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Showing posts from July, 2025

The love formula

$$\huge x^2+(\frac{5y}{4} -\sqrt {|x|})^2=1$$ Just playing around, off course any non graphics calculator cannot render the graph. But its a cute equation.

Using the DM15L for simple business calculations

 Although the DM15L is an advanced scientific calculator, and the venerable HP12C is still available, it can easily be used for basic business calculations. I guess it's like driving your Ferrari to buy milk around the corner. Just imagine how much fun buying milk is. So by basic business calculations I mean product margins etc., not financial calculations, I think the HP12C or DM12L is more suited. I have to admit, the HP10Bii Plus is so much more suited to business calculations than both the HP12C and DM15L, but if you can drive around in a Ferrari why bother with a Tata? In any business, you have to calculate margins (MU), gross profit (GP), VAT, or GST. It's all about percentages. The STO and RCL functions of the DM15L are ideal for storing and recalling these percentages that you use over and over. Let's setup a hypothetical situation. The following markups (MU) are used and stored in registers R1 to R9: R0: 15% VAT (1.15) R1: 35% (0.65) R2: 30% (0.70) R3: 25: (0.75) R...

Solving the exponent of exponent expression on the HP15C or DM15L

 Solving the equation below on a modern CAS or RPN calculator is quite easy, but doing it on the older HP15C or the latest DM15L is a little different. On an HP35s or HP Prime, even the HP50C enter the equation into the equation writer or solver, then solve for 'x' without thinking much. On the other hand the HP15C forces you to understand the flow of calculations and their relation to each other. In my opinion, a fundamental aspect missing in today's math's education. $$x^{x^2}=256$$ I posted this because I got it wrong and forgot the rules of exponents. A lot of people start from the bottom and work upwards to 'x', while the correct way is working from 'x' down to 2. So $$(x^x)^2 \ne x^{(x^2)} $$ Below is the program you can enter on the HP15C or DM15L (I assume the HP11C will work the same, even the venerable HP41 range, albeit with some changes in key selection. [f][PGRM] [g][P/R] [F][LBL][C] [2] [yx] [yx] [2][5][6] [-] [g][RTN] [g][P/R] To run the p...

Solving a cubic expression with two x variables.

 The first time a saw this expression it looked unsolvable and more like a riddle. That is to my layman's eyes off course. Experienced mathematicians solve it during a morning jog. Anyway, it looked challenging enough. Sometimes the simplest things are the hardest to solve. $$\large x^4 = 2^x $$ In order to solve this expression we need to set it to equal zero. $$\large x^4 - 2^x = 0 $$ [f][R↓]     [g][R/S] [f][SST]C [4][yx][X<>Y] [2][X<>Y][yx][-] [g][GSB] [g][R/S] There are actually two roots. With a little insight to your equation, you can get acurate solutions. To solve for the lower root we enter the following key sequence: [0][ENTER] [2][0] [f][SOLVE][C] First root is -0.8613 To find the second root change the range: [1][0][ENTER] [2][0] [f][SOLVE][C] The answer should be 16 Enjoy! Acknowledgment: I have to admit I got stuck with this small program for several months. After so many futile attempts I thought to get help from Edward Shore. He gracefull...

Solving a double exponent with one variable

 A double exponent equation that is easily solved with the DM15L. The short program stores the keystrokes in the number 2 on the keypad or R2 registry. $${2^3}^x=512$$ To solve for 'x' using a DM15L or HP15C enter the following keystroke program: [f][PRGM] .... (Clears program memory and starts at line 001) [g][P/R] .... (Starts program mode) [f][LBL][2] .... (Stores the program in numeric keypad 2) [3]  .... (The start of the equation with the first value) [yx] [2] [x<>y] .... (swap the x and y registry) (Key 34, third row from the top, fourth column) [yx] [5][1][2] [-]  .... (End of the equation) [g][RTN] [g][P/R] To run the program enter the following Enter a range between 1-5 that you guess the answer should lie  [1] ENTER [5]  .......(Don't press ENTER) [f] [SOLVE] ....... (Select the solver) [2] ....... (The program is stored in the number 2 button) Answer should be = 2, enjoy.

What is RPN keystroke programming

 RPN (Reverse Polish Notation) is a type of keystroke programming that is used in calculators and computer programs to perform mathematical operations. In RPN, instead of writing expressions in the traditional way (e.g. 2 + 3 = 5), the operands (i.e. the numbers) are entered first, followed by the operator (e.g. +). For example, to add 2 and 3 in RPN, you would first enter the number 2, then enter the number 3, and finally press the + key to perform the addition. The result of the calculation (5) would then be displayed. RPN entry [2] [ENTER] [3] [+] Algebraic entry [2] [+] [3] [=] The answer is given in the LCD panel as 5. There is no '=' (equal) sign. The calculation is done when you pressed '+'. The main advantage of RPN is that it eliminates the need for parentheses, which can be confusing and error-prone, especially for complex expressions. (10-5)(3+7x2)  = 85 RPN entry [7] [ENTER] [2] [*] [3] [+] [10] [5] [-] [*] Algebraic entry [7] [*] [2] [+] [3] [m+] ... Store ...

Solving linear equations with two points using the DM15L with STO and RCL

 The DM15L makes it very easy to solve a linear equations programmatically. A stored program makes it possible to calculate the slope and y intercept of many linear equations without re-entering all the calculation steps. A small easy program saves time and reduces the chance of calculation errors.   The standard form form for a linear equation is: $$ y=ax+c$$ If we have two points of the data set, the angle of the line can be calculated as: $$ a= \frac {y_2-y_1}{x_2-x_1}$$ When the slope of the graph is known, we can determine the y intersect c: $$ c= y_2-x_2a$$ That is all that is needed to solve the equation. Since the keystroke program will use STO and RCL, we must use registers 6-9 (R6-R9) for the variables and output. The following registers will be used for the various variables. R7: y2 R8: y1 R4: x2 R5: x1 R9: a R6: c Enter the following keystroke program: Keystrokes    Comment [f][PRRM]    Sets the program memory to line 000. [G][P/R]  ...

How to find the roots of a quadratic equation using the DM15L

 How to find the roots of a quadratic equation using the DM15L Polynomial expression are best solved by applying Horner's method (Page 79 in HP15C's Owners Manual). Since the DM15L is so incredibly fast, speed is not such an issue compared with the original HP15C. Repeated calls to the same copy of the <em>x</em> storage register is prevented, thus speeding up the calculation. You might not notice the different in quadratic polynomials but there is a difference in the cubic and fourth degree polynomials. The sample below is a simple quadratic expression and easy to solve with the DM15L. $$  3-x=2x^2 $$ That format is no good for the solver and must be set equal to zero. $$ 2x^2-3+x=0 $$  Still not right, the exponents must be removed for optimal speed of the processor. Not that it really matters on the DM15L, but it is much more efficient. $$  x(2x+1)-3=0$$  The short keystroke program follows: [f][R↓] [g][R/S] [f][SST][0] [2] [×] [1][+] [×] [3]...

Not a DM15L Review

  This is not a review, I don’t write reviews because I don’t know how. This is an opinion written late one night from the sofa. I just felt I had to write my opinion of this calculator because it is such an icon. It is amazing that SwissMicros had the genius to revive it in all its glory. I bought a DM15L, not because I need it for work, but because I’m nostalgic and love calculators. My collection and what I paid for each calculator is testament how many times I’ve slept here, on this particular sofa, alone, in the dark, with no music playing to break the tension of my diminishing investment capital for my retirement. If you love the HP15C and want to relive the 80’s and the way math's was done, buy one on eBay. Don’t buy a DM15L because you want a HP15C! The DM15L is not a replacement for it. It is a copy. It does the same thing blindingly fast. But it is not as refined as the original. Yes, it is built like a tank, much more so than the original. It stays a very well made cop...