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44 Pages

### Ti83PlusSilverChapter2

Course: PHYSICS 001, Spring 2008
School: East Los Angeles College
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Word Count: 4959

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2: Chapter Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a...

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2: Chapter Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5. 1. Begin on the home screen. Press | to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press . Press 5 to enter the probability of heads. Press . Press 40 to enter the number of simulations. Press . TI-83 Plus Math, Angle, and Test Operations 61 2. Press to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on. 3. Press ~ or | to view the additional counts in the list. Ellipses (...) indicate that the list continues beyond the screen. 4. Press y L1 to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram (Chapter 12). Note: Since randBin( generates random numbers, your list elements may differ from those in the example. TI-83 Plus Math, Angle, and Test Operations 62 Keyboard Math Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length. + (Addition), N (Subtraction), (Multiplication), (Division) You can use + (addition, ), N (subtraction, ), (multiplication, ), and (division, ) with real and complex numbers, expressions, lists, and matrices. You cannot use with matrices. valueA+valueB valueAvalueB valueA N valueB valueA valueB Trigonometric Functions You can use the trigonometric (trig) functions (sine, ~; cosine, TM; and tangent, s) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example, sin(30) in Radian mode returns L.9880316241; in Degree mode it returns .5. TI-83 Plus Math, Angle, and Test Operations 63 sin(value) cos(value) tan(value) You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent, y A) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. sinL1(value) cosL1(value) tanL1(value) Note: The trig functions do not operate on complex numbers. ^ (Power), 2 (Square), ( (Square Root) You can use ^ (power, >), 2 (square, ), and ( (square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use ( with matrices. value^power L1 value2 (value) (Inverse) You can use L1 (inverse, oe) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1x. valueL1 TI-83 Plus Math, Angle, and Test Operations 64 log(, 10^(, ln( You can use log( (logarithm, ), 10^( (power of 10, y G), and ln( (natural log, ) with real or complex numbers, expressions, and lists. log(value) 10^(power) ln(value) e^( (Exponential) e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. e^(power) e (Constant) e (constant, y [e]) is stored as a constant on the TI-83 Plus. Press y [e] to copy e to the cursor location. In calculations, the TI-83 Plus uses 2.718281828459 for e. TI-83 Plus Math, Angle, and Test Operations 65 L (Negation) M (negation, ) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices. Mvalue EOSTM rules (Chapter 1) determine when negation is evaluated. For example, LA2 returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (LA)2. Note: On the TI-83 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press . p (Pi) p (Pi, y B) is stored as a constant in the TI-83 Plus. In calculations, the TI-83 Plus uses 3.1415926535898 for p. TI-83 Plus Math, Angle, and Test Operations 66 MATH Operations MATH Menu To display the MATH menu, press . MATH 2: 4Dec 3: 3 4: 3( 5: x 6: fMin( 7: fMax( 8: nDeriv( 9: fnInt( 0: Solver... NUM CPX PRB 1: 4Frac Displays the answer as a fraction. Displays the answer as a decimal. Calculates the cube. Calculates the cube root. Calculates the xth root. Finds the minimum of a function. Finds the maximum of a function. Computes the numerical derivative. Computes the function integral. Displays the equation solver. 4Frac, 4Dec 4Frac (display as a fraction) displays an answer as its rational equivalent. You can use 4Frac with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4Frac following value. TI-83 Plus Math, Angle, and Test Operations 67 value 4Frac 4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4Dec following value. value 4Dec 3(Cube), 3( 3 (Cube Root) (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices. value3 3( (cube root) returns the cube root of value. You can use 3( with real or complex numbers, expressions, and lists. 3(value) TI-83 Plus Math, Angle, and Test Operations 68 x x (Root) (xth root) returns the xth root of value. You can use x with real or complex numbers, expressions, and lists. xthrootxvalue fMin(, fMax( fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1L5). fMin(expression,variable,lower,upper[,tolerance]) fMax(expression,variable,lower,upper[,tolerance]) Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]). TI-83 Plus Math, Angle, and Test Operations 69 nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1L3). nDeriv( is valid only for real numbers. nDeriv(expression,variable,value[,H]) nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points. f ' ( x) = f (x + ) - ( f (x - ) 2 As H becomes smaller, the approximation usually becomes more accurate. You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-83 Plus can return a false derivative value at a nondifferentiable point. TI-83 Plus Math, Angle, and Test Operations 70 fnInt( fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1L5). fnInt( is valid only for real numbers. fnInt(expression,variable,lower,upper[,tolerance]) Tip: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s. TI-83 Plus Math, Angle, and Test Operations 71 Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers. When you select Solver, one of two screens is displayed. The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty. The interactive solver editor is displayed when an equation is stored in eqn. Entering an Expression in the Equation Solver To enter an expression in the equation solver, assuming that the variable eqn is empty, follow these steps. 1. Select 0:Solver from the MATH menu to display the equation editor. 2. Enter the expression in any of three ways. TI-83 Plus Math, Angle, and Test Operations 72 Enter the expression directly into the equation solver. Paste a Y= variable name from the VARS Y.VARS menu to the equation solver. Press y K, paste a Y= variable name from the VARS Y.VARS menu, and press . The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it. 3. Press or . The interactive solver editor is displayed. The equation stored in eqn is set equal to zero and displayed on the top line. Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed. The default lower and upper bounds appear in the last line of the editor (bound={L199,199}). TI-83 Plus Math, Angle, and Test Operations 73 A \$ is displayed in the first column of the bottom line if the editor continues beyond the screen. Tip: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor. Entering and Editing Variable Values When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable. You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration. You can store equations to any VARS Y.VARS variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions referenced in the equation. TI-83 Plus Math, Angle, and Test Operations 74 Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press or . 3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-83 Plus will attempt to display the solution that is closest to your guess. TI-83 Plus Math, Angle, and Test Operations 75 The default guess is calculated as (upper+lower) . 2 4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-83 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L199,199}. 5. Move the cursor to the variable for which you want to solve and press \ (above the key). The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen. Note: When a number continues beyond the screen, be sure to press ~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent. The values of the variables are updated in memory. TI-83 Plus Math, Angle, and Test Operations 76 leftNrt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to leftNrt= indicates that the equation has been evaluated at the new value of the variable for which you solved. Editing an Equation Stored to eqn To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation. Equations with Multiple Roots Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions. Further Solutions After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and leftNrt=diff disappear. Move the cursor to the variable for which you now want to solve and press \. TI-83 Plus Math, Angle, and Test Operations 77 Controlling the Solution for Solver or solve( The TI-83 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions. Using solve( on the Home Screen or from a Program The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is L199. The default for upper is 199. solve( is valid only for real numbers. solve(expression,variable,guess[,{lower,upper}]) expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format. TI-83 Plus Math, Angle, and Test Operations 78 MATH NUM (Number) Operations MATH NUM Menu To display the MATH NUM menu, press ~. MATH NUM 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd( CPX PRB Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor abs( abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices. abs(value) Note: abs( is also available on the MATH CPX menu. TI-83 Plus Math, Angle, and Test Operations 79 round( round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits. round(value[,#decimals]) iPart(, fPart( iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices. iPart(value) fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices. fPart(value) TI-83 Plus Math, Angle, and Test Operations 80 int( int( (greatest integer) the returns largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers. min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared, min( returns a list of the smaller of each pair of elements. If list and value are compared, min( compares each element in list with value. TI-83 Plus Math, Angle, and Test Operations 81 max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value. min(valueA,valueB) min(list) min(listA,listB) min(list,value) max(valueA,valueB) max(list) max(listA,listB) max(list,value) Note: min( and max( also are available on the LIST MATH menu. lcm(, gcd( lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, lcm( returns a list of the lcm of each pair of elements. If list and value are specified, lcm( finds the lcm of each element in list and value. gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, gcd( returns a list of the gcd of each pair of elements. If list and value are specified, gcd( finds the gcd of each element in list and value. TI-83 Plus Math, Angle, and Test Operations 82 lcm(valueA,valueB) lcm(listA,listB) lcm(list,value) gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) TI-83 Plus Math, Angle, and Test Operations 83 Entering and Using Complex Numbers Complex-Number Modes The TI-83 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes. a+bi (rectangular-complex mode) re^qi (polar-complex mode) On the TI-83 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer. TI-83 Plus Math, Angle, and Test Operations 84 Real mode a+bi mode \$ \$ Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed. Note about Radian Versus Degree Mode Radian mode is recommended for complex number calculations. Internally, the TI-83 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions. In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode. TI-83 Plus Math, Angle, and Test Operations 85 Interpreting Complex Results Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (re^qi) and Radian modes are set. Rectangular-Complex Mode Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is the real component, b is the imaginary component, and i is a constant equal to -1. To enter a complex number in rectangular form, enter the value of a (real component), press or , enter the value of b (imaginary component), and press y V (constant). TI-83 Plus Math, Angle, and Test Operations 86 real component(+ or N)imaginary component i Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to -1. To enter a complex number in polar form, enter the value of r (magnitude), press y J (exponential function), enter the value of q (angle), press y V (constant), and then press . magnitudee^(anglei) TI-83 Plus Math, Angle, and Test Operations 87 MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( 2: real( 3: imag( 4: angle( 5: abs( 6: 4Rect 7: 4Polar Returns the complex conjugate. Returns the real part. Returns the imaginary part. Returns the polar angle. Returns the magnitude (modulus). Displays the result in rectangular form. Displays the result in polar form. conj( conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers. conj(a+bi) returns aNbi in a+bi mode. conj(re^(qi)) returns re^(Lqi) in re^qi mode. TI-83 Plus Math, Angle, and Test Operations 88 real( real( (real part) returns the real part of a complex number or list of complex numbers. real(a+bi) returns a. real(re^(qi)) returns rcos(q). imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers. imag(a+bi) returns b. imag(re^(qi)) returns rsin(q). TI-83 Plus Math, Angle, and Test Operations 89 angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp<q<p. abs( abs( (absolute value) returns the magnitude (modulus), (real2+imag2) , of a complex number or list of complex numbers. abs(a+bi) returns (a2+b2) . abs(re^(qi)) returns r (magnitude). TI-83 Plus Math, Angle, and Test Operations 90 4Rect 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Rect returns a+bi. 4Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi). TI-83 Plus Math, Angle, and Test Operations 91 MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |. MATH NUM CPX PRB 1: rand 2: nPr 3: nCr 4: ! 5: randInt( 6: randNorm( 7: randBin( Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution rand rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of random-numbers, specify an integer > 1 for numtrials (number of trials). The default for numtrials is 1. rand[(numtrials)] Tip: To generate random numbers beyond the range of 0 to 1, you can include rand in an expression. For example, rand5 generates a random number > 0 and < 5. TI-83 Plus Math, Angle, and Test Operations 92 With each rand execution, the TI-83 Plus generates the same randomnumber sequence for a given seed value. The TI-83 Plus factory-set seed value for rand is 0. To generate a different random-number sequence, store any nonzero seed value to rand. To restore the factoryset seed value, store 0 to rand or reset the defaults (Chapter 18). Note: The seed value also affects randInt(, randNorm(, and randBin( instructions. nPr, nCr nPr (number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nPr number nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. TI-83 Plus Math, Angle, and Test Operations 93 items nCr number ! (Factorial) ! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ,L.5 and 69. value! Note: The factorial is computed recursively using the relationship (n+1)! = nn!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L12)!=p is used to complete the calculation. Hence: n!=n(nN1)(nN2) ... 21, if n is an integer ,0 n!= n(nN1)(nN2) ... 12p, if n+12 is an integer ,0 n! is an error, if neither n nor n+12 is an integer ,0. (The variable n equals value in the syntax description above.) TI-83 Plus Math, Angle, and Test Operations 94 randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1. randInt(lower,upper[,numtrials]) randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1. randNorm(m,s[,numtrials]) TI-83 Plus Math, Angle, and Test Operations 95 randBin( randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be , 1. prob (probability of success) must be , 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions. TI-83 Plus Math, Angle, and Test Operations 96 ANGLE Operations ANGLE Menu To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-83 Plus's interpretation of ANGLE menu entries. ANGLE 1: 2: ' 3: r 4: 8DMS 5: R8Pr( 6: R8Pq( 7: P8Rx( 8: P8Ry( Degree notation DMS minute notation Radian notation Displays as degree/minute/second Returns r, given X and Y Returns q, given X and Y Returns x, given R and q Returns y, given R and q Entry Notation DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (), the minute symbol ('), and the second symbol ("). degrees must be a real number; minutes and seconds must be real numbers , 0. degreesminutes'seconds" TI-83 Plus Math, Angle, and Test Operations 97 For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use so that the TI-83 Plus can interpret the argument as degrees, minutes, and seconds. Degree mode Radian mode (Degree) (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use to convert degrees to radians. value {value1,value2,value3,value4,...,value n} also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format. Note: " is not on the ANGLE menu. To enter ", press []. TI-83 Plus Math, Angle, and Test Operations 98 r r (Radians) (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees. valuer Degree mode 8DMS 8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line. answer8DMS TI-83 Plus Math, Angle, and Test Operations 99 R8Pr (, R8Pq(, P8Rx(, P8Ry( R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists. R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set. TI-83 Plus Math, Angle, and Test Operations 100 TEST (Relational) Operations TEST Menu To display the TEST menu, press y :. This operator... TEST 1: = 2: 3: > 4: , 5: < 6: LOGIC Returns 1 (true) if... Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to =, , >, ,, <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists. For = and only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are matrices, both must have the same dimensions. Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values. TI-83 Plus Math, Angle, and Test Operations 101 valueA=valueB valueA>valueB valueA<valueB valueAvalueB valueA,valueB valueAvalueB Using Tests Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1). The expression 2+2=2+3 returns 0. The TI-83 Plus performs the addition first because of EOS rules, and then it compares 4 to 5. The expression 2+(2=2)+3 returns 6. The TI-83 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3. TI-83 Plus Math, Angle, and Test Operations 102 TEST LOGIC (Boolean) Operations TEST LOGIC Menu To display the TEST LOGIC menu, press y TEST ~. This operator... TEST LOGIC 1: and 2: or 3: xor 4: not( Returns a 1 (true) if... Both values are nonzero (true). At least one value is nonzero (true). Only one value is zero (false). The value is zero (false). Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true). and, or, xor and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists. TI-83 Plus Math, Angle, and Test Operations 103 valueA and valueB valueA or valueB valueA xor valueB valueA valueB and or xor 0 0 0 0 0 0 0 0 returns returns returns returns 1 0 0 0 1 1 1 0 0 1 1 0 not( not( returns 1 if value (which can be an expression) is 0. not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C. TI-83 Plus Math, Angle, and Test Operations 104
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Pasadena - PHYSICS - 1B
Chapter 16 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 17 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 17 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 18 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 18 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 19 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 19 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 20 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 20 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 21 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 21 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 21 (part 3) Lecture NotesPlease note: In the video lecture, the formula for the bulk modulus was presented as B = (1/V)(dP/dV), as seen above. This is a typo - the correct formula is B = V (dP/dV), which gives B = P for isothermal process
Pasadena - PHYSICS - 1B
Chapter 22 (part 2) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 21 (part 1) Lecture Notes
Pasadena - PHYSICS - 1B
Chapter 12 Lecture NotesTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-s
Pasadena - PHYSICS - 1B
Chapter 13 (part 1) Lecture NotesTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTi
Pasadena - PHYSICS - 1B
Chapter 14 (part 1) Lecture NotesTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTime TIFF (Uncompressed) z,-sTMz',^oe TM QuickTi
Maryland - BSCI - 342
6/17/08 Hypotheses about puberty: 1.) Gonadostat hypothesis: a.) During the pre-pubertal stage of development, the gonads release low, but constant, levels of gonadal steroids that exert a negative feedback on the hypothalamic neurons. Evidence again
Maryland - BSCI - 342
6/18/08 Coitus; Sexual Response Coitus (copulation): direct contact between the penis and the vagina. Sexual response cycle: 4 sequential phases: 1.) Excitement 2.) Plateau 3.) Orgasm 4.) Resolution EPOR 1.) Excitement: Sexual Arousal -could be preci
Maryland - BSCI - 342
6/19/08 Ovulated secondary oocyte arrested in metaphase II (a.k.a. ovum) -The ovum is released to the surface of the ovary. The cilia (located at the end of the fimbriae) beat vigorously at the time of ovulation to create a current that sweeps the ov
Maryland - BSCI - 342
6/20/08 Review: More calcium = destabilized CF, destroyed MPF = completion of 2 nd meiotic division = 2 unequal haploid cells: (1) a second polar body (dies) and (2) the female pronucleus (woo hoo!) The fusion of the sperm with the oolemma causes an
Maryland - BSCI - 342
6/16/08 Puberty 1.) Puberty is a developmental stage when the individual transforms from a sexually immature to a sexually mature individual. 2.) Puberty is marked by physiological, morphological, and behavioral changes. 3.) In lower animals, the est
Middlesex CC - CRJ - 1123
CJ 1123 Criminal Evidence and Procedure (15) Identification Procedures Identification Procedures 15-1 Definitions Used for Identification Procedures 3 basic procedures used: Lineups Victim or eyewitness is asked to view a group of ppl and select the
Virginia Tech - EDHL - 1514
Taking Charge of Your HealthWellness: The New Health Goal Wellness Optimal health and vitality. The Dimensions of Wellness Physical Emotional Intellectual Spiritual Interpersonal and Social Environmental or Planetary The six dimensions o
Virginia Tech - EDHL - 1514
Stress: The Constant ChallengeWhat is Stress? Stressor Physical Responses to Stressors Two Major Control Systems Nervous system Endocrine systemChapter Two2008 McGraw-Hill Companies. All Rights Reserved.2Actions of the Nervous system
Virginia Tech - EDHL - 1514
Psychological HealthPsychological Health What Psychological health is not. Not the same as psychological normality Conforming to social norms Never seeking help for personal problems &quot;Mentally ill&quot; Peoples appearanceChapter Three2008 McGr
Virginia Tech - EDHL - 1514
Developing Intimate Relationships Be willing to give of themselves Share their ideas, feelings, time, and needs Self-Concept and Self-Esteem Feel good about ourselves Roots of our identity and self Developed during childhood Relationships wi
Virginia Tech - EDHL - 1514
Human SexualitySexual Identity Germ cells Ova (eggs) in females Sperm in malesMales: testes hormone - testosterone Females: ovaries hormone - estrogen &amp; progesterone Produces the sex hormones Puberty Secondary sex characteristics2Di
Virginia Tech - EDHL - 1514
ContraceptionContraceptivesDefinition. Preventing conception by blocking the female's egg from uniting with the male's sperm, thereby preventing pregnancy. Modern contraception are much more predictable and effective than in the past. Many
Virginia Tech - EDHL - 1514
Pregnancy and ChildbirthDeciding to Become a Parent Physical health and age Financial circumstances Birth to 18 years old \$250,000 Relationship with your partner Education, career and child care plans Emotional readiness Social support P
Virginia Tech - EDHL - 1514
The Use and Abuse of Psychoactive DrugsAddictive Behavior Habits that have gotten out of control, with a resulting negative effect on a persons health. Addiction is the habitual use of a drug produced chemical changes in the user's body. Charac
Virginia Tech - EDHL - 1514
The Responsible Use of AlcoholChemistry of Alcohol Psychoactive ingredient Depressant Ethyl Alcohol only alcohol that can be consumed Beer 3-6% alcohol by volume Malt Liquors 6-8% alcohol by volume Table wines 9-14% alcohol by volumeF
Virginia Tech - EDHL - 1514
Exercise for Health and FitnessChapter 131 2008 McGraw-Hill Higher Education. All rights reserved.What is Physical Fitness? Set of physical attributes that allows the body to respond or adapt to the demands and stress of physical effort Five
Virginia Tech - EDHL - 1514
Cardiovascular HealthIntroductionCardiovascular Disease (CVD) Leading cause of death in the U.S. Claims one life every 35 seconds CVD is due to our way of lifeChapter 152008 McGraw-Hill Companies. All Rights Reserved.2The Cardiovasc
Virginia Tech - EDHL - 1514
Immunity and InfectionThe Chain of InfectionLinks in the Chain Transmitted through a chain (six links) Pathogen - disease causing microorganism Reservoir - natural environment of the pathogen: Person, animal or environmental component Portal
Virginia Tech - EDHL - 1514
Sexually Transmitted DiseasesAcquired Immunodeficiency Syndrome (AIDS) Leading cause of death in many parts of the world. Worldwide, AIDS is the leading cause of death for people age 15-59 Approximately 65 Million people around the world are in
Virginia Tech - EDHL - 1514
Conventional and Complementary Medicine: Skills for the Health Care ConsumerSelf-Care: Managing Medical Problems Self Assessment Decision Making: Knowing When to See a Physician Severe Unusual Persistent Recurrent Major trauma or injury Unc
Loyola Chicago - FINC - 450
Chapter 03Use the following financial statements to answer Balance Sheet 900 Accounts payable 1,500 Long-term debt 4,700 Common stock 33,400 Retained earnings \$40,500 Total liab. &amp; equity \$ Income Statement Sales \$22,000 Cost of goods sold 16,500 D
Loyola Chicago - FINC - 450
Chapter 05_ 1.Alpha Bank pays interest of 4 percent compounded annually. Beta Bank pays 4 percent simple interest. Which one of the following statements is true if you invest \$1,000 in each bank for five years? a. Alpha Bank will pay you a total
Loyola Chicago - FINC - 450
Chapter 06_ 1.You can afford car payments of \$265 a month for three years. The interest rate is 7.5 percent, compounded monthly. How much can you afford to borrow to buy a car? a. \$8,269.67 b. \$8,271.83 c. \$8,519.20 d. \$8,572.44 You want to retir
Loyola Chicago - FINC - 450
7_ 1.A semiannual corporate bond has a face value of \$1,000, a yield to maturity of 7.2 percent, and a coupon rate of 7.5 percent. The bond matures 10 years from today. This bond: a. pays interest payments of \$75.00 every six months. b. sells at
Loyola Chicago - FINC - 450
8_ 1.You would like to earn a 9.5 percent rate of return on a 9 percent preferred stock. How much are you willing to pay for 10 shares? a. \$94.74 b. \$105.56 c. \$947.37 d. \$1,055.56 The common stock of Andy's Sporting Goods sells for \$25.40 a shar
Loyola Chicago - FINC - 450
9 Use the following information to answer questions 1 through 3. You are analyzing a proposed project and have compiled the following information: Year Cash flow 0 -\$145,000 1 \$ 33,400 2 \$ 70,500 3 \$ 82,100 Required payback period 3 years Required re
Loyola Chicago - FINC - 450
10 Round all answers to whole dollars._ 1.A proposed project is expected to decrease accounts receivable by \$10,000, decrease inventory by \$4,000, and increase accounts payable by \$6,000. What is the amount of the initial cash flow for this proje
Loyola Chicago - FINC - 450
12_ 1.One year ago, you purchased a stock at a price of \$36.24 a share. You received an annual dividend of \$1.80 a share and sold the stock today for \$32.12 a share. What was your capital gains rate of return? a. -11.28 percent b. -11.37 percent
Loyola Chicago - FINC - 450
19 _ 1. Which one of the following is a use of cash? a. a decrease in inventory b. an increase in accounts payable c. increase in fixed assets d. increase in long-term debt A firm has an accounts payable period of 46 days, an inventory period of 56 d
Ole Miss - ACCY - 201
CHAPTER 1 INTRODUCTION TO ACCOUNTING AND BUSINESSCLASS DISCUSSION QUESTIONS1. The objective of most businesses is to maximize profits. Profit is the difference between the amounts received from customers for goods or services provided and the amou
Ole Miss - ACCY - 201
CHAPTER 2 ANALYZING TRANSACTIONSCLASS DISCUSSION QUESTIONS1. An account is a form designed to record changes in a particular asset, liability, stockholders' equity, revenue, or expense. A ledger is a group of related accounts. 2. The terms debit a
Ole Miss - ACCY - 201
CHAPTER 3 THE MATCHING CONCEPT AND THE ADJUSTING PROCESSCLASS DISCUSSION QUESTIONS1. a. Under cash-basis accounting, revenues are reported in the period in which cash is received and expenses are reported in the period in which cash is paid. b. Und
Ole Miss - ACCY - 201
CHAPTER 4 COMPLETING THE ACCOUNTING CYCLECLASS DISCUSSION QUESTIONS1. a. The financial statements are the most important output of the accounting cycle. b. Yes, all companies have an accounting cycle that begins with analyzing and journalizing tran
Ole Miss - ACCY - 201
CHAPTER 5 ACCOUNTING FOR MERCHANDISING BUSINESSESCLASS DISCUSSION QUESTIONS1. Merchandising businesses acquire merchandise for resale to customers. It is the selling of merchandise, instead of a service, that makes the activities of a merchandising
Ole Miss - ACCY - 201
CHAPTER 6 ACCOUNTING SYSTEMS, INTERNAL CONTROLS AND CASHCLASS DISCUSSION QUESTIONS1. The knowledge that job rotation is practiced and that one employee may perform another's job at a later date tends to discourage deviations from prescribed procedu
Ole Miss - ACCY - 201
CHAPTER 7 RECEIVABLESCLASS DISCUSSION QUESTIONS1. Receivables are normally classified as (1) accounts receivable, (2) notes receivable, or (3) other receivables. 2. Transactions in which merchandise is sold or services are provided on credit genera
Ole Miss - ACCY - 201
CHAPTER 8 INVENTORIESCLASS DISCUSSION QUESTIONS1. To protect inventory from customer theft, retailers use two-way mirrors, cameras, security guards, locked display cabinets, and inventory tags that set off an alarm if the inventory is removed from