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## What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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## Math Solver

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Get accurate solutions and step-by-step explanations for algebra and other math problems, while enhancing your problem-solving skills!

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## How to Use a Scientific Calculator For Algebra

Last Updated: January 2, 2024

## Basic Operational Functions

Common functions for algebra.

This article was co-authored by JohnK Wright V . JohnK Wright V is a Certified Math Teacher at Bridge Builder Academy in Plano, Texas. With over 20 years of teaching experience, he is a Texas SBEC Certified 8-12 Mathematics Teacher. He has taught in six different schools and has taught pre-algebra, algebra 1, geometry, algebra 2, pre-calculus, statistics, math reasoning, and math models with applications. He was a Mathematics Major at Southeastern Louisiana and he has a Bachelor of Science from The University of the State of New York (now Excelsior University) and a Master of Science in Computer Information Systems from Boston University. This article has been viewed 173,283 times.

A scientific calculator provides functions that make common calculations easy. While each calculator is slightly different, every model has the basic functions needed for middle and high school math courses. Once you understand how to use its features, it will help you on your way towards mathematical success.

- You have to hit the equals (=) sign to complete a calculation using these symbols.

- Hit the beginning parentheses before you hit your first number, and hit the ending parentheses after you hit your last number. The calculator will complete that calculation before you enter your next functions.
- If you need, you can also nest parentheses, though be sure that you can keep track of them.

## Community Q&A

- Remember that you are responsible for converting the answer after the calculator does its job. It is much more useful to have those skills than to be skilled at using a particular model. Thanks Helpful 0 Not Helpful 0
- The TI-30X IIS is pretty loose with closing parentheses for operations. For example, you do not need to close the parentheses when evaluating logarithms or trig functions. Thanks Helpful 0 Not Helpful 0
- When choosing a scientific calculator, consider what math classes besides algebra you'll be using it for. You should choose a calculator that will take you through several years of the math classes you anticipate taking. In recent years, it is more beneficial to use a graphing calculator for more advanced courses, like calculus. Thanks Helpful 0 Not Helpful 0

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## Online Equation Solver

Solve linear, quadratic and polynomial systems of equations with wolfram|alpha.

- Natural Language

## More than just an online equation solver

Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. It also factors polynomials, plots polynomial solution sets and inequalities and more.

Learn more about:

- Equation solving

## Tips for entering queries

Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to formulate queries.

- find roots to quadratic x^2-7x+12
- plot inequality x^2-7x+12<=0
- solve {3x-5y==2,x+2y==-1}
- plot inequality 3x-5y>=2 and x+2y<=-1
- solve 3x^2-y^2==2 and x+2y^2==5
- plot 3x^2-y^2>=2 and x+2y^2<=5
- View more examples

## Access instant learning tools

Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator

- Step-by-step solutions
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## About solving equations

A value is said to be a root of a polynomial if ..

The largest exponent of appearing in is called the degree of . If has degree , then it is well known that there are roots, once one takes into account multiplicity. To understand what is meant by multiplicity, take, for example, . This polynomial is considered to have two roots, both equal to 3.

One learns about the "factor theorem," typically in a second course on algebra, as a way to find all roots that are rational numbers. One also learns how to find roots of all quadratic polynomials, using square roots (arising from the discriminant) when necessary. There are more advanced formulas for expressing roots of cubic and quartic polynomials, and also a number of numeric methods for approximating roots of arbitrary polynomials. These use methods from complex analysis as well as sophisticated numerical algorithms, and indeed, this is an area of ongoing research and development.

Systems of linear equations are often solved using Gaussian elimination or related methods. This too is typically encountered in secondary or college math curricula. More advanced methods are needed to find roots of simultaneous systems of nonlinear equations. Similar remarks hold for working with systems of inequalities: the linear case can be handled using methods covered in linear algebra courses, whereas higher-degree polynomial systems typically require more sophisticated computational tools.

## How Wolfram|Alpha solves equations

For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems. In some cases, linear algebra methods such as Gaussian elimination are used, with optimizations to increase speed and reliability. Other operations rely on theorems and algorithms from number theory, abstract algebra and other advanced fields to compute results. These methods are carefully designed and chosen to enable Wolfram|Alpha to solve the greatest variety of problems while also minimizing computation time.

Although such methods are useful for direct solutions, it is also important for the system to understand how a human would solve the same problem. As a result, Wolfram|Alpha also has separate algorithms to show algebraic operations step by step using classic techniques that are easy for humans to recognize and follow. This includes elimination, substitution, the quadratic formula, Cramer's rule and many more.

## Diamond Problem Calculator

What is a diamond problem diamond math problems, how to do diamond problems case 1: given two factors, case 2: given one factor, and the product or sum, case 3: given product and sum, while searching for factors, how to use diamond problem calculator.

Welcome to our diamond problem calculator, also known as a diamond problem solver . This intuitive tool allows you to enter any two numbers and the two others will appear. We've also prepared a compendium that answers all your burning questions about this topic.

Let's start by introducing what a diamond problem is and continue smoothly to some how to do diamond problems of various types tips. Are you ready?

Despite what you might think, the diamond problem doesn't have a lot in common with gemstones💎 or diamond rings💍 — though we can teach you how to calculate a diamond's weight . It is more closely related to what is often called a diamond in math ♦️ or cards🃏 - the rhombus, a quadrilateral shape. The diamond problem is a type of exercise that happens in a diamond shape 💠 - which we can also represent as a cross with 4 sections.

So, what is the diamond problem in math ? It's where you fill in all four fields, related by some mathematical operation . The pattern of the numbers is constant:

- On the left and right side of the diamond, you have two numbers, sometimes called factors;
- In the top part you can find their product; and
- In the bottom section - their sum.

Solving the diamond problem means that you know only two numbers out of four, and you need to find the missing ones . And that's all!

There are three main types of diamond problems, and the diamond problem calculator can deal with all of them. If you're wondering how to do diamond problems in each of these cases, scroll down to the next sections.

This is the easiest case: you have two numbers, A and B, and you need to find the sum and product of them. For example, let's say that we want to solve the diamond problem for factors 13 13 13 and 4 4 4 :

- Calculate the product = 13 × 4 = 52 = 13 \times 4 = 52 = 13 × 4 = 52 , and write the number on top.
- Find the sum = 13 + 4 = 17 = 13 + 4 = 17 = 13 + 4 = 17 , and input the value into the bottom part of the diamond.

You might meet this type of a diamond math problem in the first lesson about the diamonds - when your teacher first introduces the concept.

Let's have a look at a slightly more complicated case, where you have one of the basic numbers, and a product or a sum. The first thing to do is to calculate the factor missing from the diamond. Transform your equation is such a way to solve for the unknown value:

a) When you're given one factor and the sum , you can find a second factor by a simple subtraction:

With both factors in hand, simply multiply them to get the last number: product = 5 × 6 = 30 = 5 \times 6 = 30 = 5 × 6 = 30 .

b) If you know one factor and the product , divide the product by the factor to find the second product:

Then calculate the sum , use the following expression: sum = factor A + factor B = 9 + 7 = 16 = \text{factor}\ A + \text{factor}\ B = 9 + 7 = 16 = factor A + factor B = 9 + 7 = 16 .

Remember, you can always quickly solve these diamonds or verify your answers with our diamond problem calculator.

Now we're coming to the last issue and the most common diamond problem: the case where you know the sum and the product of the two numbers, but you don't actually know the numbers themselves.

This type of diamond math problem is helpful when you're learning about factoring a quadratic equation. Why?

Let's say that we have a quadratic equation:

We would like to factor this equation, meaning that we'd like to present it in a form:

How to find these numbers - the roots of the quadratic equation ? You know that their product must be equal to 12 12 12 , and that their sum is equal to 7 7 7 . And that's exactly what you're trying to find out in the diamond problem! 🙂 You can rewrite this question in the form of a diamond:

How to solve such a problem?

- Start with the top number - the product of two numbers. Write down all possible pairs of numbers that give this as their product. You can, for example, calculate the prime factorization if it's a more complicated case. In our example, the product is equal to 12 - which two integer numbers could be multiplied together? The order of the factors doesn't matter, as multiplication (and addition) are commutative:

Don't forget the negative numbers:

- Sum these two numbers , and check which combination gives the desired sum of 7:

And here it is! We can stop here, as we've found the two numbers which meet the condition 🎉

🙋 Eager to know more about quadratic formulas? Visit our quadratic formula calculator !

Sometimes it's very easy to guess the solution, as there are not many options. We're sure that you'll solve this a diamond problem in no time!

If not, enter the numbers into our diamond problem solver. That wasn't so difficult, was it? 🤦

It's really easy, believe us!

All you need to do is to input any two numbers and the diamond problem solver will find out the other two . What's more, the tool displays the solution in a diamond form. What more could you wish for? 😎

Please notice that in some specific cases you'll need to hit the refresh button ⟳ to use the calculator again 👍

## What are the other numbers in the diamond if the left and right are -4 and 8?

The top number is -32, and the bottom is 4. To find the top, we multiply the side numbers. We add them together to find the bottom.

## What is the diamond problem used for in mathematics?

We use the diamond problem in addition, subtraction, multiplication, and division in maths. It is used to calculate integers, decimals, and fractions and for factoring trinomials.

## How do I solve the diamond for fractions?

Assuming that you are given two fractions on the left and right sides, say 1 / 2 and 5 / 6 , follow these steps to solve the problem:

Find the product of the fractions: 1 / 2 × 5 / 6 = 5 / 12

Place this answer ( 5 / 12 ) at the top:

Find the sum of the fractions: 1 / 2 + 5 / 6 = 6 / 12 + 10 / 12 = 16 / 12

Place this answer ( 16 / 12 ) at the bottom.

Voila! You solved the diamond problem.

## How do I find the right and left numbers in the diamond?

Assuming the top number is 35 , and the bottom is 12 . Follow these steps to find the numbers to the right and left:

- Find the factors of the top number: 35, 1 7, 5
- Identify the factors which, when added together, equal to the bottom number: 7, 5
- Place these numbers on either side.

That's it. You have solved the diamond problem for the right and left numbers.

## Car crash force

Cube calc: find v, a, d, percent error.

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## Quadratic Formula Calculator

What do you want to calculate.

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About the quadratic formula, quadratic formula video lesson.

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March 12, 2024

## The Simplest Math Problem Could Be Unsolvable

The Collatz conjecture has plagued mathematicians for decades—so much so that professors warn their students away from it

By Manon Bischoff

Mathematicians have been hoping for a flash of insight to solve the Collatz conjecture.

James Brey/Getty Images

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo Kakutani told him that during the cold war, “for about a month everybody at Yale [University] worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.”

The Collatz conjecture—the vexing puzzle Kakutani described—is one of those supposedly simple problems that people tend to get lost in. For this reason, experienced professors often warn their ambitious students not to get bogged down in it and lose sight of their actual research.

The conjecture itself can be formulated so simply that even primary school students understand it. Take a natural number. If it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. Proceed in the same way with the result x : if x is odd, you calculate 3 x + 1; otherwise calculate x / 2. Repeat these instructions as many times as possible, and, according to the conjecture, you will always end up with the number 1.

## On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

For example: If you start with 5, you have to calculate 5 x 3 + 1, which results in 16. Because 16 is an even number, you have to halve it, which gives you 8. Then 8 / 2 = 4, which, when divided by 2, is 2—and 2 / 2 = 1. The process of iterative calculation brings you to the end after five steps.

Of course, you can also continue calculating with 1, which gives you 4, then 2 and then 1 again. The calculation rule leads you into an inescapable loop. Therefore 1 is seen as the end point of the procedure.

Following iterative calculations, you can begin with any of the numbers above and will ultimately reach 1.

Credit: Keenan Pepper/Public domain via Wikimedia Commons

It’s really fun to go through the iterative calculation rule for different numbers and look at the resulting sequences. If you start with 6: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. Or 42: 42 → 21 → 64 → 32 → 16 → 8 → 4 → 2 → 1. No matter which number you start with, you always seem to end up with 1. There are some numbers, such as 27, where it takes quite a long time (27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → ...), but so far the result has always been 1. (Admittedly, you have to be patient with the starting number 27, which requires 111 steps.)

But strangely there is still no mathematical proof that the Collatz conjecture is true. And that absence has mystified mathematicians for years.

The origin of the Collatz conjecture is uncertain, which is why this hypothesis is known by many different names. Experts speak of the Syracuse problem, the Ulam problem, the 3 n + 1 conjecture, the Hasse algorithm or the Kakutani problem.

German mathematician Lothar Collatz became interested in iterative functions during his mathematics studies and investigated them. In the early 1930s he also published specialist articles on the subject , but the explicit calculation rule for the problem named after him was not among them. In the 1950s and 1960s the Collatz conjecture finally gained notoriety when mathematicians Helmut Hasse and Shizuo Kakutani, among others, disseminated it to various universities, including Syracuse University.

Like a siren song, this seemingly simple conjecture captivated the experts. For decades they have been looking for proof that after repeating the Collatz procedure a finite number of times, you end up with 1. The reason for this persistence is not just the simplicity of the problem: the Collatz conjecture is related to other important questions in mathematics. For example, such iterative functions appear in dynamic systems, such as models that describe the orbits of planets. The conjecture is also related to the Riemann conjecture, one of the oldest problems in number theory.

## Empirical Evidence for the Collatz Conjecture

In 2019 and 2020 researchers checked all numbers below 2 68 , or about 3 x 10 20 numbers in the sequence, in a collaborative computer science project . All numbers in that set fulfill the Collatz conjecture as initial values. But that doesn’t mean that there isn’t an outlier somewhere. There could be a starting value that, after repeated Collatz procedures, yields ever larger values that eventually rise to infinity. This scenario seems unlikely, however, if the problem is examined statistically.

An odd number n is increased to 3 n + 1 after the first step of the iteration, but the result is inevitably even and is therefore halved in the following step. In half of all cases, the halving produces an odd number, which must therefore be increased to 3 n + 1 again, whereupon an even result is obtained again. If the result of the second step is even again, however, you have to divide the new number by 2 twice in every fourth case. In every eighth case, you must divide it by 2 three times, and so on.

In order to evaluate the long-term behavior of this sequence of numbers , Lagarias calculated the geometric mean from these considerations in 1985 and obtained the following result: ( 3 / 2 ) 1/2 x ( 3 ⁄ 4 ) 1/4 x ( 3 ⁄ 8 ) 1/8 · ... = 3 ⁄ 4 . This shows that the sequence elements shrink by an average factor of 3 ⁄ 4 at each step of the iterative calculation rule. It is therefore extremely unlikely that there is a starting value that grows to infinity as a result of the procedure.

There could be a starting value, however, that ends in a loop that is not 4 → 2 → 1. That loop could include significantly more numbers, such that 1 would never be reached.

Such “nontrivial” loops can be found, for example, if you also allow negative integers for the Collatz conjecture: in this case, the iterative calculation rule can end not only at –2 → –1 → –2 → ... but also at –5 → –14 → –7 → –20 → –10 → –5 → ... or –17 → –50 → ... → –17 →.... If we restrict ourselves to natural numbers, no nontrivial loops are known to date—which does not mean that they do not exist. Experts have now been able to show that such a loop in the Collatz problem, however, would have to consist of at least 186 billion numbers .

The length of the Collatz sequences for all numbers from 1 to 9,999 varies greatly.

Credit: Cirne/Public domain via Wikimedia Commons

Even if that sounds unlikely, it doesn’t have to be. In mathematics there are many examples where certain laws only break down after many iterations are considered. For instance,the prime number theorem overestimates the number of primes for only about 10 316 numbers. After that point, the prime number set underestimates the actual number of primes.

Something similar could occur with the Collatz conjecture: perhaps there is a huge number hidden deep in the number line that breaks the pattern observed so far.

## A Proof for Almost All Numbers

Mathematicians have been searching for a conclusive proof for decades. The greatest progress was made in 2019 by Fields Medalist Terence Tao of the University of California, Los Angeles, when he proved that almost all starting values of natural numbers eventually end up at a value close to 1.

“Almost all” has a precise mathematical meaning: if you randomly select a natural number as a starting value, it has a 100 percent probability of ending up at 1. ( A zero-probability event, however, is not necessarily an impossible one .) That’s “about as close as one can get to the Collatz conjecture without actually solving it,” Tao said in a talk he gave in 2020 . Unfortunately, Tao’s method cannot generalize to all figures because it is based on statistical considerations.

All other approaches have led to a dead end as well. Perhaps that means the Collatz conjecture is wrong. “Maybe we should be spending more energy looking for counterexamples than we’re currently spending,” said mathematician Alex Kontorovich of Rutgers University in a video on the Veritasium YouTube channel .

Perhaps the Collatz conjecture will be determined true or false in the coming years. But there is another possibility: perhaps it truly is a problem that cannot be proven with available mathematical tools. In fact, in 1987 the late mathematician John Horton Conway investigated a generalization of the Collatz conjecture and found that iterative functions have properties that are unprovable. Perhaps this also applies to the Collatz conjecture. As simple as it may seem, it could be doomed to remain unsolved forever.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

## The Effects of Climate Change

The effects of human-caused global warming are happening now, are irreversible for people alive today, and will worsen as long as humans add greenhouse gases to the atmosphere.

- We already see effects scientists predicted, such as the loss of sea ice, melting glaciers and ice sheets, sea level rise, and more intense heat waves.
- Scientists predict global temperature increases from human-made greenhouse gases will continue. Severe weather damage will also increase and intensify.

## Earth Will Continue to Warm and the Effects Will Be Profound

Global climate change is not a future problem. Changes to Earth’s climate driven by increased human emissions of heat-trapping greenhouse gases are already having widespread effects on the environment: glaciers and ice sheets are shrinking, river and lake ice is breaking up earlier, plant and animal geographic ranges are shifting, and plants and trees are blooming sooner.

Effects that scientists had long predicted would result from global climate change are now occurring, such as sea ice loss, accelerated sea level rise, and longer, more intense heat waves.

## The magnitude and rate of climate change and associated risks depend strongly on near-term mitigation and adaptation actions, and projected adverse impacts and related losses and damages escalate with every increment of global warming.

Intergovernmental Panel on Climate Change

Some changes (such as droughts, wildfires, and extreme rainfall) are happening faster than scientists previously assessed. In fact, according to the Intergovernmental Panel on Climate Change (IPCC) — the United Nations body established to assess the science related to climate change — modern humans have never before seen the observed changes in our global climate, and some of these changes are irreversible over the next hundreds to thousands of years.

Scientists have high confidence that global temperatures will continue to rise for many decades, mainly due to greenhouse gases produced by human activities.

The IPCC’s Sixth Assessment report, published in 2021, found that human emissions of heat-trapping gases have already warmed the climate by nearly 2 degrees Fahrenheit (1.1 degrees Celsius) since 1850-1900. 1 The global average temperature is expected to reach or exceed 1.5 degrees C (about 3 degrees F) within the next few decades. These changes will affect all regions of Earth.

The severity of effects caused by climate change will depend on the path of future human activities. More greenhouse gas emissions will lead to more climate extremes and widespread damaging effects across our planet. However, those future effects depend on the total amount of carbon dioxide we emit. So, if we can reduce emissions, we may avoid some of the worst effects.

## The scientific evidence is unequivocal: climate change is a threat to human wellbeing and the health of the planet. Any further delay in concerted global action will miss the brief, rapidly closing window to secure a liveable future.

Here are some of the expected effects of global climate change on the United States, according to the Third and Fourth National Climate Assessment Reports:

## Future effects of global climate change in the United States:

## U.S. Sea Level Likely to Rise 1 to 6.6 Feet by 2100

Global sea level has risen about 8 inches (0.2 meters) since reliable record-keeping began in 1880. By 2100, scientists project that it will rise at least another foot (0.3 meters), but possibly as high as 6.6 feet (2 meters) in a high-emissions scenario. Sea level is rising because of added water from melting land ice and the expansion of seawater as it warms. Image credit: Creative Commons Attribution-Share Alike 4.0

## Climate Changes Will Continue Through This Century and Beyond

Global climate is projected to continue warming over this century and beyond. Image credit: Khagani Hasanov, Creative Commons Attribution-Share Alike 3.0

## Hurricanes Will Become Stronger and More Intense

Scientists project that hurricane-associated storm intensity and rainfall rates will increase as the climate continues to warm. Image credit: NASA

## More Droughts and Heat Waves

Droughts in the Southwest and heat waves (periods of abnormally hot weather lasting days to weeks) are projected to become more intense, and cold waves less intense and less frequent. Image credit: NOAA

## Longer Wildfire Season

Warming temperatures have extended and intensified wildfire season in the West, where long-term drought in the region has heightened the risk of fires. Scientists estimate that human-caused climate change has already doubled the area of forest burned in recent decades. By around 2050, the amount of land consumed by wildfires in Western states is projected to further increase by two to six times. Even in traditionally rainy regions like the Southeast, wildfires are projected to increase by about 30%.

## Changes in Precipitation Patterns

Climate change is having an uneven effect on precipitation (rain and snow) in the United States, with some locations experiencing increased precipitation and flooding, while others suffer from drought. On average, more winter and spring precipitation is projected for the northern United States, and less for the Southwest, over this century. Image credit: Marvin Nauman/FEMA

## Frost-Free Season (and Growing Season) will Lengthen

The length of the frost-free season, and the corresponding growing season, has been increasing since the 1980s, with the largest increases occurring in the western United States. Across the United States, the growing season is projected to continue to lengthen, which will affect ecosystems and agriculture.

## Global Temperatures Will Continue to Rise

Summer of 2023 was Earth's hottest summer on record, 0.41 degrees Fahrenheit (F) (0.23 degrees Celsius (C)) warmer than any other summer in NASA’s record and 2.1 degrees F (1.2 C) warmer than the average summer between 1951 and 1980. Image credit: NASA

## Arctic Is Very Likely to Become Ice-Free

Sea ice cover in the Arctic Ocean is expected to continue decreasing, and the Arctic Ocean will very likely become essentially ice-free in late summer if current projections hold. This change is expected to occur before mid-century.

## U.S. Regional Effects

Climate change is bringing different types of challenges to each region of the country. Some of the current and future impacts are summarized below. These findings are from the Third 3 and Fourth 4 National Climate Assessment Reports, released by the U.S. Global Change Research Program .

- Northeast. Heat waves, heavy downpours, and sea level rise pose increasing challenges to many aspects of life in the Northeast. Infrastructure, agriculture, fisheries, and ecosystems will be increasingly compromised. Farmers can explore new crop options, but these adaptations are not cost- or risk-free. Moreover, adaptive capacity , which varies throughout the region, could be overwhelmed by a changing climate. Many states and cities are beginning to incorporate climate change into their planning.
- Northwest. Changes in the timing of peak flows in rivers and streams are reducing water supplies and worsening competing demands for water. Sea level rise, erosion, flooding, risks to infrastructure, and increasing ocean acidity pose major threats. Increasing wildfire incidence and severity, heat waves, insect outbreaks, and tree diseases are causing widespread forest die-off.
- Southeast. Sea level rise poses widespread and continuing threats to the region’s economy and environment. Extreme heat will affect health, energy, agriculture, and more. Decreased water availability will have economic and environmental impacts.
- Midwest. Extreme heat, heavy downpours, and flooding will affect infrastructure, health, agriculture, forestry, transportation, air and water quality, and more. Climate change will also worsen a range of risks to the Great Lakes.
- Southwest. Climate change has caused increased heat, drought, and insect outbreaks. In turn, these changes have made wildfires more numerous and severe. The warming climate has also caused a decline in water supplies, reduced agricultural yields, and triggered heat-related health impacts in cities. In coastal areas, flooding and erosion are additional concerns.

1. IPCC 2021, Climate Change 2021: The Physical Science Basis , the Working Group I contribution to the Sixth Assessment Report, Cambridge University Press, Cambridge, UK.

2. IPCC, 2013: Summary for Policymakers. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

3. USGCRP 2014, Third Climate Assessment .

4. USGCRP 2017, Fourth Climate Assessment .

## Related Resources

## A Degree of Difference

So, the Earth's average temperature has increased about 2 degrees Fahrenheit during the 20th century. What's the big deal?

## What’s the difference between climate change and global warming?

“Global warming” refers to the long-term warming of the planet. “Climate change” encompasses global warming, but refers to the broader range of changes that are happening to our planet, including rising sea levels; shrinking mountain glaciers; accelerating ice melt in Greenland, Antarctica and the Arctic; and shifts in flower/plant blooming times.

## Is it too late to prevent climate change?

Humans have caused major climate changes to happen already, and we have set in motion more changes still. However, if we stopped emitting greenhouse gases today, the rise in global temperatures would begin to flatten within a few years. Temperatures would then plateau but remain well-elevated for many, many centuries.

## Discover More Topics From NASA

Explore Earth Science

Earth Science in Action

Earth Science Data

Facts About Earth

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- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Mean, Median & Mode
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
- Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
- Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
- Linear Algebra Matrices Vectors
- Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
- Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
- Physics Mechanics
- Chemistry Chemical Reactions Chemical Properties
- Finance Simple Interest Compound Interest Present Value Future Value
- Economics Point of Diminishing Return
- Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
- Pre Algebra
- One-Step Addition
- One-Step Subtraction
- One-Step Multiplication
- One-Step Division
- One-Step Decimals
- Two-Step Integers
- Two-Step Add/Subtract
- Two-Step Multiply/Divide
- Two-Step Fractions
- Two-Step Decimals
- Multi-Step Integers
- Multi-Step with Parentheses
- Multi-Step Rational
- Multi-Step Fractions
- Multi-Step Decimals
- Solve by Factoring
- Completing the Square
- Quadratic Formula
- Biquadratic
- Logarithmic
- Exponential
- Rational Roots
- Floor/Ceiling
- Equation Given Roots
- Newton Raphson
- Substitution
- Elimination
- Cramer's Rule
- Gaussian Elimination
- System of Inequalities
- Perfect Squares
- Difference of Squares
- Difference of Cubes
- Sum of Cubes
- Polynomials
- Distributive Property
- FOIL method
- Perfect Cubes
- Binomial Expansion
- Negative Rule
- Product Rule
- Quotient Rule
- Expand Power Rule
- Fraction Exponent
- Exponent Rules
- Exponential Form
- Logarithmic Form
- Absolute Value
- Rational Number
- Powers of i
- Partial Fractions
- Is Polynomial
- Leading Coefficient
- Leading Term
- Standard Form
- Complete the Square
- Synthetic Division
- Linear Factors
- Rationalize Denominator
- Rationalize Numerator
- Identify Type
- Convergence
- Interval Notation
- Pi (Product) Notation
- Boolean Algebra
- Truth Table
- Mutual Exclusive
- Cardinality
- Caretesian Product
- Age Problems
- Distance Problems
- Cost Problems
- Investment Problems
- Number Problems
- Percent Problems
- Addition/Subtraction
- Multiplication/Division
- Dice Problems
- Coin Problems
- Card Problems
- Pre Calculus
- Linear Algebra
- Trigonometry
- Conversions

## Most Used Actions

Number line.

- -x+3\gt 2x+1
- (x+5)(x-5)\gt 0
- 10^{1-x}=10^4
- \sqrt{3+x}=-2
- 6+11x+6x^2+x^3=0
- factor\:x^{2}-5x+6
- simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
- x+2y=2x-5,\:x-y=3
- How do you solve algebraic expressions?
- To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
- What are the basics of algebra?
- The basics of algebra are the commutative, associative, and distributive laws.
- What are the 3 rules of algebra?
- The basic rules of algebra are the commutative, associative, and distributive laws.
- What is the golden rule of algebra?
- The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
- What are the 5 basic laws of algebra?
- The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

algebra-calculator

- High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential...

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