Manual / Guide · 1974
TI SR-50 Owner's Manual
Texas Instruments' owner's manual for the SR-50 scientific calculator.
Manual / Guide · 1974
Texas Instruments' owner's manual for the SR-50 scientific calculator.
slide rule calculator pep TABLE OF CONTENTS DESCRIPTION . Features . Daplay Description . Battery Operation DATAENTRY . . . Negatve Number Enery. Scientific Notation . Error Correction. ARITHMETIC OPE RATIONS Addition and Subtraction , Multiplication and Division Error Correction =. " SPECIAL FUNCTIONS Squares , Square Roots Reciprocals . Factoriats . TRIGONOMETRIC AND HYPERBOLIC CALCULATIONS. Trig Function Calculations Hyperbole Function Calculations . LOGARITHMIC CALCULATIONS POWERS AND ROOTS Powers : Roots. . . MEMORY USE . COMPLEX CALCULATIONS . Sumof Products. . Intermediate Results Product of Sums Calculation Examples SAMPLE PROBLEMS . Business . Architecturat Eng neering ‘ Chemical Engineering Civil Engineering. Electrical Engineering Mechanical Engineering Metric Unit Conversions CONVERSION TABLES GENERAL FORMULAS SPECIAL FORMULAS. REGISTER LEVEL PROCESSING SERVICE INFORMATION BS SBSLKSSSSELL SSVRR BN B38 SECTION 1 DESCRIPTION Your SR-50 Slide Rule Calculator is designed for use by scientists, engineers, and students who require accuracy and reliability in a portable scientific calculator. The SR-5SO is a powerful computational tool capable of processing a wide range of problems from simple arithmetic to complex scientific calculations. Your SR-5O has been designed with state-of-the-art MOS solid state circuitry, constructed with high quality components throughout, and assembled with precise workmanship. Features Algebraic Entry — The SR-50 uses the aigebraic entry method to simptify data entry into the calculator. For simple problems, the numbers and algebraic functions are entered into the calculator in the same sequence as they are stated aigebraically. For example, the problem of adding 15 to 25 and then subtracting 30 is normally stated as: 25+ 15—30= 10 and is entered into the SR-50 as: 25 (4115 (= 30 (=)10 Toll-Free Telephone Assistance For assistance with your SR-50 calculator, call one of the following toll-free numbers if necessary: 800-527-4980 (within all continental states except Texas) 800-492-4298 (within Texas) See inside back and back cover for further information on service. Sover photo background courtesy of The Bettmann Archive, Inc. 1 Sum of Products — The SR-50 provides sum-of-product capability without use of special keys. For example, the expression: (2 X 3) + (4 X §) + (6 X 7) = 68 is entered into the SR-50 as: 2003 (414 x) 5 (416 0) 7 (=) 68 Similar catculations, such as sum (or difference) of quotients, powers, roots, factorials, etc., are entered in the same straightforward manner. Accuracy — Calculates answers to 13 significant digits and displays answers rounded off to 10 significant digits. The displayed number is accurate to within +1 in the tenth displayed digit. For maximum accuracy, the SR-50 uses ail 13 significant digits for subsequent calculations. Versatility — Performs simple arithmetic, reciprocals, factorials, exponentiation, roots, trigonometric, hyperbolic, and logarithmic functions, all in full floating decimal point or in scientific notation. Scientific Notation — Computes and displays numbers as large as +9.999999999 X 1099 and as small as +1,000000000 X 10-9? Automatically converts answers to scientific notation when the calculated answer is greater than 10!° or tess than 1071. Automatic Clearing — The SR-50 calculator automatically clears itself. When the [=] key is pressed to complete the evaluation of an expression, the calculation is completed, the answer is dispiayed, and the calculator is cleared for the start of a new problem. It is not necessary to press the clear key between problems. Calculation Time — Most calculations except large factoriais are performed in less than a tenth of a second. Memories — Three data r yne memory register for data storage. Fully Portable — Extremely lightweight. Battery or AC ated Long Life — Solid state components, integ Battery Pack — The fast-charge rechargeable battery pack, model BP-1. Under t the battery pack e 4 to 6 hours 3-50 comes complete with a ours of recharging d directly f xa ts Services Facility as liste et AC Adapter/Charger — Battery pack operation from standard t plished with th C Ada arg AC9200 included used with the SR-10 and SR-11) ) harged; it can t Display Description er-on indication and numerica’ isplay provides indication of a negative t, overflow and error mantissa Minus Sign — Appears to the left of the 10-digit mantissa to indicate negative numbers, and appears to the left of the exponent (right of mantissa) to indicate negative exponents. Decimal Point — Automatically assumed to be to the right of any number entered unless placed in another position with the (> ]key. When entering numbers, the decimal will not appear until (2 ] is pressed. Overflow and Error Indication — The display will flash for the following reasons: 1. Entry or calculation result outside the range of the calculator, +1. X 10799 to 19.999999999 X 1099. 2. Factorial of any value except a positive integer. 3. Inverse of a trig function with a nonvalid value for the argument, such as arcsin 1 with n greater than 1. 4. Square root or logarithm of a negative number. 5. The SR-5O uses the logarithm equation fog y* = x log y in processing the [¥*] and [#4] functions. Since the log of a negative number is invalid, the SR-50 considers as invalid raising a negative number to any power or taking the root of a negative number. Indication Removal — The flashing display caused by overflow or error will continue during subsequent calculation until the [C ] key is pressed. Battery Operation The fast-charge nickel-cadmium battery pack BP-1 furnished with the SR-50 calculator was fully charged at the factory before shipping. However, due to sheif life discharging, it may require charging before initial operation. With the battery pack properly instatied in the bottom of the SR-50, charging is accomplished by plugging the AC Adapter/Charger AC9200 into a convement outlet and Plugging the atteched cord into the SR-50 socket. The SR-50 can be used while it is being charged. A full charge requires about 3 hours with the power switch off and about 6 hours with the switch on for norma! operation. Do not attempt to operate the SR-5SO with the charger plugged in wrtless the battery pack is in place or the calculator operation will be erratic. Note: When batteries become discharged, calculator operation may become erratic with random flashing of display digits shortly before display fades away. Attach SR-5O to charger and allow batteries ta recharge for a moment before resuming use. If the SR-50 is left on for an extended period of time after the batteries become discharged, one of the batteries may be driven into reverse charge. This con- dition is indicated by failure of the calculator to operate after being recharged for a few minutes. The battery can usually be restored to operating condition by charging the calculator overnight. Repeated reverse charging will permanently damage batteries. SECTION 2 DATA ENTRY On/Off Switch — Located on the top right front surface of the calculator. Sliding it to the right applies power, and sliding it to the left removes power from the calculator, The power-on condition is indicated by a number in the display. Note: After turning the calculator on and before performing the first calculation, press the [€] key. (8) through [9] Digit Keys — Enter numbers 0 through 9 10 a limit of a 10-digit mantissa and a 2-digit exponent. [=] Decimal Point Key — Enters a decimal point. (Ce) Pi Key — Enters the value of pi (m) to 13 significant digits (3.141592653590); display indicates value rounded off to 10 significant digits (3.141592654). [E€] Enter Exponent Key — Instructs the calculator that the subsequent number is to be entered as an exponent of 10. After the [££] key has been pressed, the calculator will display ail further results in scientific notation until the (E] key is pressed. [2 Change Sign Key — Changes the sign of the number appearing in the display. [CE] Clear Entry Key — Clears the last keyboard entry. (E] Clear Key — Clears (erases) information in the caiculator and display and sets the calculator to zero for the start of a new problem. The contents of the memory are not affected by this key. Negative Number Entry A negative sign is assigned to a number by pressing the key directly after entering the number. For example, to enter —125: Enter Press Display 125 as 125 Scientific Notation Any number can be entered into the SR-50 in scientific notation — that is, as a number (mantissa) multiplied by 10 raised to some power (exponent). For exampie 1000 can be written as 1. X 10°. Enter Press Dispiay 1 (#€] 1 00 3 1 03 Note: The last two digits on the right side of the display are used to indicate exponents. Very large and very small numbers must be entered in scientific notation. For example, 120,000,000,000 is written as 1.2 X 10!!. Enter Press Display 1.2 (ee) 1.2 00 W 2 49 In both these examples, the exponent indicates how many places the decimal should be moved to the rigért. If the exponent is negative, the decimal should be moved to the left. For exampie 1.2 X 10-'! = 0.000000000012. Enter Press Display 1.2 a3) 1.2 00 " #4 12-11 To change the mantissa or its sign after the [EE] key has been pressed, simply press the key and make the appropriate entry on the keyboard. To change the exponent or its sign, simply press the [££] key again and make the appropriate entry. Enter Press Displsy Remarks 1.327 [t€) 1.327. 00 21 1.32724 ET 13271021 To change mantissa 65 ito —1.32765 21 (@) -1.32765 21 To change exponent 22 BE = -1.32765 -22 Data in scientific notation form may be entered intermixed with data in normal form. The calculator will convert the entered data for proper calculation. For example: 12575 + 3.2 X 10° + 2855 = 1.863 X 10°. Enter Press Display 12575 x3 12575. 3.2 {ee} 3.2 00 3 ca 3.2 03 2855 = 1863 04 Error Correction Incorrect number key entries are corrected by pressing the [G£] key before pressing the next function key in the calculation. Example: 3X & 5=15 Enter Press Dispiay Remarks 3 Go 3. 4 4, Error (e] 0. Correction 5 [=] 15. Pi is entered as a calculated value and is not cleared by this key, If the L#] key is inadvertently pressed, it can be nullified by simply entering the correct number. For exampie, in entering 2.395, the [# ] key might be pressed accidentally instead of the [9 ]key. Enter Press Dispiay Remarks 23 2.3 (=) 3.141592654 Error 2.395 2.395 Correction ARITHMETIC OPERATIONS (4) Add Key — Adds to the previous entry or result the next entered quantity. (=) subtract Key — Subtracts from the previous entry or result the next entered quantity. [X] Multiply Key — Multiplies the previous entry or result by the next entered quantity. [4) Divide Key — Divides the previous entry or result by the next entered quantity. [=] Equats Key — Completes the calculation of all the previously entered data and algebraic functions. This key is used to obtain both intermediate results and final results, Performing arithmetic calculations with your SR-50 calculator is simple and direct. Numbers and functions are entered in the same sequence as the expression is written. The following examples illustrate the operation of the calculator. Addition and Subtraction Example: 12.32-7+16=6.92 Enter Press Display 12.32 i) 12.32 7 Cf) 5.32 16 =] 692 Multiplication and Division Example: (4 X 7.3) +2= 146 Enter Press Display 4 3) 4. 7.3 & 29.2 2 =) 14.6 Error Correction The SR-50 has been designed to facilitate correction of the most common function key errors. If a[4_ key is inadvertently pressed instead of a [| = ] key (or vice versa), the error is corrected by sirnply pressing the correct function key. Example: 5 # —2=3 Enter Press Display Remarks 5 <3) 5. Error © 5. Correction 2 f= 3. The calculator automatically inserted a zero to complete the erroneous function key entry. Thus, the above key sequence is calculated as 5 + O — 2 = 3. The sequence §(—] [+] 2[=] is calculated as 5 —O+2=7. if a (XJ or (#)key is pressed instead of any other arithmetic operator key, the error is corrected simply by pressing the correct key. ” Example: 5 # +2=7 Enter Press Display Remarks 5 {) 5. Error ik) 5. Correction 2 3) % In this case, the calculator completes the erroneous function by inserting a one before entering the [+] function. Thus, this key sequence is calculated as (5+ 1) + 2= 7. The key sequence 5[_ [+ /2 [S]is caiculated as (5 X 1) + 2=7. Note: An accidental double entry of any arithmetic operation key is automatically corrected because the SR-5O inserts a zero between two (+ J or [=] operations and a one between two [X] or [+] operations. (fa (+) or (=) key is inadvertently pressed instead of a DO or +] key, you can correct the error by pressing the (=) key and then the correct function key. Example: 5 # X2=10 Enter Press Display Remarks 5 | S Error 2 & 10. Again the calculator automatically inserts a zero after the [+] key but the [=] has to be pressed to complete the erroneous [+ ] function because of the sum of products capability. Thus, the above sequence is calculated as (5 + 0) X 2= 10. If the [=] key had been omitted, the calculator would have calculated the data as § + (0 X 2) = 5. 12 Pressing the |=] key immediately after any arithmetic operation key effectively replaces the arithmetic operation by an [=] function. Thus, 5 [+] 2 (+ ] [=] is calculated as 5 +2+0=7 and §(X]2[X) |=] is calculated as 5X 2X 1= 10. Thus, the =] key can be used to complete any arithmetic operation key that was erroneously pressed. SPECIAL FUNCTIONS The special function keys operate only on the quantity displayed, either a number entry or a calculated result. They do not complete any previously entered function. [*] Square Key — Finds the square of the number displayed (that is, multiplies the number displayed by itsetf). [4] Square Root Key — Finds the square root of the number displayed (that is, finds the number which multiplied by itself, equats the number displayed). (We) Reciprocal Key — Finds the reciprocal of the number displayed (that is, divides the number displayed into 1). (a?) Factorial Key — Finds the factorial of the number displayed (that is, the product of all integer numbers from one through the integer value displayed). The largest factorial the SR-5O can compute without an overflow condition is 69! Squares Example: (4.2)2 = 17.64 Enter Press Display 42 t#) 17.64 13 Square Roots Example: VES =25 Enter Press 6.25 {#) Example: 4+ /9=5 Enter Press 4 we) 9 (4) &) Reciprocals 1 xample: —— = 1 E Se 0.3125 Enter Press 3.2 () Factorials Example: 7! = 5040 Enter Press 7 2) 14 Disptay 25 Display Display 0.3125 Display 60 Example: ra =25 Enter Press Display 60 & 60. 4 2) 24 =) 25 When the factorial of a noninteger number is computed, only the whole number is considered and the display flashes indicating the fractional part was ignored. The [€] key must be pressed to remove the flashing condition of the display. Example: 7.3! = 5040 Enter Press Display Remarks 73 G)> © oso40: Flashing display The 13 internal digits of a calculated result are rounded off for the displayed 10 digits. This means that a displayed integer may actually have a rounded off fractional portion. Because of this, if the “2?] key is to be used on a calculated result, the [f€] key should be pressed immediately before the [x] key, After the [EE] key is pressed only the 10 displayed digits will be processed by the factorial function, and not the full 13 internal digits. Exampie: iJon =6 Enter Press Dispiay 9 Le] 3. (ee. 3 0 (st 6. 00 15 TRIGONOMETRIC AND HYPERBOLIC CALCULATIONS The [sa], [cos], {ten}, and [are] keys are used in determining both trigonometric and hyperbolic functions. These keys Operate on the displayed data as soon as the key is pressed. They do not affect any other previously calculated result. To obtain a trig function, the argument is entered (through the keyboard or as a prior calculated result) and then the function key is pressed. The angle for trig functions is selected as degrees or radians by the setting of the Deg/Rad switch. Deg/Rad Switch — Located on the top left front surface of the calculator. The calculator interprets a displayed angle as being in degrees if the switch is to the right (D) and in radians if it is to the teft (R). (0/8) Angle Change Key — If the Deg/Rad switch is set for degrees, pressing the key instructs the calculator to convert the displayed angle from radians to degrees. If the switch is set for radians, pressing this key instructs the caiculstor to convert the displayed angle from degrees to radians. (If the key is pressed a second time the calculator will assume that the displayed radian quantity is in degrees and will convert this quantity to radians. To switch back to degrees, set the Deg/Rad switch back to D and press the 0/8) key.) [sa] Sine Key — Determines the sine of the displayed angie. [ces] Cosine Key — Determines the cosine of the disployed angie. [tan] Tangent Key — Determines the tangent of the displayed angle. 16 (hye) Hyperbolic Function Key — Determines the hyperbolic function of the displayed quantity when pressed before the (sin), [c08], or [149] key. [a] Inverse Trigonometric and Hyperbolic Key — Determines the angle of the selected trig function whose value is the displayed quantity, when pressed before the [ue], [ces]or [tan] key. When both the [2] and [tye] keys are pressed before the[sia] , {cos} or [tan] keys, they instruct the calculator to determine the inverse hyperbolic function of the displayed quantity. Trig Function Calculation The SR-50 will calculate trig values for angles greater than 360 degrees (2n radians) or tess than —360 degrees (~2r radians). As long as the trig function is displayed in normal form rather than in scientific notation, al! 10 displayed digits are accurate for the range of —36000 to 36000 degrees (—200z to 200x radians). In general, the accuracy decreases one digit for each decade outside this range. If the magnitude of the angle is 1.001 X 1014 degrees or larger, the SR-50 interprets it as 0 degrees. The value of pi entered by the Le | key or used in converting from degrees to radians is correct to 13 digits only. Asa result, inaccuracies in the 3 nondisplayed digits can occur that result in trigonometric values closer to zero than 10-10. Any answer less than 10-10 should be interpreted as zero. Throughout the manual, the notation Angle: Deg means set the Deg/Rad switch to D and Angle: Rad means set the Deg/Rad switch to R. Example: sin 30” =0.5 Angle:Deg Enter Press Display 30 [sa] os Example: cos == 05 Angie: Deg Enter Press Display C=) 3.141592654 3 & 1.047197551 om 60. [cos] 0s Example: 14.3 tan 1.385 = 76.0783255 Aagle: Rad Enter Press Display 143 Co) 14.3 1.385 —_[tan| (=) 76.0783255 Example: arcsin 0.5 = 30” Angie:Deg Enter Press Display Os [are] (sie) 30. Example: = + arctan 1 = 1570796321 Angie: Red Enter Press Display C) (+) 3.141592654 4 @ .7853981634 1 (we) (ta](=] = 1.570796327 18 Hyperbolic Function Calculations Exampie: tanh 6.43 = 0.9999943 Enter Press Display 643 (nye) [tan] 0.9999948 To calculate inverse hyperbolic functions, the reiative order of pressing the [ae ]and [ays]does not matter, but both must be pressed before the/ sin |,[cos], or [tan key. Example: arcsinh .886 = 0.7984245338 Enter Press Display 886 [we] [nvej[se]0.7984245338 Alternate method: Enter Press Display 886). ove [wei [we] 0.7984245338 LOGARITHMIC CALCULATIONS The logarithmic function keys provide for processing of logarithmic quantities to base ¢ or base 10. The log keys process only the displayed number, either an entered quantity or a calculated result. [te] Common Logarithm Key — Determines the logarithm to the base 10 of the displayed number. [In] Natural Logarithm Key — Determines the logarithm to the base ¢ of the displayed number, [e]e to the x Power — Raises the value of e to the displayed power. 19 Example: In 5.4 = 1.686398954 Enter Press Display 54 (ins) 1.686398954 Example: 31.78 + 4 In 19.3 = 43,62042038 Enter Press Display 31.78 <3] 31.78 4 Gd 4. 19.3 (irae) 2.960105096 (=) 43.62042038 Example: e3-8 = 44.70118449 Enter Press Dispiay 3.8 irl] 44.70118449 Example: log 1573 = 3.196728723 Enter Press Display 1573 (tee) 3.196728723 The antilog of a number can be easily calculated using the [*]key described below since antilog x = 10*. POWERS AND ROOTS These two-variable function keys process two numbers in a single operation. The numbers can be a keyboard entry, a calculated result, a stored quantity, or a combination of these. [¥*] ¥ to the X Power Key — Raises a number to a power. [54] The xth Root of Y Key — Finds the root of a number. | Exchange Key — Exchanges the x and y values entered for the functions [7*] and #4] . The #:7] key also exchanges the two operands in division. In both [¥*] and [74] the first quantity entered is the value assigned to y. The second value is entered as the value of x. After the second value is entered, the values for x andy can be exchanged by pressing the #9] key. Powers Example: (8)3 = 612 Enter Press Display 8 iE a3} 8. 3 t=) 612. Example: (2)3+4 = (2)7 = 128 Enter Press Display Remarks 3 (cz 3. 4 E14) ¥; 2 2 = 7. Exchange x and y f=) 128. Example: Antilog 3.19673 = 10*'**? = 1573.004626 Enter Press Display 10 LF 2) 10 3.19673 (=) 1573.004627 21 To determine the antilog of a calculated quantity (already in the display), the[¥* and #:9] keys are used: Enter Press Display 3.19673 (z5] 3.19673 10 ey 3.19673 = 1573.004627 Example: 34.7 + (8.7)2-6 = 311.8724475 Enter Press Display 34.7 (2), 34.7 8.7 5) 8.7 26 [=] 311.8724475 The following complex functions can be calculated easily with the SR-50: y1/*, yVX, ysin x, yin x, etc, Example: 4.2! 3.7 = 6537587302 Enter Press Display 4.2 (y*} 4.2 3.7 (ina) 1.30833282 {= 6.537587302 Roots Example: "3/48 = 3.342194507 Enter Press Display 48 (4) 48 13 (=) 3342194507 22 Example: “2/215 + 6.86 = 8995187378 Enter Press Display 215 (a) 215. 4.7 <3) 3.135187378 5.86 [=] 8.995187378 MEMORY USE The memory keys allow data to be stored and retrieved for additional flexibility in calculation. (SQ Store Key — Stores the displayed quantity in the memory. Any previously stored quantity is cleared. {Ri Recall Key — Retrieves stored data from the memory. The REt) key does not clear the memory. [2] Sum and Store Key — Algebraically sums the displayed number to the number in memory, and stores the result in memory. The use of this key does not affect the displayed quantity nor the previously calculated data. The memory may be used to store a constant for iterative calculation, or to store a calculated result for subsequent additional calculation. 23 Example: 3.7 (2.14396)3 + 9.7 (2.14396)2 + 13.3 = 94,3496219 Enter Press Display 2.14396 SIojly*) 2.14396 3 6-3) 9.854850386 3.7 (+7 Rey) 2.14396 GAb0 = 4.s96564482 9.7 +) 81.0496219 13.3 [=] 94.3496219 The memory is used to store the results of the [2] key. This result can then be recalled for subsequent calculation. The [€] key does not erase the contents of the memory. Therefore, either the first quantity should be entered using the STO key, or a zero should be stored before entering the first quantity using the [2] key. Exampie: —19.95 + 118.80 — 13.94 — 37.50 — 2.98 + 15.35 — 44.29 = 134.15 — 118.66 = 15.49 In order to retain the credit and debit amounts, each positive item will be summed to memory as the items are entered to be aigebraically accumulated. This summed credit arnount will then be subtracted from the net amount to yield the debit amount. Enter Press 19.95 BF)T+) 118.80 §16(=) 13.94 [=] 37.50 [=] 208 (+) 15.35 (2)(-) 44.29 (=) ea (=) Display —19.95 98.85 84.91 4741 44.43 59.78 15.49 134.15 —118.66 Remarks Net amount Credit amount Debit amount To sum a negative quantity to the above credit amount, enter the number, press [4] key, and then press "3 ] key. Example: Reduce the above credit amount by 60.10. Enter Press 50.10 = [##-) ie 3) fret) Display —50.10 —80.10 84.05 Remarks Change sign Sum Check result SECTION 3 COMPLEX CALCULATIONS Sum of Products The SR-50 has been designed to calculate sum of products and similar problems in a straightforward manner. Included in this category are sum and difference of products, quotients, powers and roots. Calculations such as these are the most common applications of a calculator memory, In the SR-50, a separate register (the Z register) has been dedicated to this use. This permits computation of this type of problem without use of special memory keys. Example: 2X3 + 4X5 = 26 Enter Press Display 2 oq) 2. 3 <2) 6 4 8) 4 5 &) 26. Example: 1/2 — 3/4 = —0.25 Enter Press Display 1 & 1. 2 eI 05 3 ic) 3. 4 & 0.25 Example: 25 — 23 = 24 Enter Press Display 2 (ys) % 5 Cs] 32, 2 [ys] = 3 = 24, Example: 6 + 4/625 = 7 Enter Press Display 8 Ca) 8. 3 <3] 2 625 wi] 625. 4 &) 7. All of the single function keys on the SR-50 (logarithmic, trigonometric, factorial, etc.) operate onty on the displayed quantity; they do not complete any prior instruction. Thus, the sum of products capability can be extended to these functions. Example: sin 30 cos 60 + cos 30 sin 60= 1 Angle: Deg Enter Press Display 30 (ee) 3) 05 60 fees) 0.25 60 (se) [=] + Example: 22 X 32 + 42x 52 = 436 Enter Press Display 2 Gg 4. 3 ir) 36. 4 i Ba) 16. 5 ee 436. Although all of the preceding examples have used the minimum number of quantities (4) for illustration pruposes, the sum of products capability of the SR-50 is not limited to these simple applications. x 3 ¢ 2x32 x4, YBIxs _, Example: 5 10 4 Enter Press Display 2 0x] pi 3 C+] 6. 4 x3] 1.5 2 [Fa 2. 3 Gd 8. 4 32. 5 cs 79 81 areal 81. 4 x) 3. 5 15. 10 f=) 9.4 Intermediate Results In the preceding problems; the [+] or [=] key always completes a prior [x ],(+], [¥*) or [74] command, but the reverse is not true. Thus to caiculete (2X3+4)X5=50 it is necessary to complete the expression within the parenthesis — just as you would do to solve the problem manually. This‘is done by pressing the [=] key. Enter Press Display 2 ea) 2. 3 =) 6. 4 oa 10. 5 3) 50. Notice that it is necessary to use parentheses to write this problem in a single line. The [=] key essentially performs the close parenthesis function. A general rule of when the [=] key should be pressed to obtain an intermediate result is: Write the expression in a single line (no complex fractions) using parentheses. Press the [=] key for every close parenthesis. With a little practice, it is easy to learn when the [=] key does not have to be pressed for a close parenthesis (such as when the next function is a [+] or [=] key). Examples of when the [=] key should be_used include: sin (a +b), cosh (a X b), (a — b)2, and \/a/. Note that the last example involves the quantity a divided by b even though the expression is usually written without parentheses. Similarily, the expression (2 X 3 + 4)/5 is frequently written on two lines without parenthesis as: 2X3+4 5 Again, with a little practice, it often is not necessary to rewrite the expression to determine when the [=] key should be used to obtain an intermediate result. Product of Sums As mentioned previously, the SR-50 was designed to facilitate calculation of the frequently encountered sum of products type of problem, As a result, solving the much rarer product of sums. is not as direct and requires use of the memory. Example: (2 + 3) X (4 +5) = 120 Enter Press Display 2 2. 3 (=) S19 5. 4 4. 5 60 9. 4 Example: = =-0.2 a+ Enter Press Display 4 cs) 4. 6 (=) S19 10. 2 © 2. 4 f=) 2. key [=] 0.2 In this problem, the numerator could have been calculated first and stored in the memory, but another step would be required. The [#:¥] key would have to be pressed before the final [=] key. Alternate solution Enter Press Display 2 tsJ 2 4 [=] S19) -2, 4 3) 4 6 3) 10. Ret) 7} [=) -0.2 In general, it is shorter to calculate the denominator first. In some cases, the [i] key can be used instead of the memory. 2x3 2+3 =%42 31 Enter Press Display 2 ca 2. 3 t=) 5. [We] DE] 0.2 2 Gd 04 3 (= 1.2 A variation of the product of sums occurs in equations using nested parentheses. Example: ((3+7)2+6)4+5=109 Enter Press Display 3 (4 = § 7 16a 10. 2 Ce) 20, 6 [31,090 26, 4 (¥) 104, 5 tf 109. Note that the problem is solved sterting with the innermost set of parentheses and working outward. This is true regardless of the order in which the problem is stated. For example, the preceding problem can be written as: 5+4(6+2(3+7))= 109 The problem would obviously be solved in the same order as shown above, Calculation Examples 2X3+ 4X5 Example: exe 7 0-619087619 Enter Press Display 3 Ga 3. 4 Ee 12. 5 od 5. 6 [=] [st9} 42. 2 ie-4) 2 3 3] 6. 4 ica} 4. 5 (=) 26. rea} (=) 0619047619 (2#3)-K (4+5) Example: Fay x ere)” 0-0044158844 Enter Press Display 3 is) 3. 4 [=] sro % 5 <2) ; 6 (160 11. fe [=) St} 77. 2 <2) 2. 3 Si) 5. Ret (=) Sto) .0649350649 4 4) 4 5 (=100 9. aa (=) 5844155844 SECTION 4 SAMPLE PROBLEMS Your SR-50 calculator is a useful and versatile problem- solving too!. To improve your understanding of its versatility, it is recommended that you use your SR-50 to step through the sample problems in this section. A wide range of problems from several disciplines has been included. Several problems are included to illustrate certain data manipulation and procedural techniques that are quite useful in problem solving. An understanding of the steps as presented can aid you in solving other problems. Business Accumulated Amount — If $15,000 is invested at 74% interest compounded annually, what will be the accumulated amount at the end of eight years? An=P(1+i)" = 15,000 (1 + .0775)8 = $27,253.95 Enter Press Display 1 2) a 0775 (=) Lvs) 1.0775 8 ea) 1.816930146 15000 3) 27253.95219 Present Value — What is the present vaiue of the future amount $35,570 in 13 years? The interest rate is 6.3% compounded quarterly. A P= i\ na 1+— (3) a 35570 ( 063 ) 13X4 t+t— 4 = $15,782.24 Enter Display 1 4, 063 0.063 4 1.01575 13 1.225261544 4 -4436952589 35570 15782.24036 Sinking Fund — If a fixed investment of $3500 is made at the end of each successive year for nine years at an interest rate of 7.25% compounded annually, what will be the accumulated amount of the sinking fund? 14) - Pep A ital (1+ .0725)9 - 1 0725 = 36500 X = $42,361.18 Enter Press Display 1.0725 (5) 1.0725 9 (=) 1.877481679 1 (=) (+) «8774816789 0725 oa 12.10319557 3500 =) 42361.1845 Investment Decisions — A decision must be made for a capital equipment investment. What is the maximum recommended purchase price Q of a machine with projected earnings for five years of $1200, $1500, $1750, $1300, and $900. Assume a value of zero after five years. Use an interest rate of 6.25%. RI R2 R3 —— + W4+n (g4en2 (end Omax = R4 Fi RS (44 (1408 + _ 1200_ , _1500_, __1750 (1.0625) (1.0625)2 (1.0625) pO. 900 (1.0625)4 = (1.0625)5 = $5601.84 Please note the use of the [#25] exchange key in the processing of this example. Each denominator is processed before division is performed. The numerator of each quotient is entered as the divisor. Pressing the 9) key prior to the next function key exchanges the numerator and denominator values before the division is performed. Enter Press Display 1.0625 519) 1.0625 1200 =) >) 1129.411765 Rc) (+) ~—-1.12890625 1500 fey) F] 2458.131488 RCL) |7*) 1.0625 3 (=) 1,199462891 1750 &yj 3917.117851 Rev [y*] 1.0625 4 3] 1.274429321 1300 ACs) 4937.182265 Rea] (7*] 1.0625 5 Ce) 1.354081154 900 @y =] 5601.839622 Boating Sailboat Ratings — What are the measured rating, MR, and the rating, R, of a boat with the dimensions given below? sail area, S = 256.8 sq. ft. length, L = 22.375 ft. beam, B= 7.917 ft. draft, D = 3.750 ft. draft correction, DC = 0.350 fr. freeboard correction, FC = 0.275 ft. engine and propeller factor, EPF = 0.9975 center of gravity factor, CGF = 1.0125 7 Measured rating, 013L 5 & MR = +0.25L+0.20\S+DC+FC VBxXD 0.13 X 22.375 X 256.8 = + 0.25 X 22.375 VT917 X 3.750 + 0.20 X /256.8 + 0.350 + 0.275 = 17.979 feet Enter Press Display 797—id 7.917 3.75 [=] ] [Me] [X] .1836287234 13 it -3) 0.023858734 22.375 |X] 5338391741 256.8 i) 8.554762355 25 Px 0.25 22.375 (e} 14.14851235 2 ea) 0.2 256.8 (@)(+) 17.35350845 35 cz 17.70350845 276 2~C«CS) 17.97850845 Rating, R = MR X EPF X CGF = 17.979 X .9975 X 1.0125 = 18.158 feet Enter Press Display 17.979 [x] 17.979 9975 ica 17.9340525 1.0125 {=] 18.15822816 Velocity Made Good — A sail boat sails an effective course into the wind by tacking back and forth at an angie to the wind. If the wind velocity and boat velocity are drawn as vectors, the component of boat velocity directly into the wind is the velocity made good, VMG. Using the vector diagram and quantities shown, determine the VMG of the boat. Va Vy Vw = apparent wind velocity, 17 knots Vg = boat's true speed, 9 knots a= apparent angie of wind, 28” This problem can be solved using vector equations. Each upper case V represents a vector and each lower case v represents a vector magnitude. Va=—-Vw Vx + Vy = Va x ti vy = VA vy =a sina = 17sin 28 = 7.981016567 Vx = Vg COS a = 17 cos 28 = 15.01010908 VD = %x — YB = 15.01010908 —9 = 6.010109079 VT =vp + ivy = Tb = 6.010109079 + j 7.981016567 =V(6.010109079)2 + (7.981016567)* 6010109079 = 9.990897687 /53.01840377° VMG = vg cos b = 9 cos §3.01840377 = §.414026187 knots Enter 7 7 6.010109079 Navigation Press [sin] [=] S19) ea) es) (S1) f=) (CT et) (=I L4] a+) (=) [ere] [tan] [eos] (X] f=) Display ¥2; 7.981016567 17. 15.01010908 6.010109079 7.981016567 9.990897687 7.981016567 53.01840377 6015584653 5414026187 Remarks os bet 3 ‘5 my, VMG The wind triangle used in flight planning problems consists of three vectors and six factors as shown in the following diagram. a Vector Heading Velocity AB TC, True Course PGS, Predicted Ground Speed AC WD, Wind Direction WV, Wind Velocity cB TH, True Heading TAS, True Air Speed In preflight plans, the known data are true course, wind direction, wind velocity, and true air speed. True Heading — Find the true heading of a planned flight if the following data are known: TC = 40°, WD = 105”, TAS = 120 mph, WV = 47 mph. TH = TC — arcsin [WV sin (WO — TC)/TAS] = 40 — arcsin [47 sin (105 — 40)/120} = 19.20836054" Angie: Deg Enter Press Display 105 Ee) 105. 40 (= } (eel 3c] 0.906307787 47 ic 42.59646599 120 = | [arc] (sin) oe [4] —20.79163946 40 = 19.20836054 Predicted Ground Speed — For the flight plan in the previous problem, determine the predicted ground speed. PGS = WV cos (WD — TC) + ViWv cos (WD — TC)]2 — (wv)2 + (TAS)? = 47 cos (105 — 40) + V[47 cos (105 — 40)] 2 — (47)2 + (120)2 = 132.0483563 mph 42 Angle: Deg Enter Press Display 105 (J 105 40 El ieG9 4226182617 47 E1s9G5-) 394.5410851 47 fle] —1814.458915 120 (S141) eeu =) 132.0483563 Drift Correction — During a flight it is determined that the plane is 12 miles off course. If the distance flown is 136 miles and the remaining distance is 68 miles, determine the angle for a parallel course, the correction angle to coverge at destination, and the total correction t0 converge on the destination. Parallel course, eee a= arc sin 126 = 5.062092964" Angle:Deg Enter Press Display 12 =| 12. 136 [=] [we] [se] S10} §.062092964 43 Correction angie, wae b= arc sin ry = 10.16424862" Angle:Deg Enter = Press Display 12 [+] 12. 68 [=] lore] [sie] 10.16424862 Total correction c=bta = arc sin — + arcsin ALE 6 136 = 10.16424862 + RCL = 15.22634159” =15° 13’ 35” The decimal degrees can be converted to minutes by multiplying the fractional portion of the degrees by 60. The resulting decimal minutes can be converted to seconds by multiplying the fractional portion of the minutes by 60. Enter Press Display 10.16424862 [+ )[Rci)(-] 15.22634159 15 (2160 .226341586 60 | 13.58049516 13 (10) -5804951576 60 [=] 34.82970946 Remarks Degrees Minutes Mathematics Combinations — Find the number of ways in which six differently colored biocks can be arranged using any number at a time. D=n! [1+ + : + : + + L =n St} +... + uaisn (n— 1)! 1 1 1 1 1 D=6! ee Ww 2 St 4! St Display 1. 2. 25 2.666666667 2.708333333 2.716666667 1956. Combinations With Fixed Arrangements — What is the number of combinations of 35 marbies taken 6 at a time? nt cin, r= rlin—s)! 35! 61 (35 — 6)! = 1,623,160 ¢ (35, 6) = 45 Enter Press Display 35 (es) 35 6 (=) 7) ]~=—s«-8. 841761994 30 6 rane 6.366068635 33 35 wf) 1623160 Mean Variance, and Standard Deviation — Find the mean, variance, and standard deviation for the values 3, 5, 3, 7, 4. 1 “gta esy +e =44 Variance (unbiased) 2 =x\? rx-nee OM =) N-1 N-1 as asaseenean_s( : 4 ebegszst =28 Standard Deviation (unbiased) a= Jot =/28- = 1673320053 46 All three of these values can be determined in a single calculation, The values of x are summed in the memory and the values of x2 are summed in the z register. Enter Press Dispiay Remarks 3 S10 Ca") [+0 9. 5 GG wu, 3 C3) fe) Ge) 43. 7 (3) fe) Ce) 92. 4 =) 108. ke 22. Exchange x & with memory 5 eS 44 Mean Ce") 64 GO) 19.36 5 (2) eo 3 Ge} 41.2 4 &} 2.8 Variance (#) 1.673320053 Standard deviation To calculate the biased variance and standard deviation, the denominator of the variance equation is N instead of N — 1. In this example, 11.2 would be divided by 5 to yield a biosed variance of 2.24 and a biased standard deviation of 1.496662955. The biased and unbiased expressions converge, of course, for large values of N. 47 Poisson Distribution — If the average value of occurrences of an event during time interval T is 2.5, find the Probability of 5 occurrences during T. 5 P (5) =e-2.5 t=—| 5! P (5) = 06680 or 6.68% Enter Press Display 25 (¥*) 25 5 cs 97.65625 5 (=) 120 ba 8138020833 25 (=) [=] ~— 0668009428 Physics Thrown Object — If a bail is thrown upward with a velocity of 86 feet per second, what is its velocity and height at the end of 1.75 seconds? Use g = 32.2 feet per sec2, Velocity, v=vo—gt = 86 — (32.2) (1.75) = 29.65 ft/sec Enter Press Display 86 (=) 86. 32.2 [x] 32.2 1.75 {=] 29.65 48 Height, 1 = ane ge? t $= Vo! 27% = (86) (1.75) - (92.2) (1.75)2 = 101.19 feet Enter Press Display 86 Go 86. 1.75 e 150.05 32.2 Bo 32.2 1.75 fe) 98.6125 2 f= 101.19375 Gas Pressure — The internal pressure of a tank of gas is 1300 psi at room temperature. What is the internal pressure if the temperature rises by 25°C (from 298°K to 323°K)? Pi T2 Pos 2 Ty 1300 X 323 298 = 1409.060403 psi Enter Press Display 1300 ic3) 1300. 323 ie] 419900, 298 f& 1409.060403 Density of Gas — What is the density of helium gas ina tank at a pressure of 125 atm at room temperature, 298" K? The universal gas constant is 8317 nt m/kg’K, the atomic mass of helium is 4.004, and 1 atm = 1.013 X 105 nt/m2, 49 P= 125 atm R = 8317 nt m/kg’K M = 4.004 T= 298°K PM o-— RT _ 125 X 1.013 x 105 x 4.004 8317 X 298 = 20.4564638 Kg per m2 Enter Display 125 126. 1.013 1.013 5 1.26625 4.004 5.070065 8317 6.096026211 298 S&S 2.04564638 Coordinate Conversion — Convert the rectangular 00 07 07 03 o1 coordinates x = 35.6, y = 18.4 to the polar form A #. A= Jx2+y2 = Ji35.6)2 + (18.412 =401 Angle:Deg Enter 35.6 18.4 18.4 35.6 Press Display (a) 2) 1267.36 (=) (=) [@) 40.07393168 18.4 (=) [ae] [4s] 27.33235949 Remarks A Convert the polar coordinates 141 /76.5° to the rectangular form (x, y), x=Acos@ = 141 cos 76.5 = 32.9157963 vy=Asing = 141sin 76.5 = 137.1041588 Angie: Deg Enter Press 76.5 S10) (cos) OC) 141 t=] 141 (ic) fey) (sie) [=] Disptay .2334453639 32.9157963 137.1041588 Architectural Engineering Duct System — What are the pressure losses in a 3000 fpm