The tutor shows an example of a graph crossing its horizontal asymptote. A graph can’t cross a vertical asymptote because it’s undefined at that value of x. However, a graph can cross a horizontal asymptote. Consider, for example, the graph …
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The tutor defines cofactor (aka signed minor) with an example. In my post from Nov 24, 2014 I tell how to evaluate a determinant by hand. Example: Evaluate the determinant of matrix A: 1 0 -7 0 2 1 3 …
The tutor tells how to have Excel evaluate a determinant for you. Here’s how: Key in your matrix values. Let’s imagine you use the range a1:d4. Select a cell away from the range, let’s say f6. Key in =mdeterm(a1:d4) then …
Spreadsheets: finding the determinant of a matrix using Excel Read more »
The tutor explains a consequence of octal logic. Octal logic focuses on numbers in base 8. An octal number has the following form: p(20)+q(21)+r(22) which evaluates to p(1)+q(2)+r(4) where p,q,r have possible values 0 or 1 (“off” or “on”). The …
The tutor translates p→q to the boolean expression ¬A or B. In my beginning post about symbolic logic, I mention that the statement p implies q, also stated p→q, has the following truth table: p q p→q 0 0 1 …
Math: symbolic logic meets digital circuits: p→q means ¬A or B Read more »
The tutor shows the quadratic method (pka, characteristic equation) behind 2nd order LDEs w/ constant coefficients. An exponential function of the form y=ekt has the first derivative y’=kekt and second derivative y”=k2ekt Seeing an equation like, for example, y” -3y’ …
The tutor shows an example of how to solve a system of three equations using a spreadsheet. Example: solve the system -3x + 2y + z = 16 x – y – 3z = -19 2x + y + 7z …
Linear Algebra: solving a three-variable linear system with Excel or LibreOffice Calc Read more »
The MINVERSE() function can be tricky to use; the tutor tells how. Example: find the inverse of matrix A: -5 0 1 3 8 9 0 1 0 Solution: Enter the matrix in Excel or LibreOffice Calc. Let’s imagine, for …
Spreadsheets: Matrix inverse on Excel or LibreOffice Calc Read more »
The tutor shows an example of solving a three-variable linear system algebraically. Example: Solve the following system of equations: -3x + 2y + z = 16 x – y – 3z =-19 2x + y + 7z = 30 The …
Algebra: how to solve a system of three equations by hand Read more »
The tutor shows an example to find the equation of a quadratic function from three points. The method is to construct and solve a three-variable linear system. Example: Find the quadratic function that passes through the points (2,17), (6,5), and …
Math: finding a quadratic function from three points when you don’t know the vertex Read more »