Member SHRUTI SINGH
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Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
History
The theorem is named after a greek Mathematician called Pythagoras.
Pythagoras Theorem Formula
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.
Consider three squares of sides a, b, c mounted on the three sides of a triangle having the same sides as shown.
By Pythagoras Theorem –
Area of square “a” + Area of square “b” = Area of square “c”
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BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.
It explains the order of operations to be performed while solving an expression. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Solving the problem in the wrong order will result in a wrong answer.
Note: The “O” in the BODMAS full form is also called “Order”, which refers to the numbers which involve powers, square roots, etc. Check the examples below to have a better understanding of using the BODMAS rule.
Example- Solve <nobr>(12+14)of16</nobr>
Solution- <nobr>(12+14)of16</nobr>
Step 1: Solving the fraction inside the bracket first-
<nobr>12+14=34</nobr>
Step 2: Now the expression will be <nobr>34of16</nobr> =
<nobr>34×16</nobr> <nobr>=12</nobr>
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Efficiency signifies a peak level of performance that uses the least amount of inputs to achieve the highest amount of output. Efficiency requires reducing the number of unnecessary resources used to produce a given output including personal time and energy. It is a measurable concept that can be determined using the ratio of useful output to total input. It minimizes the waste of resources such as physical materials, energy, and time while accomplishing the desired output.
KEY TAKEAWAYS
Efficiency is the fundamental reduction in the amount of wasted resources that are used to produce a given number of goods or services (output).Economic efficiency results from the optimization of resource-use to best serve an economy.Market efficiency is the ability for prices to reflect all of the available information.Operational efficiency is a measure of how well firms convert operations into profits.
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. Start Your Day With H2O
Start your morning off right with a big glass of water. After fasting all night, this first drink of water will help to hydrate your cells and wake you up. Pssst, getting yourself a Hydroflask will encourage you to drink more water through out the day. Plus, it can keep your water cold or warm all day. It may seem strange, but having a water bottle on you all day helps to remind you to drink water!
2. Meal Prep It!
Making your meals ahead of time will end up saving you plenty of time and stress in the long run! Getting yourself some handy dandy meal prep containers will also be a game-changer for this meal prep hack. You can find plenty of great recipes for meal prepping online, that freeze and reheat really well. You can also make quick on-the-go snacks such as this vegan cookie recipe. Or, if you are too busy to prep a week of cooking, there are food services such as Purple Carrot and Freshly that can help you have balanced meals with minimal cooking!
3. Buy Your Groceries Online
Buying your groceries online is a lot less stressful than hustling and bustling through your local grocery stores to find the best bargains in the shortest amount of time! Shipt is an amazing way to order your groceries online. Shipt provides you with a delivery service that offers delivery as soon as 1 hour, committed shoppers who do your grocery shopping for you, up-to-the-minute updates with your order and a pleasant shopping experience with your favorite retailers every time!
4. Keep Your Immunity Strong
It’s increasingly important to keep your immunity strong by getting your daily source of nutrition and vitamins. If you’ve been lacking on keeping your medicine drawer full, check out Rite Aid for almost anything you would need. They have everything from cold medication to vitamins and vaccines. Don’t forget to keep up on your health regimen!
5. Prioritize Your Sleep
Sleep is an important part of health and if you don’t get enough of it, it can negatively impact your energy levels, motivation, concentration and even appetite regulation. Make sure you prioritize your sleep and keep a consistent bedtime routine with your busy lifestyle to maintain good health and reach your goals. A sleep aid device might help you to get a better night’s sleep and help you to fall asleep faster. If you struggle with getting a good night’s sleep, these additional tips and products may help you! Also, the mattress you have can really affect how you sleep, so if you are due for a new mattress. Be sure to get a high quality one from Nectar, Idle Sleep, Eco Terra Beds or Puffy Mattress. There’s also Molecule and Purple if you are looking for a mattress that really hits all your priorities!
6. Exercise and Socialize
Exercise can help you feel energized and improve your sleep and overall well being. Instead of forcing yourself to do a form of exercise you don’t enjoy, try out a new activity like yoga, hiking, pilates, biking or swimming. This will help you make exercise a sustainable habit, and you’ll also gain more physical, mental and emotional benefits from something you enjoy.
There are many online resources and products to help you remain active at home. For example, there are plenty of online yoga sessions, so you don’t have to do it by yourself. There’s Yoga Class Plan and Yoga Download. There’s also Openfit, which offers full body workouts that you can follow to keep you motivated.
7. Eat More Fish
Living a busy lifestyle means your brain is constantly working, which is why you should try and eat foods that benefit the brain and boost brain function. Fish is a great source of omega-3 fatty acids which help build membranes around each cell in the body, including the brain cells. Therefore, they can improve the structure of brain cells known as neurons. Research suggests that eating foods rich in omega-3’s, such as oily fish, may boost brain function. Like salmon, mackerel and tuna. So do yourself and your brain a favor and get some fish on your dish! Wild Alaskan is a great place to get all your seafood needs at a high quality and they deliver straight to your door.
8. Practice Self-Care
No matter how busy your life gets, make sure you prioritize yourself and your health and practice self-care. This can be as simple as meditating, putting on a face mask or getting enough sleep. Or, you can try making your own face mask with this DIY recipe! Or get an air humidifier and essential oils. Self care differs from person to person, so it’s all about finding what works for you. Here are ten different ways you can practice self care. In order to have a healthy lifestyle, there needs to be a balance between your work and health.
Practicing self-care doesn’t have to be pricy, check out Dollar Tree and treat yourself to a nice bubble bath or face mask!
9. Make a Schedule!
One of the best ways to stay on top of your busy lifestyle, keep organized and maintain healthy habits is to create a realistic schedule and use lists as much as possible. Your schedule will dictate how you go about completing each task throughout the day, and where you can fit-in your healthy lifestyle activities. This might seem more stressful by creating more work for yourself, however, sticking to a schedule will help you feel less stressed and more organized which can improve your productivity and overall well being. Or, use journaling as a method to capture your eating habits, sleep, or water intake. Being aware of your daily habits can help you to create small lifestyle changes that result in a healthier you!
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complementary angles are defined with respect to the addition of two angles. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
When two line segments or lines meet at a common point (called vertex), at the point of intersection an angle is formed. When a ray is rotated about its endpoint, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position.
In fig. 1 if the ray <nobr>OP−→−</nobr> is rotated in the direction of the ray <nobr>OQ−→−</nobr>, then the measure of its rotation represents the angle formed by it. In this case, the measure of rotation that is the angle formed between the initial side and the terminal side is represented by Ɵ.
Complementary Angles
When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Here we say that the two angles complement each other.
Suppose if one angle is x then the other angle will be 90<sup>o</sup> – x. Hence, we use these complementary angles for trigonometry ratios, where on ratio complement another ratio by 90 degrees such as;
sin (90°- A) = cos A and cos (90°- A) = sin Atan (90°- A) = cot A and cot (90°- A) = tan Asec (90°- A) = cosec A and cosec (90°- A) = sec A
Hence, you can see here the trigonometric ratio of the angles gets changed if they complement each other.
Complementary Angles
The measure of angle BOD is 60<sup>o</sup> and angle AOD measures 30<sup>o</sup>. On adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary angles.
The complementary to each other as the measure of the sum of both the angles is 90<sup>o</sup>. ∠POQ and ∠ABC are complementary and are called complements of each other.
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Christmas is celebrated on 25th December every year. This festival commemorates the birth anniversary of Jesus Christ – the Messiah of God. Although it is a Christian festival, people from different communities celebrate it with great fervour and enthusiasm.
A Christmas tree is an artificial pine tree which is decorated with lights, artificial stars, flowers, toys and bells all over it. It looks beautiful when the decoration is complete. Churches are decorated with lights during Christmas and people hang star lanterns outdoors to mark the onset of the festive season. All members of the family sit and pray together in praise of Jesus Christ.
Kids are especially enthusiastic about Christmas as they expect Santa Claus to visit them and bring gifts to their homes on the night of Christmas Eve and the early hours of Christmas day. Presents are placed under the Christmas tree which are wrapped in gift boxes and opened on the day of Christmas.
Kids sing Christmas carols like, “Jingle Bell, Jingle Bell, Jingle all the way” and perform various skits celebrating the auspicious day. Christmas is a festival which is cherished by people from all faiths and religions.
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Darkness! Because not even a fraction of sunlight reaches the depths. Since no light, no plants.Pressure! The water exerts tremendous pressure as u go deeper and at great depths of say > 1000 meters, the pressure is crushingCold! Lack of sunlight and the fact that water is a bad conductor of heat means the bottom layers of the ocean are very very coldOccasionally violent! The bottom of the sea represents the thinnest part of the earths crust and hence most prone to earthquakes, volcanoes, tsunamis etc.Rich topography! Mountains, valleys, rivers and beaches … each larger than their counterparts on the surface means a whole undiscovered planetLonely! The cold and dark means that except a few rare organisms like sponges that are specially adapted, there is practically nothing living at the bottom of the sea
2 billion years from now when the sun starts cooling and expanding, it will have engulfed the earth but the heat would have melted the ice on moons like Titan providing mankind wit the next home. However, all such homes are likely to be water planets and how we adapt to living on and below the endless oceans on these planets will determine whether we continue to survive as a species.
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Our universe is but one in an unimaginably massive ocean of universes called the multiverse.
If that concept isn’t enough to get your head around, physics describes different kinds of multiverse. The easiest one to comprehend is called the cosmological multiverse. The idea here is that the universe expanded at a mind-boggling speed in the fraction of a second after the big bang. During this period of inflation, there were quantum fluctuations which caused separate bubble universes to pop into existence and themselves start inflating and blowing bubbles. Russian physicist Andrei Linde came up with this concept, which suggests an infinity of universes no longer in any causal connection with one another – so free to develop in different ways.
Cosmic space is big – perhaps infinitely so. Travel far enough and some theories suggest you’d meet your cosmic twin – a copy of you living in a copy of our world, but in a different part of the multiverse. String theory, which is a notoriously theoretical explanation of reality, predicts a frankly meaninglessly large number of universes, maybe 10 to the 500 or more, all with slightly different physical parameters.
And then there’s the quantum multiverse. Physicist Hugh Everett came up with this idea, which is predicted by his “many worlds” interpretation of quantum physics. Everett’s theory is that quantum effects cause the universe to constantly split. It could mean that decisions we make in this universe have implications for other versions of ourselves living in parallel worlds.
However, we recommend restricting your concerns to entities in the current plane of existence. Rowan Hooper..
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Most of the glass boards we’ve seen use a layer of glass that is about ¼” thick (5-6mm). A magnet at the surface has to reach across that distance to attract to the steel underneath. A modestly sized magnet that sticks well to a refrigerator or regular whiteboard won’t be strong enough to hold well to a glass whiteboard.
Bigger magnets are needed.
We certainly have bigger, stronger magnets that can hold. Unfortunately, picking the right magnet isn’t so simple. If you just choose really big magnets, they might attract to each other much more than the steel underneath. This can make an unpredictable, slamming-together mess.
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Most of the glass boards we’ve seen use a layer of glass that is about ¼” thick (5-6mm). A magnet at the surface has to reach across that distance to attract to the steel underneath. A modestly sized magnet that sticks well to a refrigerator or regular whiteboard won’t be strong enough to hold well to a glass whiteboard.
Bigger magnets are needed.
We certainly have bigger, stronger magnets that can hold. Unfortunately, picking the right magnet isn’t so simple. If you just choose really big magnets, they might attract to each other much more than the steel underneath. This can make an unpredictable, slamming-together mess.
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According to a legend, the first magnet was discovered by a Greek shepherd named Magnes. It is said that the nails in his shoes and the iron tip of his staff got stuck to a large black rock on which he was standing. Greeks named this strange type of rock ‘magnetite’. The Chinese also knew about magnets. Ancient Chinese sailors used magnets for navigation.
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Here are the basics in 10 steps.
1. Choose a container.
Seed-starting containers should be clean, measure at least 2-3 inches deep and have drainage holes. They can be plastic pots, cell packs, peat pots, plastic flats, yogurt cups, even eggshells. As long as they are clean (soak in a 9 parts water to one part household bleach for 10 minutes), the options are endless. You can also buy seed-starting kits, but don’t invest a lot of money until you’re sure you’ll be starting seeds every year. If you start seeds in very small containers or plastic flats, you’ll need to transplant seedlings into slightly larger pots once they have their first set of true leaves. Keep in mind that flats and pots take up room, so make sure you have enough sunny space for all the seedlings you start.
2. Start with quality soil.
Sow seeds in sterile, seed-starting mix or potting soil available in nurseries and garden centers. Don’t use garden soil, it’s too heavy, contains weeds seeds, and possibly, disease organisms. Wet the soil with warm water before filling seed-starting containers.3. Plant at the proper depth.
You’ll find the proper planting depth on the seed packet. The general rule of thumb is to cover seeds with soil equal to three times their thickness – but be sure to read the seed packet planting instructions carefully. Some seeds, including certain lettuces and snapdragons, need light to germinate and should rest on the soil surface but still be in good contact with moist soil. Gentle tamping after sowing will help. After planting your seeds, use a spray bottle to wet the soil again.4. Water wisely.
Always use room-temperature water. Let chlorinated water sit overnight so chlorine can dissipate or use distilled water. Avoid using softened water. It’s important to keep soil consistently moist, but avoid overwatering, which promotes diseases, that can kill seedlings. Try not to splash water on leaves. An easy way to avoid this – as well as overwatering – is to dip base of your containers in water and allow the soil to absorb moisture from the bottom until moist. Some seed-starting kits supply a wicking mat that conducts water from a reservoir to dry soil. This may be the most goof-proof method of watering seedlings but you still have to be careful that the soil doesn’t stay too wet. Whatever you do, don’t miss a watering and let seeds or seedlings dry out. It’s a death sentence.5. Maintain consistent moisture.
Prior to germination, cover your container to help trap moisture inside. Seed-starting kits typically come with a plastic cover. You can also use a plastic bag, but it should be supported so it doesn’t lay flat on the soil. Remove covers as soon as seeds sprout. Once seedlings are growing, reduce watering so soil partially drys, but don’t let them wilt.6. Keep soil warm.
Seeds need warm soil to germinate. They germinate slower, or not at all, in soils that are too cool. Most seeds will germinate at around 78°F. Waterproof heating mats, designed specifically for germinating seeds, keep soil at a constant temperature. You can buy them in most nurseries and garden centers. Or, you can place seed trays on top of a refrigerator or other warm appliance until seeds sprout. After germination, air temperature should be slightly below 70°F. Seedlings can withstand air temperature as low as 50°F as long as soil temperature remains 65-70°F.7. Fertilize.
Start feeding your seedlings after they develop their second set of true leaves, applying a half-strength liquid fertilizer weekly. Apply it gently so seedlings are not dislodged from the soil. After four weeks, apply full-strength liquid fertilizer every other week until transplanting.8. Give seedlings enough light.
Not enough light leads to leggy, tall seedlings that will struggle once transplanted outdoors. In mild winter areas, you can grow stocky seedlings in a bright south-facing window. Farther north, even a south-facing window may not provide enough light, especially in the middle of winter. Ideally, seedlings need 14-16 hours of direct light per day for healthiest growth. If seedlings begin bending toward the window, that’s a sure sign they are not getting enough light. Simply turning the pots won’t be enough – you may need to supply artificial lighting. Nurseries and mail order seed catalogs can provide lighting kits. Follow instructions carefully.9. Circulate the air.
Circulating air helps prevents disease and encourages the development of strong stems. Run a gentle fan near seedlings to create air movement. Keep the fan a distance away from the seedlings to avoid blasting them directly.10. Harden off seedlings before transplanting outdoors.
Before moving seedlings outdoors, they need to be acclimatized to their new, harsher surroundings. This procedure is called “hardening off.” -
All liquids ultimately boil at some temperature. The vegetable oils are not easy to evaporate, because of high molecular weights and more than that the presence of the highly polar triester glyceride functional group. The glyceride ester function renders the oils vulnerable to decomposition at high temperatures, before the oil gets any chance to evaporate, under atmospheric pressure and open to the surroundings which would lead to oxidation and oxidative decomposition of the molecules. However, if you want you may distill oils under reduced pressure.
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Evaporation happens at room temperature. When we heat something, boiling and vaporization happens.
Vegetable oils when heated start producing smoke first. The smoke is nothing but the oil molecules game vaporized or getting decomposed and then vaporized. If we continue hearing it further, the oil will reach its auto ignition temperature and will catch fire.
