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Calculate the molar mass of water (H2O) by adding up the atomic masses of hydrogen (H) and oxygen (O) atoms. Remember to consider the number of atoms in the molecule when calculating the molar mass.

Using the research information provided, write an original thought 4-8 sentence summary IN YOUR OWN WORDS for each of the three topics.

Research Information:

Who invented the logarithm and why?

Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. The objective of both men was to simplify mathematical calculations. Napier's approach was algebraic and Burgi's approach was geometric. Neither men had a concept of a logarithmic base. Napier defined logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents. The possibility of defining logarithms as exponents was recognized by John Wallis in 1685 and by Johann Bernoulli in 1694. The invention of the common system of logarithms is due to the combined effort of Napier and Henry Briggs in 1624. Logarithms are useful in many fields from finance to astronomy. Moreover, because the logarithmic function log(x) grows very slowly for large x, logarithmic scales are used to compress large-scale scientific data.

Where does the word 'algebra' come from?

The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi.The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabr was to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation. In fact, the title has been translated to mean "science of restoration (or reunion) and opposition" or "science of transposition and cancellation" and "The Book of Completion and Cancellation" or "The Book of Restoration and Balancing."Jabr is used in the step where x - 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is "restored" or "completed" back to x in the second equation.Muqabalah takes us from x + y = y + 7 to x = 7 by "cancelling" or "balancing" the two sides of the equation.Eventually themuqabalah was left behind, and this type of math became known as algebra in many languages.

When and where was trigonometry first used?

The complex origins of trigonometry are embedded in the history of the simple word "sine," a mistranslation of an Arabic transliteration of a Sanskrit mathematical term! The complex etymology of "sine" reveals trigonometry's roots in Babylonian, Greek, Hellenistic, Indian, and Arabic mathematics and astronomy.Its origins lie in the world of astronomy and spherical triangles. Before the sixteenth century, astronomy was based on the notion that the earth stood at the center of a series of nested spheres. To calculate the positions of stars or planets, one needed to use concepts we now refer to as trigonometry.

The earliest uses of trigonometric functions were related to the chords of a circle, and the recognition that the length of the chord subtended by a given angle x was (in modern terms) 2sin(x/2). The Greek astronomer and mathematician Hipparchus produced the first known table of chords in 140 BC. His work was further developed by astronomers Menelaus (ca. AD 100) and Ptolemy (ca. AD 100), who relied on Babylonian observations and traditions.Babylonian and Greek influences mingled with rich native mathematical developments in India around AD 500 to produce a trigonometry closer to its modern form.

Solve the following integral: ∫(2x^3 + 5x^2 - 3x + 4) dx

Remember to use the power rule for integration and follow the steps to find the antiderivative of the function.

Fully explain how you would go about finding a soution in a way that a struggling classmate could understand and learn from you method.

Subject: Writing in Mathematics

Explain in detail how to add rational expressions when denominators are the same. Give an example with your explination.

Please present the problem as if you are explaining what you did to a classmate that was absent or one who doesn't understand the concept. Then fully explain how you would go about finding the solution. Please explain all steps in a way that a struggling classmate could understand and learn from your methods.

Question: In your own words, describe a step-by-step approach for solving algebraic word problems.

Imagine I gave you an airplane ticket that leaves tomorrow for anywhere in the world. Answer the following questions in 1 paragraph, and make sure your sentences match the tenses of the questions.

1) Where will you go?

2) What will you be doing while you are on the airplane?

3) What time does your flight leave tomorrow?

4) When are you arriving at your destination?

5) By the time you come back to HCMC, what will you have done during your trip?

Being successful in mathematics requires understanding as opposed to simple memorization. For example, the formula to find the perimeter of a rectangle is P = 2L + 2W (where L is length and W is width). Memorizing the formula could be helpful, but if we understand that the perimeter is the distance around the rectangle, we are able to construct the formula and apply it to real-world situations correctly.

Find another formula that you use in your daily life, and explain the meaning behind it.

Being successful in mathematics requires understanding as opposed to simple memorization. For example, the formula to find the perimeter of a rectangle is P = 2L + 2W (where L is length and W is width). Memorizing the formula could be helpful. However, if we understand that the perimeter is the distance around the rectangle, we are able to construct the formula and apply it to real-world situations correctly.

Choose another math concept that you have learned. Share your understanding of the concept in your own words.

Communication is considered an important component of mathematics education in order for deep learning to occur. Choose a specific algebra concept that you think you understand well, and explain it in your own words. Then, present a math problem for your classmates to solve, making use of this concept.

What would you say to someone who has a great balance in their schedule at college?

Basics of education?

Explain why a feather falls at the same rate as a hammer on the moon

What strategic plan for yourself to begin planning for a job after graduation? Include your: value proposition, targeted organization, objectives, strategies, the internal and external factors that may affect your plans. 

Balance the following chemical equation: 

Fe + O2 -> Fe2O3