07Mar 2014 by Vincent Summers 2 Comments

More High School Math

Mathematics
[caption id="attachment_5627" align="alignright" width="400"] Calculations[/caption] The most practical math for people to understand is undoubtedly high school math, rather than college math. After all, how much calculus is used when you go grocery shopping, get your plumbing fixed, or you go skiing on the weekend? High School Math You've got to love it. Here's the first high school math problem. Problem 1: Simplify the mathematical expression: (x-2y3)4 (x-3y4)-2 Simplifying the first parenthetical expression, we get (x-8y12) It is the powers we multiply when powers are raised to powers. Doing similarly with the second parenthetical expression, we get for that (x6y-8) The equation now reads, (x-8y12) (x6y-8) When we multiply numbers, we add and subtract powers. This gives, (x-2y4) [Answer] ------------------------- Problem 2: 2/10 divided by n equals 3-1/2. What does…
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07Mar 2014 by Vincent Summers No Comments

Secondary School Math Problems Plus Solutions

Mathematics
[caption id="attachment_5613" align="alignright" width="480"] Fractal[/caption] For some, it's actually fun when they come across secondary school math problems plus solutions. It's because they are no longer accountable, since they graduated years ago. Math Problems Plus Solutions Problem 1: Find the slope intercept form of the line passing through the point (– 1, 5) and parallel to the line – 6x – 7y = – 3. The line given is rewritten (in slope-intercept form, y = mx + b) as y = – 6/7 x + 3/7 Thus the slope m = – 6/7 Now two lines are parallel if they have the same slope. So, y = – 6/7 x + b is the formula for the new line, with the intercept not yet solved. We do so by inserting…
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07Mar 2014 by Vincent Summers No Comments

Eight Middle and High School Math Problems with Solutions

Mathematics
Not only current students. but old-timers as well will find these middle and high school math problems informative. Middle and High School Math Problem 1: Leaves from a tree were reported by four different European students to be 2.9 cm, 3.33 cm, 3.9 cm, and 3.12 cm in length. List the numbers in order of decreasing length. For the beginner, the easiest way to evaluate which of these number is smaller and which is larger, is to make the number of digits to the right of the decimal the same. Now the maximum number of such digits here is two. Adding zeros to the right of the last digit does not change a number’s value. When that is done, the numbers become: 2.90, 3.33, 3.90 and 3.12 In decreasing order,…
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04Mar 2014 by Vincent Summers 2 Comments

Sample High School Math Problems with Answers

Mathematics
[caption id="attachment_5578" align="alignright" width="440"] Fractal - CCA Share Alike 3.0 Unported by Wolfgang Beyer[/caption] Want some sample high school math problems with answers? Well then here you go! High School Math Problems Problem 1:     A change purse has 100 nickels and dimes. The total value of the coins is $7. How many coins of each type does the purse contain? If the number of nickels is N and the number of dimes is D, then 5N + 10D = 700 (the 5, 10 and 700 representing the number of cents) However, N + D = 100 (the number of nickels plus the number of dimes equals 100) So, solving for N for both equations, we get as the result N = – 2D + 140 and N = 100 – D…
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03Mar 2014 by Vincent Summers No Comments

Propane and Oxygen Combustion Question

Chemistry
[caption id="attachment_16612" align="alignright" width="480"] Propane[/caption] Problem: We desire to learn how much oxygen is needed to completely consume a certain quantity of propane gas. Our hydrocarbon and oxygen combustion question follows the basic reaction path, C3H8 + 5 O2 → 4 H2O + 3 CO2 If we have the following conditions: Temperature = 75 Celsius (348 Kelvin) Pressure = 720 / 760 mm = 0.95 atm Moles propane = 40.8 grams / 44.1 grams molecular weight = 0.93 moles How Much Oxygen to Burn the Propane? What volume of oxygen is needed to accomplish the burning of the 0.93 moles of the hydrocarbon? 5 times 0.93 moles of C3H8 burned = 4.65 moles of oxygen The ideal gas law reads: PV = nRT where P= the pressure, V= the volume, and…
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28Feb 2014 by Vincent Summers 1 Comment

Vintage Movies: Will They Disappear?

The Arts
[caption id="attachment_5554" align="alignright" width="380"] A young Lionel Barrymore.[/caption] Vintage movies - what will become of them? The previous few generations were the first to enjoy movies and television. Video added another dimension previously unknown in recorded entertainment. First there were the silents. Not offering speech, rather than presenting films in dead silence, musical accompaniment, perhaps by an organist, was provided. Later, approximately 1927, “talkies” began to feature human speech. A New Era Black and white films experienced tremendous growth in quality of cinematography, although some of the actors--those with a background in the silents—over-dramatized their characters. In the late 1930’s, basically black-and-white films had embedded within them a few scenes in color. Of course, in time, most motion pictures were entirely filmed in color. Moving On Up Larger screens and…
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24Feb 2014 by Vincent Summers No Comments

Math Equations for Parallel and Perpendicular Lines

Mathematics
It's fun and very instructive to figure out the math equations for parallel and perpendicular lines. The basic mathematical equation for a line is, ax + by = c Here are three examples of line equations: 2x + 3y = 6 4x – 2y = –5 –x/3 + 2.47y = √3 Slope-Intercept Form One of the most useful formats for the equation of a line is the slope-intercept form. That form is written, y = mx + b The variables here are x and y. The letters m and b are constants that represent the rise or tilt of the line (slope, m) and the point at which the line crosses the y-axis (intercept, b). So the first of the three equations for a line listed above is written in…
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21Feb 2014 by Vincent Summers 1 Comment

Determining the Equation for a Line from Two Points

Mathematics
Lines can be drawn in three dimensions, but most analytical geometry courses stick to lines in two dimensions, generally using the Cartesian or XY coordinate system. The generic equation for a line may follow the form: y = mx + b where m is the slope (measure of tilt or steep-ness) of the line, while b is its intercept or intersection with the y-axis. Equation for a Line from Two Points A line can be determined and an equation derived from two points. In the Cartesian system, for instance, take two points, (2 , 3) and (– 1 , 5). The first number in each pair represents the x-value of a point and the second number in each pair represents the y-value. Writing these points into the general equation y…
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21Jan 2014 by Vincent Summers No Comments

Transition from Ice to Water to Vapor

Physics
[caption id="attachment_5490" align="alignright" width="440"] Hydrogen Bonding - CCA SA 3.0 Unported by Magasjukur2[/caption] The transition from ice to water to steam. What happens? A block of ice has a temperature well below freezing and is warmed gradually. It reaches above the boiling point. What transitions occur along the way? What are the processes? Transition: Solid to Liquid At first, the heat supplied simply increases the temperature of the ice. The temperature of the surface is somewhat warmer than the ice inside. It takes time for heat to penetrate. Eventually, the outer layer of the ice reaches the melting point. The outside ice melts first—then the inner ice. [caption id="attachment_5491" align="alignleft" width="220"] Melting Ice[/caption] During melting, the heat energy is spent breaking the stiff hydrogen bonds. None of it is spent…
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20Jan 2014 by Vincent Summers 1 Comment

Organic Chemistry: Pushing Electrons

Chemistry
Scientists desire to solve complex problems with exact precision, but sometimes it just is not practical. Simplifying is necessary. For the organic chemist, one form of simplifying is the idea of pushing electrons. To illustrate, high school physics instructors introduce the concept of massless strings and frictionless pulleys. No such things exist. Still, this fiction enables the beginning student to isolate what is important. Spark Notes informs us that college entrance examinations generally employ such contrivances. Constructs, Artifices, Contrivances Physicists are not the only ones to employ constructs and contrivances to simplify problems and arrive at an answer. The organic chemist must understand very complex compounds and the reactions leading to their formation. One of the best known contrivances is that of pushing electrons or pushing arrows. The great thing…
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