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Solvers

Numeric Equation Solver

prompts you for the equation and the values of the variables. You then

select the variable you want to solve.

Example

For the following equation shown, solve for the variable

Reminder:

If you have already defined variables, the solver will assume those values.

Num-solv

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Math Tools

Содержание MathPrint TI-30X Pro

Страница 1: ...TI 30X Pro MathPrint Scientific Calculator Guidebook This guidebook applies to software version 1 0 To view the latest version of the documentation go to education ti com eguide...

Страница 2: ...for special collateral incidental or consequential damages in connection with or arising from the purchase or use of these materials and the sole and exclusive liability of Texas Instruments regardle...

Страница 3: ...Variables 10 Math Functions 13 Fractions 13 Percentages 15 Scientific Notation EE 16 Powers Roots and Inverses 17 Pi symbol Pi 17 Math 18 Number Functions 19 Angles 21 Rectangular to Polar 23 Trigonom...

Страница 4: ...on 62 Constants 63 Conversions 64 Complex Numbers 67 Reference Information 70 Errors and Messages 70 Battery Information 74 Troubleshooting 75 General Information 76 Online Help 76 Contact TI Support...

Страница 5: ...mathematical expressions and functions along with other instructions The answers are displayed on the Home screen The TI 30X Pro MathPrint screen can display a maximum of four lines with a maximum of...

Страница 6: ...is inserted in front of the cursor location Placeholder box for empty MathPrint template Use the arrow keys to move into the box MathPrint cursor Continue entering in the current MathPrint template o...

Страница 7: ...ut key to enter a number in scientific notation format The result displays in the numeric notation format selected in the mode menu FLOAT 0 1 2 3 4 5 6 7 8 9 Sets the decimal notation mode Float float...

Страница 8: ...mple Square root example Square root example Cube root example Cube root example Multi Tap Keys A multi tap key is one that cycles through multiple functions when you press it Press to stop multi tap...

Страница 9: ...a menu and return to the Home screen press s h key with a single menu RECALL VAR 1 x 0 2 y 0 3 z 0 4 t 0 5 a 0 6 b 0 7 c 0 8 d 0 d key with multiple menus MATHS NUM DMS R P 1 4n d Un d 2 lcm 3 gcd 4...

Страница 10: ...moves the cursor to the history Press from an input or output in history to paste that expression back to the cursor position on the edit line Press from the denominator of a fraction in the expressi...

Страница 11: ...are both displayed Examples ans 3 V 3 V 3 3 c i Note The variable ans is stored and pastes in full precision which is 13 digits Order of Operations The TI 30X Pro MathPrint calculator uses Equation Op...

Страница 12: ...the input expression Note End of expression operators and Base n conversions such as 4Bin angle conversion 4DMS 4Pfactor and complex number conversions 4Polar and 4Rectangle are only valid in the Hom...

Страница 13: ...Matrix Numeric Solver Polynomial Solver and System Solver Clears an error message Clears characters on entry line J Deletes the character at the cursor When the cursor is at the end of an expression i...

Страница 14: ...cted variable If this variable already has a value that value is replaced by the new one z is a multi tap key that cycles through the variable names x y z t a b c and d You can also use z to recall th...

Страница 15: ...The first one measures 350 metres by 560 metres the second one measures 340 metres by 610 metres What volume of gravel does the company need to extract from each excavation to reach a depth of 150 met...

Страница 16: ...cubic metres to reach a depth of 150 metres and extract 41 16 million cubic metres to reach a depth of 210 metres 150 V z z 210 V z z For the second excavation the company needs to extract 31 11 milli...

Страница 17: ...value can display within the limits of the fraction format supported by the calculator and no decimal value was entered in the input expression If decimal numbers are used or calculated in a fraction...

Страница 18: ...sion brackets may be displayed to clearly indicate how it was interpreted and calculated by the calculator If it is not what you expected copy the input expression and edit as needed Classic Mode or C...

Страница 19: ...ue of the percentage Example 2 _ V 150 Problem A mining company extracts 5000 tonnes of ore with a concentration of metal of 3 and 7300 tonnes with a concentration of 2 3 On the basis of these two ext...

Страница 20: ...t key to enter a number in scientific notation format A number such as 1 2 x 10 4 is entered in the calculator as the number 1 2E 4 Example 2 E 5 Note Enters 2 x 105 using the calculator E notation q...

Страница 21: ...lue In complex number modes a bi and r q calculates the square root of a negative real value c Calculates the xth root of any non negative value and any odd integer root of a negative value a Inverts...

Страница 22: ...d Un d Converts between simple fractions and mixed number form 2 lcm Least common multiple Syntax lcm valueA valueB 3 gcd Greatest common divisor Syntax gcd valueA valueB 4 4Pfactor Prime factors 5 su...

Страница 23: ...c entry and in MathPrint mode Syntax fnInt expression variable lower upper tolerance Classic mode syntax Examples 4n d Un d 9 P 2 d 1 lcm d 2 6 9 gcd d 3 18 33 4Pfactor 253 d 4 sum d 5 1 4 z V 2 prod...

Страница 24: ...mber Syntax fPart value 5 int Greatest integer that is the number Syntax int value 6 min Minimum of two numbers Syntax min valueA valueB 7 max Maximum of two numbers Syntax max valueA valueB 8 mod Mod...

Страница 25: ...rom decimal degrees to degrees minutes and seconds Choose an angle mode from the mode screen You can choose from DEGREE default RADIAN or GRADIAN Entries are interpreted and results displayed accordin...

Страница 26: ...2 d 1 31 d 2 45 d 3 T 26 d 1 54 d 2 38 d 3 d 6 The result is 39 degrees 26 minutes and 23 seconds Problem It is known that 30 p 6 radians In the default mode degrees find the sine of 30 Then set the c...

Страница 27: ...ssary before starting calculations 1 P Rx Converts polar to rectangular and displays x Syntax P Rx r q 2 P Ry Converts polar to rectangular and displays y Syntax P Ry r q 3 R Pr Converts rectangular t...

Страница 28: ...Y Z multi tap keys Pressing one of these multi tap keys repeatedly lets you access the corresponding trigonometric or inverse trigonometric function Set the Angle mode Degree or Radian before your ca...

Страница 29: ...the length of the hypotenuse c Lengths are in metres Round results to one decimal place Reminder tan A 7 3 therefore m A tan 1 7 3 m A m B 90 180 therefore m B 90 m A c 3 7 2 2 Note Set mode to DEGREE...

Страница 30: ...calculations Example Set floating decimal q X X X 5 T 2 X X X X Logarithm and Exponential Functions D C multi tap keys D pastes the natural logarithm ln of a number to the base e The argument of the...

Страница 31: ...pastes the numerical derivative template from the keypad to calculate the numerical derivative with the default tolerance H is 1EM5 Example A A z F T 5 z M 1 To change the default tolerance H and obse...

Страница 32: ...point f x f x f x 2 As H becomes smaller the approximation usually becomes more accurate to approximate the slope of the tangent line at the given point x Because of the method used to calculate the...

Страница 33: ...modify the tolerance as needed for an investigation of the numerical integral result Example in DEGREE Angle Mode d MATH 8 fnInt with optional tolerance q d 8 0 3 z G 5 Classic Mode or Entry In Classi...

Страница 34: ...regression equations share the same variables a b c and d If you perform any regression calculation the regression calculation and the 2 Var statistics for that data are stored in the StatVars menu u...

Страница 35: ...s values for r2 and r 7 QuadraticReg Fits the second degree polynomial y ax2 bx c to the data It displays values for a b and c it also displays a value for R2 For three data points the equation is a p...

Страница 36: ...n for a given area under the normal distribution curve specified by mean mu and standard deviation sigma It calculates the x value associated with an area to the left of the x value 0 area 1 must be t...

Страница 37: ...l y values Sx Both Sample standard deviation of x Sy 2 Var Sample standard deviation of y sx Both Population standard deviation of x sy 2 Var Population standard deviation of y Gx or Gx2 Both Sum of a...

Страница 38: ...ing frequencies expressed as percentages or parts that add up to 1 However the sample standard deviation Sx is undefined for non integer frequencies and Sx Error is displayed for that value All other...

Страница 39: ...the following scores Tests 2 and 4 were given a weight of 0 5 and tests 1 and 3 were given a weight of 1 Test No 1 2 3 4 Score 12 13 10 11 Weight 1 0 5 1 0 5 1 Find Anthony s average grade weighted av...

Страница 40: ...error Find Anthony s new average grade v v v 12 13 10 11 1 5 1 5 u 2 Anthony has an average v of 11 33 to the nearest hundredth On the calculator n represents the total sum of the weights n 1 0 5 1 0...

Страница 41: ...he braking distance required for a vehicle travelling at 55 kph A hand drawn scatter plot of these data points suggest a linear relationship The calculator uses the least squares method to find the li...

Страница 42: ...sion for the following data 1 2 3 4 5 5 8 11 14 17 Clear all data v v Data 1 2 3 4 5 5 8 11 14 17 Regression s u Press to examine all the result variables Regression Example 2 Calculate the exponentia...

Страница 43: ...tistical or regression calculation Examine the table of values of the regression equation I 1 0 1 Warning If you now calculate 2 Var Stats on your data the variables a and b along with r and r2 will b...

Страница 44: ...th 20 trials and a success probability of 0 6 Enter the x values in list L1 store the results in L2 and then find the sum of the probabilities and store in the variable t Clear all data v v Data 3 6 9...

Страница 45: ...n and r non negative integers The order of objects is important as in a race displays a menu with the following options rand Generates a random real number between 0 and 1 To control a sequence of ra...

Страница 46: ...advertises that it makes 25 flavours of home made ice cream You like to order three different flavours in a dish How many combinations of ice cream can you test over a very hot summer 25 H H 3 You ca...

Страница 47: ...set an operation and then recall it 1 Press n 2 Enter any combination of numbers operations and or values 3 Press to store the operation 4 Press m to recall the stored operation and apply it to the la...

Страница 48: ...isits will it take Currently you have 0 points n T 35 0 m m m m m m m m After 8 visits to the store you will have 280 points which is enough for your download Data Editor and List Formulas v Pressing...

Страница 49: ...elect the appropriate menu item to add or edit a list formula in the highlighted column or clear formulas from a particular list When a data cell is highlighted pressing L is a shortcut to open the fo...

Страница 50: ...m the elements in a list and store to a variable for further investigation Example L1 v v 4 v 1 P 4 2 P 4 3 P 4 4 P 4 Formula v v j Fill a list with a sequence v 3 g z 1 4 1 Store the Sum of L1 to the...

Страница 51: ...ia M1 C Montreal Canada 4 C Convert these temperatures from degrees Celsius to degrees Fahrenheit See also the section on Conversions Reminder F 9 5 C 32 v v 4 v 5 8 M 1 4 v 1 9 W 5 V v 1 T 32 If Sydn...

Страница 52: ...a function table 1 Press I and select Add Edit Func 2 Enter one or two functions and press 3 Select the table start table step auto or ask x options and press The table is displayed using the specifi...

Страница 53: ...ng close to x 18 the point 18 324 appears to be the vertex of the parabola since it appears to be the turning point of the set of points of this function To search closer to x 18 change the Step value...

Страница 54: ...es Problem Find the intersection of the lines f x L2x 5 and g x x 4 I 1 M 2 z T 5 z U 4 2 1 Select Auto The two lines intersect at x y 3 L1 Matrices In addition to those in the Matrix MATH menu the fo...

Страница 55: ...editable 6 I3 3 3 identity matrix not editable t MATH t displays the matrix MATH menu which lets you perform the following operations 1 Determinant Determinant of a square matrix Syntax det squarematr...

Страница 56: ...52 Math Tools Define A t Set dimensions Enter values 1 2 3 4 det A s t t Transpose t t Inverse s t t rref t...

Страница 57: ...tor can be 1 dim 3 1 u Definable vector u 2 v Definable vector v 3 w Definable vector w 4 Ans Last matrix result Ans row column or last vector result Ans dim n Not editable Note Cell values can be tog...

Страница 58: ...IT menu which lets you define or edit vector u v or w Note Press r to toggle the number format in a cell as needed Example Define vector u 0 5 8 Define vector v 2 3 Calculate u v DotP u v and norm v D...

Страница 59: ...Equation Solver prompts you for the equation and the values of the variables You then select the variable you want to solve Example For the following equation shown solve for the variable b Reminder I...

Страница 60: ...hand sides of the equation evaluated at the solution This difference gives how close the solution is to the exact answer Polynomial Solver prompts you to select either the quadratic or the cubic equa...

Страница 61: ...oggle the number format of the solutions x1 x2 for quadratic or x1 x2 and x3 for cubic System of Linear Equations Solver solves systems of linear equations You choose from 2 2 or 3 3 systems Notes x y...

Страница 62: ...Solve 1 3 2 3 37 90 x y 2 5 1 5 28 75 x y Sys solv 2 2 system Enter equations 1 P 3 2 P 3 37 P 90 2 P 5 U 1 P 5 28 P 75 Solution Change number format if needed r Change number format if needed r Exam...

Страница 63: ...cients 5 M 2 3 M 9 4 3 5 4 2 4 M 2 14 Note For 3x3 notice that the first equation must be entered as 5x M2 3z M9 Solution Note Press r to change the number format if needed Example 3 3 System with Inf...

Страница 64: ...d base 1 8 Hex Converts to hexadecimal base 16 2 8 Bin Converts to binary base 2 3 8 Dec Converts to decimal base 10 4 8 Oct Converts to octal base 8 Base Type displays the TYPE menu which lets you de...

Страница 65: ...0000 2 4 o 8 Dec Boolean Logic displays the LOGIC menu which lets you perform boolean logic 1 and Bitwise AND of two integers 2 or Bitwise OR of two integers 3 xor Bitwise XOR of two integers 4 xnor B...

Страница 66: ...es parameters Pressing from a populated home screen expression pastes the content to Expr If the cursor focus is in history the selected expression will paste to Expr when is pressed If variables x y...

Страница 67: ...isplays an abbreviated name next to the character of the constant The UNITS menu has the same constants as NAMES but the units of the constant show in the menu Note Displayed constant values are round...

Страница 68: ...6208 10M19 Coulombs u atomic mass unit 1 66053904 10M27 kilograms atm standard atmosphere 101325 Pascals H0 permittivity of vacuum 8 85418781762 10M12 Farads per metre m0 permeability of vacuum 1 2566...

Страница 69: ...itres L 4 gal US litres to US gallons gal UK 4 L UK gallons to litres L 4 gal UK litres to UK gallons oz 4 gm ounces to grams gm 4 oz grams to ounces lb 4 kg pounds to kilograms kg 4 lb kilograms to p...

Страница 70: ...urs to Joules J 4 cal Joules to calories cal 4 J calories to Joules hp 4 kW horsepower to kilowatt kW 4 hp kilowatt to horsepower Pressure Conversion atm 4 Pa atmospheres to Pascals Pa 4 atm Pascals t...

Страница 71: ...er results a bi rectangular complex results r q polar complex results Notes Complex results are not displayed unless complex numbers are entered To access i on the keypad use the multi tap key g Varia...

Страница 72: ...lex result in polar form Valid only at the end of an expression 5 4a bi Displays a complex result in rectangular form Valid only at the end of an expression 6 conjugate Returns the conjugate of a comp...

Страница 73: ...Conjugate conj 6 5 U 6 g g g Real real 7 5 U 6 g g g Math Tools 69...

Страница 74: ...lower limit is greater than upper limit in summation or product function Bad Guess This error is returned when the variable entry for the solve for variable in Numeric Solver is outside the lower and...

Страница 75: ...n a distribution is invalid Expression is too long This error is returned when an entry exceeds the digit limits For example pasting an expression entry with a constant that exceeds the limit A cheque...

Страница 76: ...ed when no function is defined and a function evaluation is attempted Define functions in I List Dimension 1 dim list 50 This error is returned when in v the SUM LIST function is executed on an empty...

Страница 77: ...ver algorithm cannot return a solution due to a point at which the function is not defined Statistics This error is returned when a statistical or regression function is invalid For example when a cal...

Страница 78: ...ocal regulations How to Remove or Replace the Batteries The TI 30X Pro MathPrint calculator uses two 3 volt CR2032 batteries Remove the protective cover and turn the calculator face downwards Remove t...

Страница 79: ...uctions to make sure that certain calculations were performed properly Check the batteries to ensure that they are fresh and properly installed Change the batteries when does not turn the unit on or t...

Страница 80: ...TI Support education ti com ti cares Select your country for technical and other support resources Service and Warranty Information For information about the length and terms of the warranty or about...

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