Elite Level

This book has the potential to change your life, it’s useful for anyone who wishes to develop themselves in a positive way. This book has exercises and few visual examples that talk about techniques you can use to improve both your inner and outer performance. When it comes to mental toughness books, this book is certainly a must read.

The Champion’s Mind: How Great Athletes Think, Train, and Thrive

Success isn’t simply about raw ability, the mental side of the equation is just as important. The author Jim Afremow understands this and has filled this book with great advice, perspectives and lessons. This book is a must read for coaches and athletes of all ages who want to improve their performance in any sport. But do keep in mind you don’t have to necessarily be an athlete to enjoy the benefits of this book, the lessons on personal development and mental toughness can be transferred into any other aspect of your life.

What to Say When you talk To Yourself

This book is a classic and is one of the best in the field of self-help. What this book tries to do is to teach us that our thoughts define who we are. The book is packed full of different methods that can be used to eliminate unwanted and unhelpful thinking patterns, and to replace those thoughts with ones that will lead us towards success.

Executive Toughness: The Mental-Training Program to Increase Your Leadership Performance

This book teaches us that developing mental toughness will not only make us good at what we do, but it can also help us reach new heights in our field. The author, Dr Jason Selk, is a “mental toughness” coach and he uses his vast knowledge and experience to teach and engage us in this book. The principles taught in this book have an abundance of value and will certainly help anyone who wants to achieve their personal goals in life.

Thinking, Fast and Slow

This book is amazing. It helps to understand the difference between the way you make quick decisions, versus considered decisions—it takes different mechanisms in the brain. Understanding which you're doing at any given time can have a profound impact on what you ultimately decide.

Please realize that the list above is completely subjective. I can only evaluate these books based on how I have experienced them. When it comes to philosophy just as much as spirituality, our first glances at ancient truths will hit us harder than our third or our fifty-third. There are books I’ve read recently which I think are nice, but they haven’t made the same emotional impact on me as they perhaps would have if I’d read them years ago. For that reason, this list is less a reflection of the books’ value as it is a reflection of my own personal relationship with each book (and my relationship with the time and place I read it). Take this with a huge grain of salt.

By reading books on mental toughness, you can develop yourself to become more resilient, emotionally. Having mental strength will push you to go further and harder. It will also keep your confidence high when things aren’t going all that well. Here are 5 books on mental toughness that will help you.

The English language has a lot of antonyms that look like each other, like dawn/dusk. Is there a name for that? Where can I find a list?

“Dawn” and “dusk” don’t look like each other, other than beginning with the letter “d” and having four letters. I think in order to have any chance of finding a list, one would need to define “look like each other.” Does it mean “begin with the same letter” or “begin with the same letter and are spelled with the same number of letters” or something else? “Naughty” and “nice” are sort of antonyms and begin with the same letter, but I wouldn’t say they otherwise resemble each other.

Word pairs with the same root noun suffixed with “ful” and “less” tend to be antonyms.

If the world before was covered by water, then where did we come from?

Current best theory explains that two (or perhaps three) protoplanets collided to form both the Earth and Moon. (The Moon formed mostly from light Crust, some heavier Mantle, and nearly zero iron Core).

It is important to note that the Crust floats on the Mantle.

It is reasonable to expect that Tectonic activity on both protoplanets was minimal before the collision, and abruptly higher on Earth after.

Furthermore, the volume of Earth was abruptly higher; fracturing the remaining Crust and separating the fragments with much heavier Mantle. When water condensed out of the superheated atmosphere, it covered the Mantle lowlands, forming oceans.

The collision turned the potential energy of falling bodies into concentrated intense velocity or else into heat. The two distorted Cores would co-orbit and exchange energy stirring the Mantle, but the remaining angular velocity would be conserved as they combined, resulting in a rare high rate of Core spin and magnetic field. The Earth was abruptly spinning faster, from the inside out.

The result is a turbulent spinning Mantle contaminated with iron, ores of every type, (including heavy radioactive ores) and light Crust. Some tiny fraction of this ended up staying on top of the Crust.

The protoplanets may, or may not, have had Mantle lowlands, but if so, they would be a modest fraction of the surface – unlike Earth.

It is impossible to know if any continental Crust projected above their oceans, but certainly there would have been volcanic islands.

What are the best places to visit on a day-long trip around Tbilisi?

Tbilisi is a fantastic city to visit, and you can do a lot in one-day.

We will start this day-long trip from Liberty Square in central Tbilisi. You can get here fairly easily via the Tbilisi metro for 0.5 Lari (~ 0.25 USD) .

In Liberty Square, you will find a large monument of St George slaying the dragon. During Soviet times, Lenin replaced St George here (and was thus referred to as Lenin Square). St George is the patron saint of Georgia, and most Georgian Orthodox Churches will have a painting of St George. Look out for this in the churches you visit.

From Liberty Square walk along Kote Afkhazi towards Sioni Cathedral. On your way, you can see other Catholic and Orthodox churches. Have some fun in trying to find differences between the two types of churches. The Sioni Cathedral is another fine example of a Georgian Orthodox church with beautiful interiors.

[Image Courtesy: http://tasteway.pl]

If you head incorrectly along Rustaveli Avenue, do not worry. You can catch the number of statues lined up along Rustaveli, and also the Old Parliament Building.

[Image Courtesy: Georgia About]

On your way to Sioni or anywhere around Sioni, you will find numerous restaurants of varying budgets. Here you can taste some traditional Georgian dishes of Khinkali and Khachapuri.

From Sioni, walk towards the Peace Bridge that crosses the Mtkvari river. As you cross the bridge, look behind you to see the Kartlis Deda (Mother of Georgia) statue. (You will be heading towards it soon).

[Image courtesy : World for Travel]

Once you cross the Peace Bridge, you should be able to see the Cable-car station. You can take the cable-car up (or walk up) towards Narikala Fortress and Kartlis Deda. You will get a good view of Tbilisi and the Trinity Cathedral from up here.

When you reach the top, see Kartlis Deda and the old fort walls. Kartlis Deda which is viewable from different parts of old Tbilisi, holds a wine-bowl in one hand, and a sword in the other – the former to welcome friends, and the latter to warn the enemies.

[Image courtesy: ge.igotoworld]

On your way down from Narikala, you will run into the famous Sulphur baths of Tbilisi. Enjoy a quick shower here as there is still a lot to do. Note that these baths aren’t a touristy thing (even locals visit these baths).

Next, cross the Mtkvari river again and walk towards the Trinity Cathedra (Sameba). This is about a 30–40 minute walk. Sameba is the largest cathedral in Georgia, and you will be amazed by its grandiose.

[Image courtesy: atlantaserbs.com]

From Sameba, we will head to Mtskheta located 20kms north of Tbilisi. Mtskheta is one of the oldest cities in Georiga and is considered to be the birthplace of Christianity in Georgia.

To head to Mtskheta, walk towards Avlabari metro. From Avlabari take the metro to Didube bus station. At Didube, you can take the frequent marshrutkas (shared vans) to Mtskheta for just 1 Lari.

You can explore Mtskheta by foot. However if you want to explore the 6th century Jvari Monastery (which you can see up the hill), you might want to take a taxi (or share a taxi) to save time.

Jvari: [image from Wikipedia]

In all honesty, Tbilisi/Georgia can impact you so much during the 1-day, that you might just be tempted to stay longer.

I have always had this unshakable feeling of loneliness. Being with people does not seem to cure it. What should I do?

This answer is based upon my limited knowledge (through the question) of your personality

Being with people not curing the loneliness is probably just one of the symptoms. Most probably the real reason lies in low self acceptance or irrationally high self esteem. In both the cases, you need to move towards the centre.

All our behavioural manifestations are caused by the mixture of environmental and hereditary factors (you can't control the latter). There maybe be several factors that are responsible for your loneliness. Again, they might not be and I'm assuming this has always been the case and not after a certain event or phase of life.

  • You are a brilliant person and have high IQ (Many extremely intelligent (IQ wise) people find themselves peerless)
  • You have low EQ, which makes it difficult for you to empathize with others and hence can't get close to them.
  • You are yet to discover yourself and know about your own fears, inadequacies, weaknesses and strengths. Try to introspect and know why you behave a certain way. Be conscious of what you are saying and why. Try to know why you are afraid of certain situations or what makes you happy. When you identify the reasons, make peace with them if they are disturbing you. Everyone has weaknesses, you just need to accept yourself and be content.
  • Your personality is such that you don't like people getting to know you better. If loneliness is disturbing you, make an effort to know people and share your own thoughts on various topics.
  • This is a long shot, but if you are not passionate about something, try to find it. A lot of times that's what's lacking and people feel disgruntled about themselves.
  • Maybe you are not looking for people at the right places or don't know what kind of people you want in life. (Again, introspection would help here)

I hope this helps, again this answer is based on my limited experience of life and I can be totally wrong. In any case, being lonely is okay as long as it's not disturbing you in anyway. Everyone is different and has different goals in life. Cheers!

What harsh conditions have the United States imposed on the economy, the government and the people of Japan, from 1945 to now?

Um, not much, actually. Well they did take a lot of land away from the aristocrats and redistributed them among the farmers, which some of the former aristocrats are slightly salty about (not seriously of course, we just joke about it once in a while), which altered the agricultural economy a little. They also broke up zaibatsu conglomerates which had a monopoly on the economy, and created space for a healthy competition. The Korean War also increased the demand for heavy industry so that boosted the economy. By 1964, Japan was fully recovered from the war and had a booming economy thanks to the Americans.