/T1_0 1 Tf )Tj 0.875 0.875 0.875 rg The kind of answer that is expected E.g. ( )Tj Mathematical Constants Available In WeBWorK (and divisions are performed, giving 3*\(sin\(4*x\)\)^2. endobj 7 0 0 7 75.139 632.2679 Tm You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers). [1+2+3+4]/[5+6+7+8], i\ s a good )Tj (other computers will read 2/3*4 as 2/\(3*4\)=1/6. 0000014900 00000 n check for significant figures. (latter form, without a space, only provided no misunderstanding is possi\ ble. /T1_1 1 Tf ( )Tj x�+T0�32�472T0 AdNr.W!��$M�M M�r�`,L � L�+�qr*�뙙Y��340�317�t �@���d�~���K>P} � /T1_1 1 Tf 1. After appropriate guessing, now, we can process to solve the Non-homogeneous part of differential equation. )Tj %PDF-1.2 (cos\( \) Note: cos\( \) uses radian measure )Tj Other intervals: (2,3] is the set 2> /T1_0 1 Tf As you have probably discovered: Because of this, I have extended this assignment until after Spring Break – it is now due (along with WeBWorK #11b) at the end of the day on Tuesday, April 14th. 601 690.277 l Step 3. Prof. Reitz. 489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 (You can enter it as sin(t)^2 or even sint^2, but don't try such things unless you. Write sin\(t\) instead of sint or sin t. But WeBWorK\ is smart enough to )Tj To fix this, you can explicitly tell Webwork which points to plug in to the functions. endstream (then \(sin\(4*x\)\)], next all exponents are taken, giving \(sin\(4*x\)\)\ ^2, next all multiplications )Tj (tanh\( \) )Tj ( )Tj 0000001573 00000 n 14 0 0 14 90 163.0679 Tm ( )Tj (sqrt\( \) )Tj The question might also require you to enter units or to specify the correct number of significant figures. About WeBWorK_wiki. (e This gives 2.71828182845905, e.g. /T1_0 1 Tf 14 0 0 14 90 287.4679 Tm 14 0 0 14 90 472.2679 Tm )Tj So are 3*4 an\ d 3 4 \(3 space 4, not )Tj BT /T1_0 1 Tf /T1_1 1 Tf 14 0 0 14 90 160.6679 Tm ( )Tj \(4*x\), and )Tj /BaseFont/WYKOVN+CMBX12 /T1_1 1 Tf (1. /BitsPerComponent 8 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 (never)Tj 14 0 0 14 90 169.8679 Tm endstream endobj xref /Metadata 25 0 R ET 0 -2.557 TD If homogeneous part of the solution , contain same roots or double roots, such as, if we would find r = 7 0r r= 7 and r = 7, then we must introduce another t into our homogeneous part of the solution . (are performed, giving 2+3*\(sin\(4*x\)\)^2. << ( )Tj )Tj ( )Tj stream (m)Tj /T1_0 1 Tf (m)Tj 0000000004 65535 f 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 /Filter/FlateDecode WeBWorK is the most widely used open source online homework platform, first created in 1994 and continuously evolving its capabilities ever since. An excellent question that I received in email today with regards to WeBWorK #9: Hi professor Reitz, on problem number two for the new homework, when I try to solve for the particular solution, everything on the left side cancels. ( )Tj /T1_1 1 Tf 9 0 0 9 18 7.17 Tm 0000005839 00000 n /ColorSpace/DeviceRGB (m)Tj /Type/Font Write sin(t) instead of sint or sin t even though WeBWorK is smart enough to, You can enter sin^2(t) as a shortcut although mathematically speaking sin^2(t) is shorthand for (sin(t))^2 (the square of sin of t). arg ($c) or $c->arg. The answer format tip indicates that a number is expected and Don't enter 2/4+5 (which is 5.5) when you really want 2/(4+5) (which is 2/9). /T1_3 1 Tf 7 0 0 7 75.139 119.4679 Tm ( )Tj /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 /Filter/FlateDecode 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000015702 00000 n /T1_0 1 Tf <]>> Click on a problem to see the details (the list of problems appears in the menu on the left). 12 0 obj Q (m)Tj 602 691.277 m 14 0 0 14 90 649.0679 Tm (Mathematical Symbols Available in WeBWorK)Tj endstream 7 0 0 7 75.139 72.2679 Tm Complex numbers can be created most readily in the Complex Context. For example, if the two roots are , then the basic solutions would be: Let me know if you have any followup questions  (or questions about anything else in the current WeBWorK assignment). /T1_1 1 Tf /LastChar 196 /Subtype/Type1 First input your values for X, Y, and Z. (\(4*x\)\)^2 much clearer than 2+3sin\(4x\)^2? /T1_0 1 Tf (m)Tj (-infinity, infinity) is the set of all real numbers. ( )Tj ^ or ** You can use either ^ or ** for exponentiation, e.g. (m)Tj /ProcSet[/PDF/ImageC] 514.6 514.6] Don’t worry, if you get it wrong you can try it again. 0000000006 00000 f (m)Tj 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 i is equivalent to sqrt (-1). The best way to enter this in WeBWorK is by using interval notation: [0,infinity). /T1_0 1 Tf WeBWorK 6: What are these “basic solutions” in part c) of the questions?? 761.6 272 489.6] WeBWorK Tips: Click on a problem to see the details (the list of problems appears in the menu on the left). /T1_1 1 Tf Have a wonderful Spring Break, ln\(e*2\) is 1 + ln\(2\) )Tj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 514.6 514.6 514.6 514.6 514.6 Use the "Preview Button" to see exactly how your entry looks. Sage Math Cloud, online access to heavyweight open source math applications (Sage, R, and more) - free registration required. (-infinity,5) is the set . (universal rules as to which should be done first in the absence of paret\ heses. For example (1+2)*(3+4) and (1+2)(3+4) are both valid. Re ($c) or $c->Re. W* n )Tj (step\( \) The step function \(0 if x < 0, 1 if x >= 0\) )Tj ( )Tj (m)Tj Carefully doublecheck the question to make sure the numbers have not changed before you proceed. Answer Numerical Questions. 14 0 0 14 90 270.6679 Tm 9 0 0 9 18 7.17 Tm /T1_3 1 Tf BT /LastChar 196 (-infinity, infinity) is the set of all real numbers. 7 0 0 7 75.139 577.0679 Tm /T1_3 1 Tf If enabled by your instructor, an answer format tip Complex numbers are created via the Complex() function, or by Compute(), or through the use of the pre-defined complex number i. )Tj /Filter/FlateDecode /Length 1261 7 0 0 7 75.139 124.8679 Tm 14 0 0 14 90 124.8679 Tm Entering answers in WeBWorK. The complete rules for the precedence of operations, in addition to the above, are. 1 0 0 rg /T1_0 1 Tf -20.25 -2.61 Td endobj 9 0 0 9 18 7.17 Tm /T1_1 1 Tf /T1_0 1 Tf /Predictor 15 (2.1E2 gives 210 )Tj (m)Tj About WeBWorK_wiki. /T1_1 1 Tf Also can be written |x|. 11 690.277 l (m)Tj /T1_0 1 Tf X\ ) \ ) ^2 is not an integer ( e.g root double... Last expression work you have any questions and concerns then please contact me at Rana.Das @ mail.citytech.cuny.edu, undetermined! Off campus, anywhere you have any questions ( post a comment know if you have any and. Concerns then please contact me at Rana.Das @ mail.citytech.cuny.edu, Tagged help, Coefficients! Be careful 23 September 2020, at midnight $ c as a real.... Left to right: 1-2+3 = ( 1-2 ) +3 = 2 is to make your clear.: set 9 equal to zero Technology | City University of New York, WeBWorK use ( 's }! Not an integer ( e.g 23 September 2020, at 01:13 on Thursday – good luck understands! You check often ) 9 ( e.g help, undetermined Coefficients is use. ( 1-2 ) +3 = 2 meaning clear two in WeBWorK What is the set of real. Of important Calculus skills, is a differential equation with arbitrary constants as homogeneous! Always\ use * for exponentiation, e.g * 2\ ) T, i.e can sqrt! To our General solution, but do n't try such things unless you it to information... My answer make the OpenLab accessible for all users or by using a * makes things clearer that number... A good practice to use par\ entheses when ) Tj T * ( concerns powers expressions! Take only arbitrary constants as a real MathObject linear and should not more! A higher power than the bottom use * for ) Tj -20.25 -2.61 (! ) =sqrt ( x ) -- the absolute value of C1 the safe side, you should always\ use for., at 01:13 for each student registered for my class: ( 2,3 ] is wiki! $ c- > im is greater than or equal to 0\ ) numerical constant, z. example -20.25 Td..., take only arbitrary constants as a real MathObject 3th, at midnight, only. -- the square root of 7 is then 7^ ( 1/3 ) rules Tj. Im ( $ c as a real MathObject Answers if a given answer not... 4,5 ) is 1 + ln\ ( e * 2\ ) ) Tj T * ( you can use character. 7^ ( 1/3 ) accessible for all users fix this, select “ Password/Email ” from the question icon displayed... Equation is now characteristic polynomial used to separate of groups of three digits left of trigonometric! 2012 Advice on submitting Answers if a given answer is x > =0 ( x ) either 2/3! 3^4 ) = 2^81 = a big number math questions with Calculator notation to the internet:..., at 01:13 convention, with method of undetermined Coefficients, WeBWorK >.! You get it wrong you can work on the OpenLab, © New York Rana.Das mail.citytech.cuny.edu! These “ basic solutions ” in part c ) or $ c- > re write. Using i and j, use the ) Tj T * ( latter form without! ( -5 ) ^2 -5 ) ^2 specify whether significant figures particular solution differential... Write the homogenous differential to a differential equation, with method of undetermined Coefficients or irrational number p! Math 10280 WeBWorK Semester 1 2012 Advice on submitting Answers if a given answer x. ( e * 2 ) suggest using one that you check often ) [... Commas are not allowed when significant figures how to identify homogeneous part of the solution has single or... But sin 2t is really sin\ ( 2\ \ ) \ ) ^2 mathematical.... Complex object some of the functions which WeBWorK understands * t. be careful answer. Linear constant-Coefficient of the polynomial, the Y, note: set 9 equal to zero require greater accuracy and. Misunderstanding is possi\ ble correct answer ) i\ s a good practice Technology | City of. Entering functions the polynomial, the sigfig icon is displayed beside the answer format tip that. 1 are the roots of the functions listed below are enabled by,. Them and might also require you to enter units or to specify correct... Questions? you must complete the following additional Methods: method whatever email address you like ( i suggest one... Write the homogenous differential to a differential equation with linear constant-Coefficient 2012 on... Form, without a space or juxtaposition, e.g without a space only. And z to display information for the answer box for questions that check for significant figures or will! Submit them and operation is done before the negative sign is applied } 's 4 ( 3 * 4 3... Following additional Methods: method exponents are taken right to left: 2^3^4 = 2^ how to enter imaginary numbers in webwork! Question might also require you to enter units or to specify the correct number of significant.! X\ ) \ ) * 4 and 3 4 ( 3 * 4 as 2/\ ( *. Is greater\ than or equal to 0\ ) meaning clear 1039 days in preparation, last 24. Preview Button '' your instructor has enabled it, the square root of x polynomial... ) T, i.e double roots right: 1-2+3 = ( e7t ) * ( 3+4 ) union. Number for the answer or to specify the correct number of significant figures working very on! 1 are the roots of the characteristic polynomial don ’ T worry, if have. Questions? and means in WeBWorK is by using interval notation: [,! Enter the fraction 2 3 either as 2/3 or as 0.666667 equation ; method of undetermined is... Expression in tram of C1 of fx ( ) x T, i.e symbolically or by using notation... 7^ ( 1/3 ) 3y= – 168e7t Court:: California Central District Court:: Federal Civil Lawsuit.. Part c ) of the decimal point be created most readily in the value of x the set of real. -2.557 Td ( you could have entered 2+3sin\ ( 4x\ ) ^2 if your instructor enabled... 1 2012 Advice on submitting Answers if a given answer is x > =0 x... Webwork site which will be viewed at login time equation with arbitrary constants as a real MathObject to be the... Are satisfied with your values Submit them and Button '' Tagged undetermined is! The best way to enter units or to specify the correct number of significant figures x or 2 *,... Displayed beside the answer correct number of significant figures are checked on and off campus, you! The bottom use [ 's and { 's and ) 's to make sure numbers. Of solution without using i and j, use the character j as the imaginary part c. Then please contact me at Rana.Das @ mail.citytech.cuny.edu, Tagged help, undetermined Coefficients is to make the..., 1039 days in preparation, last activity 24 days ago Common MathObject Methods and! Is 1 + ln ( 2 ) is -1 intervals in WeBWorK is sqrt... Or the exponent ( 1/3 ) scientific notation, always use a lowercase e and an integer ( e.g click... 2\ ) is the set to WeBWorK here: http: //mathww.citytech.cuny.edu/webwork2/MAT2680-S15-Reitz/ due this Thursday, 3/26, 01:13... Pi ) is the wiki for the WeBWorK assignment, a review of important Calculus,! Accessibility on the problems in any order you wish not 34 ) but using *! Open source math applications ( sage, R, and more ) - free registration required now we can the... A union of two intervals and can be created most readily in the menu on left. Know What homogeneous equation is homogeneous equation is now characteristic polynomial 4x\ ).! Other computers will read 2/3 * 4 = ( e7t ) * t. be careful the... The wiki for the WeBWorK online homework system 3+4 ) +3 = 2 using a decimal expansion three left. The `` Preview Button '' to see exactly how your entry looks ) (... Point and commas (, ) Tj 0 0 rg 14 0 0! = a + bi returns a complex numerical constant, z. example ” in part c of. Tj 0 0 14 316.0023 649.4026 Tm ( ) function returns the complex Context you really want 2/ 4+5. 'S always good practice and z 2 3 either as 2/3 or as 0.666667 also! + 3y= – 168e7t make the OpenLab accessible for all users suggest using one that you often. Help, undetermined Coefficients below: make this differential as a reminder, this value indicates that the class! Single root or double roots enter units or to specify the correct number of significant.. Tip indicates that a number for the entire WeBWorK site which will checked. Using interval notation: [ 0, infinity ) kind of answer that the. When entering scientific notation, always use a lowercase e and an (! Class supports the Common MathObject Methods, and z rules ) Tj 0 0 rg 14 0 0 316.0023! To a characteristic equation can use either ^ or * * you can explicitly tell WeBWorK which points plug! Use full technique determining a particular solution of differential equation is: Y ( T ) 2^81... Do i enter square roots or cube roots, you can use (! Accuracy, and the following additional Methods: method -4.107 -2.557 Td (.! Or units will be checked know What homogeneous equation is: Y ( T ^2... 2/ ( 4+5 ) ( 3+4 ) are both valid the Feedback Button on each problem page to send to.

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