The tutor shows a conversion from early Math 10 Pre-Calc. Herein, I use the abbreviations oz for ounce and lb for pound. Example: Convert 1013 ounces to pounds and ounces. Solution: Realize that 16 oz=1 lb. Divide 1013 by 16 …
The tutor points out how to convert an exponential function mx to ekx. Often, when thinking of an exponential function, one might imagine the form y=e^(kx) However, y=m^x is also exponential, since the independent variable is the exponent. How do …
Exponential equations: converting to base e form Read more »
The tutor investigates numbers that have both whole number square and cube roots. Numbers that have both a whole number square root and cube root are rare. 64 is one: 64^(1/2)=8, while 64^(1/3)=4. 729 is next: 729^(1/2)=27, while 729^(1/3)=9. The …
The tutor continues about subtracting mixed numerals. Past grade 10, mixed numerals are not much found in academic math. They are common, however, in trades math, including entrance exams. In yesterday’s post I talked about subtracting mixed numerals by borrowing, …
Math: subtracting mixed numerals: the improper fraction method Read more »
The tutor shows a method of subtracting mixed numerals. Imagine facing a question such as the following: 5 1/7 – 2 2/3 A convenient approach is “number minus number, fraction minus fraction”: 5-2 + 1/7-2/3 The trouble here is, 1/7 …
The tutor explains the concept of “closed” in math. If a set is closed under a certain operation, the result you get is still in the set. For instance, the even numbers are closed under addition: when you add two …
Continuing about Pythagorean triples, the tutor considers the isosceles case. In my previous post I discussed all-integer solutions to the Pythagoras equation a^2 + b^2 =c^2 Such solutions are often called Pythagorean triples. Presently we consider the possibility of Pythagorean …
Math: Are there (integer) Pythagorean triples with two equal sides? Read more »
The tutor gives a few integer solutions to a2+b2=c2. All-integer solutions to a2+b2=c2 are called Pythagorean triples. They are comparativeley rare. Here are three sets I know: 3,4,5 5,12,13 8,15,17 From the sets above, infinitely more can be generated: multiplying …
The tutor delves deeper into when integer solutions can be expected for Ax+By=C. In my dec 16 post I discussed finding integer coordinates for a linear equation in the form Ax+By=C. I pointed out that not always can integer solutions …
Math: linear diophantine equations: integer solutions to Ax+By=C Read more »
The tutor considers a problem most students encounter sometime…. When graphing a line on a page, fraction or decimal coordinates are inconvenient. An estimate is better than nothing, but one would like to avoid decimals or fractions when possible. In …