## Laplace transform of a differential equation marke...

Hello, I am new to MAPLE TA so I hope my question makes sense:

I am asking the students to compute the Laplace transform of a differential Equation and wirte the answer which is an equation in the respose area. I use the following algorithm to generate the answer:

\$LaplaceY=maple("
with(inttrans):
ode:=diff(y(t), t) -3*y(t) = 2*exp(t);
y(0):=2;
ans:=laplace(ode, t, s);
alias( Y(s)= laplace( y(t), t, s ) );

[convert(ans,string)];
");

\$ans=switch(0,\$LaplaceY);

Here is the output of the algorthim: ans   s*Y(s)-2-3*Y(s) = 2/(s-1)

The students are supposed to enter s*Y(s)-2-3*Y(s) = 2/(s-1) in the response area using symbolic entry. I tried both Maple graded Maple syntax and Mathematical formula for the response area. It always marks the answer wrong when previewed.

I can't figure out the issue here.

Thanks

## How to program Multivariate statistics with MapleT...

My questions about Multivariate Statistics are all programmed the hard way. When using R in the classroom, which has all the commands available this looks a little awkward. Thing is that every command should give a specific answer which can be related to a question box.

A little help would be nice. I am more than happy to share questions

\$e=maple("Vector([1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])");
\$n=maple("evalf(Statistics[Count](\$e))");
\$k=2;
:// data input;
:// dependent variable Y;
\$Y=maple("[11.259,11.238,11.492,11.479,11.016,11.241,10.949,10.690,10.964,10.733,10.493,10.684,10.459,10.595,10.953,10.838,10.545,10.806,10.455,10.299,10.608,10.605,10.536,10.492]");
\$vY=maple("Vector([\$Y])");
\$nY=maple("evalf(Statistics[Count](\$Y))");
\$muY=maple("evalf(Statistics[Mean](\$Y))");
:// independent variable X1;
\$X1=maple("[7.5,7.5,6.5,7,8,7.5,7.5,8,8.5,8,8,8.5,8,8,8,8,8,8,8.5,8.5,8.5,8,8,8]");
\$vX1=maple("Vector([\$X1])");
\$nX1=maple("evalf(Statistics[Count](\$X1))");
\$muX1=maple("evalf(Statistics[Mean](\$X1))");
:// independent variable X2;
\$X2=maple("[22,22,20,22.5,21.5,22,21.5,21,21.5,21,20.35,21,20.35,20.75,21.5,21.35,20.75,21.1,20.35,20,20.75,20.75,20.75,20.35]");
\$vX2=maple("Vector([\$X2])");
\$nX2=maple("evalf(Statistics[Count](\$X2))");
\$muX2=maple("evalf(Statistics[Mean](\$X2))");
\$stdvX2=maple("evalf(Statistics[StandardDeviation](\$X2))");
:// independent variable X3;
\$X3=maple("[8.01,9.1,8.39,8.37,8.73,9.11,7.52,7.17,7.54,7.24,6.79,7.09,3.6,6.95,7.52,7.34,5.82,7.29,5.68,5.45,6.97,8.03,5.8,4.69]");
\$vX3=maple("Vector([\$X3])");
\$nX3=maple("evalf(Statistics[Count](\$X3))");
\$muX3=maple("evalf(Statistics[Mean](\$X3))");
\$stdvX3=maple("evalf(Statistics[StandardDeviation](\$X3))");
\$X3s=maple("\$vX3.\$vX3");
:// small variables based on deviation around average value;
\$y=maple("\$vY-\$muY*\$e");
\$x1=maple("\$vX1-\$muX1*\$e");
\$x2=maple("\$vX2-\$muX2*\$e");
\$x3=maple("\$vX2-\$muX2*\$e");
:// summation of deviation values;
\$sumysq=maple("\$y.\$y");
\$sumx1sq=maple("\$x1.\$x1");
\$sumx2sq=maple("\$x2.\$x2");
\$sumx3sq=maple("\$x3.\$x3");
\$sumyx1=maple("\$y.\$x1");
\$sumyx2=maple("\$y.\$x2");
\$sumyx3=maple("\$y.\$x3");
\$sumx1x2=maple("\$x1.\$x2");
\$sumx1x3=maple("\$x1.\$x3");
\$sumx2x3=maple("\$x2.\$x3");
:// calculation of the coefficients;
:// coefficient betha1;
\$b1=maple("((\$sumyx1)*(\$sumx2sq)-(\$sumyx2)*(\$sumx1x2))/((\$sumx1sq)*(\$sumx2sq)-(\$sumx1x2)^2)");
\$b2=maple("((\$sumyx2)*(\$sumx1sq)-(\$sumyx1)*(\$sumx1x2))/((\$sumx1sq)*(\$sumx2sq)-(\$sumx1x2)^2)");
\$a=maple("(\$muY)-(\$b1)*(\$muX1)-(\$b2)*(\$muX2)");
:// calculate estimate based on given values;
\$valuex1=range(8,8,1/10);
\$valuex2=range(21,21,1/10);
\$yhatvalue=\$a+(\$b1)*\$valuex1+(\$b2)*\$valuex2;
:// standard deviations;
\$stdvy=maple("evalf(Statistics[StandardDeviation](\$y))");
\$stdvx1=maple("evalf(Statistics[StandardDeviation](\$x1))");
\$stdvx2=maple("evalf(Statistics[StandardDeviation](\$x2))");
\$stdvx3=maple("evalf(Statistics[StandardDeviation](\$x3))");
:// correlation coefficients;
\$ryx1=maple("(\$sumyx1)/(\$n*\$stdvy*\$stdvx1)");
\$ryx2=maple("(\$sumyx2)/(\$n*\$stdvy*\$stdvx2)");
\$ryx3=maple("(\$sumyx3)/(\$n*\$stdvy*\$stdvx3)");
\$rx1x2=maple("(\$sumx1x2)/(\$n*\$stdvx1*\$stdvx2)");
\$rx1x3=maple("(\$sumx1x3)/(\$n*\$stdvx1*\$stdvx3)");
\$rx2x3=maple("(\$sumx2x3)/(\$n*\$stdvx2*\$stdvx3)");
:// estimated values;
\$Yhat=maple("(\$a)*\$e+(\$b1)*\$vX1+(\$b2)*\$vX2");
\$error=maple("\$vY-\$Yhat");
\$sumerror=maple("\$error.\$e");
\$sumerrorsq=maple("\$error.\$error");
:// \$errortr=maple("LinearAlgebra[Transpose](\$error)");
:// \$sumerrorsq=maple("LinearAlgebra[MatrixMatrixMultiply](\$errortr,\$error)");
\$errorstdv=maple("sqrt(\$sumerrorsq/(\$n-2-1))");
:// standard error of the coefficients;
\$errorb1=maple("\$errorstdv/sqrt(((\$sumx1sq*\$sumx2sq)-((\$sumx1x2)^2))/(\$sumx2sq))");
\$errorb2=maple("\$errorstdv/sqrt(((\$sumx1sq*\$sumx2sq)-((\$sumx1x2)^2))/(\$sumx1sq))");
:// R-squared;
\$Rsq=maple("1-\$sumerrorsq/\$sumysq");
\$Rasq=maple("1-(\$sumerrorsq/(\$n-\$k-1))/(\$sumysq/(\$n-1))");
:// hypothesis: does variable X[i] influence Y? H[0]: it does not so b=0;
\$tb1=maple("\$b1/\$errorb1");
\$tb2=maple("\$b2/\$errorb2");
\$Tdf=\$n-\$k-1;
\$alpha=range(0.05,0.05,1/100);
\$T=maple("Statistics[Quantile](StudentT(\$Tdf),(1-\$alpha/2))");
\$ptb1=maple("Statistics[CDF](StudentT(\$Tdf),\$tb1)");
\$ptb2=maple("1-Statistics[CDF](StudentT(\$Tdf),\$tb2)");

## How to use Maximum Likelyhood Estimator (MLE) in M...

Our students use R for solving digital questions about Multivariate Statistics made with MapleTA.

How to use a MLE in MapleTA. Below the code I used in a question?

Remaks about how to program this better or more easy are more than welcome.

://noise. In Dutch ruis means noise;
\$ruislow=range(1,5,1);
\$ruishigh=range(6,9,1);
://data 1;
\$x1=10+rand(\$ruislow,\$ruishigh,1);
\$x2=30+rand(\$ruislow,\$ruishigh,1);
\$x3=50+rand(\$ruislow,\$ruishigh,1);
\$x4=70+rand(\$ruislow,\$ruishigh,1);
\$x5=90+rand(\$ruislow,\$ruishigh,1);
\$x6=125+rand(\$ruislow,\$ruishigh,1);
\$x7=175+rand(\$ruislow,\$ruishigh,1);
\$X=maple("Vector([\$x1,\$x2,\$x3,\$x4,\$x5,\$x6,\$x7])");
\$displayX=maple("printf(MathML:-ExportPresentation(\$X))");
\$TX=maple("LinearAlgebra[Transpose](\$X)");
\$displayTX=maple("printf(MathML:-ExportPresentation(\$TX))");
://data 2;
\$y1=4+rand(\$ruislow,\$ruishigh,1);
\$y2=12+rand(\$ruislow,\$ruishigh,1);
\$y3=32+rand(\$ruislow,\$ruishigh,1);
\$y4=36+rand(\$ruislow,\$ruishigh,1);
\$y5=42+rand(\$ruislow,\$ruishigh,1);
\$y6=36+rand(\$ruislow,\$ruishigh,1);
\$y7=19+rand(\$ruislow,\$ruishigh,1);
\$Y=maple("Vector([\$y1,\$y2,\$y3,\$y4,\$y5,\$y6,\$y7])");
\$displayY=maple("printf(MathML:-ExportPresentation(\$Y))");
\$TY=maple("LinearAlgebra[Transpose](\$Y)");
\$displayTY=maple("printf(MathML:-ExportPresentation(\$TY))");
://data 3;
\$z1=76+rand(\$ruislow,\$ruishigh,1);
\$z2=108+rand(\$ruislow,\$ruishigh,1);
\$z3=128+rand(\$ruislow,\$ruishigh,1);
\$z4=54+rand(\$ruislow,\$ruishigh,1);
\$z5=18+rand(\$ruislow,\$ruishigh,1);
\$z6=4+rand(\$ruislow,\$ruishigh,1);
\$z7=1+rand(\$ruislow,\$ruishigh,1);
\$Z=maple("Vector([\$z1,\$z2,\$z3,\$z4,\$z5,\$z6,\$z7])");
\$displayZ=maple("printf(MathML:-ExportPresentation(\$Z))");
\$TZ=maple("LinearAlgebra[Transpose](\$Z)");
\$displayTZ=maple("printf(MathML:-ExportPresentation(\$TZ))");
://totals;
\$t1=\$y1+\$z1;
\$t2=\$y2+\$z2;
\$t3=\$y3+\$z3;
\$t4=\$y4+\$z4;
\$t5=\$y5+\$z5;
\$t6=\$y6+\$z6;
\$t7=\$y7+\$z7;
\$T=maple("Vector([\$t1,\$t2,\$t3,\$t4,\$t5,\$t6,\$t7])");
\$displayT=maple("printf(MathML:-ExportPresentation(\$T))");
:// percentage Y;
\$py1=\$y1/\$t1;
\$py2=\$y2/\$t2;
\$py3=\$y3/\$t3;
\$py4=\$y4/\$t4;
\$py5=\$y5/\$t5;
\$py6=\$y6/\$t6;
\$py7=\$y7/\$t7;
:// percentage Z;
\$pz1=\$z1/\$t1;
\$pz2=\$z2/\$t2;
\$pz3=\$z3/\$t3;
\$pz4=\$z4/\$t4;
\$pz5=\$z5/\$t5;
\$pz6=\$z6/\$t6;
\$pz7=\$z7/\$t7;
://odds;
\$o1=\$py1/\$pz1;
\$o2=\$py2/\$pz2;
\$o3=\$py3/\$pz3;
\$o4=\$py4/\$pz4;
\$o5=\$py5/\$pz5;
\$o6=\$py6/\$pz6;
\$o7=\$py7/\$pz7;
://logit;
\$ln1=ln(\$o1);
\$ln2=ln(\$o2);
\$ln3=ln(\$o3);
\$ln4=ln(\$o4);
\$ln5=ln(\$o5);
\$ln6=ln(\$o6);
\$ln7=ln(\$o7);
\$L=maple("Vector([\$ln1,\$ln2,\$ln3,\$ln4,\$ln5,\$ln6,\$ln7])");
\$displayL=maple("printf(MathML:-ExportPresentation(\$L))");
://linreg;
://\$fit1=maple("Statistics[LinearFit]([1,t],\$X,\$L,t)");
\$fit=maple("map(rhs, Statistics[Fit](a*x+b, \$X, \$L, x, output=parametervalues))");
\$intercept=maple("\$fit[2]");
\$slope=maple("\$fit[1]");
\$r=maple("evalf(Statistics[Correlation](\$X,\$L))");

Best regards,

Nico

## Can I call Matlab functions in Maple T.A.?...

I am writing questions in Maple T.A.  I want to call Matlab functions to generate answers and compare to the student's answers. I want to call both built-in functions and my own functions.  I notice that Maple has Matlab Link for this purpose.  Can it be used also within Maple T.A.?

Stig Larsson, Mathematical Sciences, Chalmers University of Technology, Sweden

## New Maple T.A. Release

by: Maple T.A.

I am pleased to announce that a new release of Maple T.A., our online testing and assessment system, is now available. Maple T.A. 2017 includes significant enhancements to learning management system integration, as well as security, performance, and other improvements. These same improvements are also available in a new version of the  Maple T.A. MAA Placement Test Suite.  For more information, see What’s New in Maple T.A.

## Histogram for Weighted data ...

Hello,

I want to insert a histogram for weighted data in my  question Maple TA. I have difficulties in my code.

Some ideas?

Thks

## Jolly Good Times in London

by: Maple T.A. Möbius

While many of us in North America were getting re-acquainted with the Fall routine, Maplesoft was involved in a major event, the Maple T.A. and Möbius User Summit. In the past, the Summit has alternated locations between Europe and North America, but following the success of last year’s Summit in Vienna, Austria, we recently broke new ground and expanded the reach of the event to include more countries around the world in order to localize the themes and to meet the growing demand from educators to take learning online.

The first event, organized by Cybernet, took place in China. The second of five events on the calendar took place in London, England. Held from September 7-8, this installment was a major stop in the tour, drawing many residents of the UK to hear talks from some of our strongest proponents of Möbius in Europe. The London Summit drew several delegates from the UK alone, many of whom were completely new contacts for us! Other attendees came from as far away as Russia, Pakistan, Sri Lanka, and Australia, as well as some from Sweden, Denmark, Italy and the Netherlands. The turnout was brilliant!

Make progress or make excuses

The bulk of the London Summit was divided into three driving themes: Showcasing the Successful Delivery of Online Education; Best Practices for Digital Testing and Assessment; and Creating Engaging and Interactive Online STEM Content. Each theme consisted of 3 user presentations delivered by representatives from renowned institutions like University of Manchester, University of Birmingham, London Imperial College, University of Waterloo, Chalmers University of Technology, and more.

Maplesoft Application Engineer Surak Perera may have inadvertently set the tone for the day when he kicked off theme 1 with a quote from Tony Robbins: Make progress, or make excuses. One thing’s for sure – excuses were nowhere to be found at One Moorgate Place. The audience was captivated and engaged, and wasted no time bouncing questions and ideas off of our presenters. In fact, they were so eager to learn from our Maple T.A. and Möbius users that Jonny Zivku, Maple T.A. Product Manager, had to interject several times in order to keep the schedule moving! Each presentation reinforced the ability of Maple T.A. and Möbius to be used for diverse purposes such as distance education or analyzing incoming students, and in a range of subjects including multidisciplinary engineering cohorts, or simply core mathematics. Each presenter demonstrated that these tools can take you as far as the user’s mind is willing to be stretched.

Evening Reception

As heads were getting full and bellies were getting empty, the group left the luxuries of modern day and stepped back into what must have felt like a scene from Downton Abbey in the Main Reception Room of the venue. On the menu was the most culturally appropriate dish: fish and chips! Oh, and don’t forget the tea and wine!

There was no better way to wrap up the Summit than with Steve Furino’s interactive presentation and open discussion “Collecting Data about Collecting Data.” Small group discussion enabled the attendees to reconcile their inspiration from Day 1 with the practicality of putting it into practice once they return to their schools.

Overall, the London Summit was a smashing hit. The centralized location drew attendees who had a lot of common experiences which made for optimal discussion. The final question posted was the most revealing of everyone’s experience: where will the Summit be next year?

While that’s not yet decided, the Toronto Summit – the next stop in the Summit Series – is just a fortnight away (November 2-3). So for now, we’re saying “Cheers” to jolly good times in London, and “Can I get a double-double, eh” to Toronto!

Until then, you can experience the London Summit as if you were there with the full presentation proceedings and videos. They’re now available on our website!

## Maple Interactive Worksheet...

I am attempting to build a text field at the bottom of this worksheet MathApps-ResistorsMark.mw  that asks users for the resistance.

I am hoping to have the value of the text field evaluated using the Module() at the bottom of the startup code, for use as a question within MapleTA.  For some reason I can get the code to work for a slider, but not a textbox.

I have limited knowledge about startup code.

Notice: I will be removing the resistance from the diagram for students after I know it works.

I appreciate any help that can be offered.

## How do you access the number that an expression ev...

I am trying to solve a system of equations (I'm using MapleTA< but I'm pretty sure that this applies to any Maple product).  I have successfully solved the system, and obtain a set of solutions, which has name Soln.  I can access the element Soln[1], which is an expression:

vn2 = 12/7

Now, I just want that 12/7, as a decimal.  I try evalf(Soln[1]), but again I end up with vn2 = 12/7.  How do I get the decimal number out, without it being an expression?

## Maple T.A. Sketch Question | Randomization...

I am building an algebra 1 course for my school, and was wanting to create simple randomly generating practice sets for graphing points / lines / etc.

However, the Sketch answer type doesn't allow for any variable input like the other questions do. Is there a work around?

Presuming a randomly generated \$x and \$y, is there any way to check to see if a student has plotted the point (\$x, \$y)?

## Output to MathML as separate fractions...

Hi all,

I am trying to display, using mathML, two seperate fractions being multiplied as two seperate expressions with a multiuply in the middle.

as of now I have:

restart:
left:=(x+3)/(x+7):
right:=(x-4)/(x-1):
XMLTools[Print](MathML[Export](left*right)):

The above Maple entry displays as:

I would like:

Mark

## Check if simplified...

Hi all,

I am looking for a boolean logic check to see if a rational expression is simplified.

For example: x/x^2  =  1/x  I want something along the lines of issimplified(x/x^2)=FALSE

Similarily, (x^2-x-12)/(x-4) = x+3  so I would like some logic test to say (x^2-x-12)/(x-4) is NOT simplified.

Mark

## How we use digital testing at TU Delft to improve...

by: Maple T.A.

Meta Keijzer-de Ruijter is a Project Manager for Digital Testing at TU Delft, an institution that is at the forefront of the digital revolution in academic institutions. Meta has been using Maple T.A. for years, and offered to provide her insight on the role that automated testing & assessment played in improving student pass rates at TU Delft.

Modern technology is transforming many aspects of the world we live in, including education. At TU Delft in the Netherlands, we have taken a leadership role in transforming learning through the use of technology. Our ambition is to get to a point where we are offering fully digitalized degree programs and we believe digital testing and assessment can play an important role in this process.

A few years ago we launched a project with the goal of using digital testing to drastically improve the pass rates in our programs. Digital testing helps organize testing more efficiently for a larger number of students, addressing issues of overcrowded classrooms, and high teaching workloads. To better facilitate this transformation, we decided to adopt Maple T.A., the online testing and assessment suite from Maplesoft. Maple T.A. also provides anytime/anywhere testing, allowing students to take tests digitally, even from remote locations.

Regular and repeated testing produces the best learning results because progressive monitoring offers instructors the possibility of making adjustments throughout the course. The randomization feature in Maple T.A. provides each student with an individual set of problems, reducing the likelihood that answers will be copied. Though Maple T.A. is specialized in mathematics, it also supports more common question types like multiple choice, multiple selection, fill-in-the-blanks and hot spot. Maple T.A.’s question randomization, possibilities for multiple response fields per question and question workflow (adaptive questions) are superior to other options. By offering regular homework assignments and analyzing the results, we gain better insight into the progress of students and the topics that students perceive as difficult. Our lecturers can use this insight to decide whether to repeat particular material or to offer it in another manner. In many courses, preparing and reviewing practice tests comprise an important, yet time-consuming task for lecturers, and Maple T.A. alleviates that burden.

At TU Delft, we require all first-year students to take a math entry test using Maple T.A in order to assess the required level of math. Since the assessment of the student’s ability is so heavily dependent upon qualifying tests, it is extremely important for the test to be completed under controlled conditions. In Maple T.A., it is easy to generate multiple versions of the test questions without increasing the burden of review, as the tests are graded immediately. Students that fail the entry test are offered a remedial course in which they receive explanations and complete exercises, under the supervision of student assistants. The use of Maple T.A. facilitates this process without placing additional burden on the teacher. When the practice tests and the associated feedback are placed in a shared item bank in Maple T.A., teachers are able to offer additional practice materials to students with little effort. It makes it considerably easier on us as teachers to be able to use a variety of question types, thus creating a varied test.

Each semester, TU Delft offers an English placement test that is taken by approximately 200 students and 50 PhD candidates, in which students are required to formulate their reasons for their program choices or research topics. It used to take four lecturers working full-time for two days to mark the tests and report the results to participants in a timely manner. The digitization of this test has saved us considerable time. The hundred fill-in-the-blank questions are now marked automatically, and we no longer have to decipher handwriting for the open questions!

TU Delft is not alone in its emphasis on digital testing; it has a prominent position on the agendas of many institutions in Europe and elsewhere. These institutions are intensively involved in improving, expanding and advocating the positive results from digital testing and digital learning experiences. Online education solutions like Maple T.A. are playing a key role in improving the quality of digital offerings at institutions.

## New user community for Maple T.A. and Möbius

by: Maple Maple T.A. MaplePrimes

I am very pleased to announce a new user community centered around Maplesoft's online testing and assessment and courseware products. The new site is specifically for instructors and administrators currently using Maple T.A. or Möbius. This community of users are a small, specialised group who we want to bring together so they can share ideas and best practices. To find the community, go to either mapletacommunity.com or mobiuscommunity.com.

"The Maple T.A. Community has grown organically to support new developers as they pool their knowledge and queries. This has resulted in a fluid searchable structure, with answers available for all levels of question - from beginner to pushing the frontiers of what Maple T.A. has been designed to do. Our summer student interns rely on the Community as they become proficient in their question writing skills - and many have become contributors as they realise that they are in a position to teach others. Opening it out more broadly will be great in sharing good practice on a 'need to know now' basis.”

----Professor Nicola Wilkin, University of Birmingham

What content is in the community?

The community has many posts from active Maple T.A. and Möbius users from beginners to advanced users. The site is broken down into categories like 'Best Practices' - longer form posts that cover a broader concept in more detail and 'Quick Code snippets' that are small piece of code that you can drop straight into your question algorithms.

Much of the content is openly available and can be found by google, however there is additional content that can only be accessed by members of the community, such as the Maple T.A. school material which teaches you how to author content in Maple T.A. and Möbius.

Who runs the community

The community is jointly run by users based at the University of Birmingham, TU Wien, The University of Turin and TU Delft.

How does this fit into Mapleprimes?

It began as an offshoot of a private, internal customer forum. As this community grows, the ultimate goal is to eventually roll it into MaplePrimes proper. But this alternative site gave us the quickest way to get up and running. Maple T.A. and Möbius questions and posts are still welcome on MaplePrimes, and will continue to be monitored by Maplesoft.

How do I access the community?

You can find the community by going to either mapletacommunity.com or mobiuscommunity.com.

Where else can I get support for Maple T.A. and Mobiüs?

Official support for Maple T.A. and Möbius is provided by the wonderful Customer Success Team at Maplesoft. You can contact them at help@maplesoft.com. For other contact methods see www.maplesoft.com/support/.

## Bug in MapleTA?...

When I execute the following code in Maplesoft on my computer, there are no problems.  However when I execute the same code in mapleTA occasionally Maple only finds a single input value corresponding with h_given.  Anybody have any idea what is going on?

Basically I have a function, f,  that I am only interested in plotting and analyzing real-valued inputs, t, from =0 to 100 (or so).  At some point I assign an output value, h_given, and I wish to find the correlated real-valued inputs.  From the graph you can clearly see that there are 2 inputs, however the script occassionally only produces 1 output. (when running on mapleTA).

with(Optimization):
with(plots):
restart:
randomize():
a := MapleTA:-Builtin:-range(1800, 2300, 100):
b := (1/10)*MapleTA:-Builtin:-range(4, 8, 1):
timeT := MapleTA:-Builtin:-range(70, 100, 10):
f := -t*(b*t-b*timeT)^2*(cos(.15*t+4)^2-3)/a:
maxs := NLPSolve(f, t = 0 .. timeT, maximize):
maxim := maxs[1]:
graph := plot(f, t = 0 .. timeT, gridlines = true, 0 .. maxim+10, labels = [t, h(t)], labeldirections = [horizontal, vertical]);
h_given := 10;
expr := h_given-f:
answer_t := Student:-Calculus1:-Roots(expr, t = 0 .. timeT+5);