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, here are the results of benchmarking for and foreach .

For each of int and double , I created an array and a List<T> , filled it with random data (the same for the list as the array) and ran each of the following ways of summing the collection:

I won’t show the complete code in this post, but it’s you can download it and then build it against the benchmarking framework . Here’s a taste of what it looks like – the code for a list instead of an array, and double instead of int is pretty similar:

List< int > intList = Enumerable.Range(0, Size) .Select(x => rng.Next(100)) .ToList(); int [] intArray = intList.ToArray();

var intArraySuite = TestSuite.Create( “int[]” , intArray, intArray.Sum()) .Add(input => { int sum = 0; for ( int i = 0; i < input.Length; i++) sum += input[i]; return sum; }, “For” ) .Add(input => { int sum = 0; int length = input.Length; for ( int i = 0; i < length; i++) sum += input[i]; return sum; }, “ForHoistLength” ) .Add(input => { int sum = 0; foreach ( int d in input) sum += d; return sum; }, “ForEach” ) .Add(IEnumerableForEach) .Add(Enumerable.Sum, “Enumerable.Sum” ) .RunTests();

static int IEnumerableForEach(IEnumerable< int > input){ int sum = 0; foreach ( int d in input) { sum += d; } return sum;}

(I don’t normally format code quite like that, and wouldn’t even use a lambda for that sort of code – but it shows everything quite compactly for the sake of blogging.)

Before I present the results, a little explanation:

Happy with that? Here are the results…

——————– Doubles ——————– ============ double[] ============ For 1.00 ForHoistLength 1.00 ForEach 1.00 IEnumerableForEach 11.47 Enumerable.Sum 11.57

============ List<double> ============For 1.99ForHoistLength 1.44ForEach 3.19IEnumerableForEach 18.78Enumerable.Sum 18.61

——————– Ints ——————–============ int[] ============For 1.00ForHoistLength 2.03ForEach 1.36IEnumerableForEach 15.22Enumerable.Sum 15.73

============ List<int> ============For 2.82ForHoistLength 3.49ForEach 4.78IEnumerableForEach 25.71Enumerable.Sum 26.03

I found the results interesting to say the least. Observations:

Expert solutions on video to physics homework problems from the OpenStax College Physics textbooks

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Final Answer

The best way to practice is to try the problem first, then check the final answer to quickly see if you got it right. Final answers are , so just take a look .

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Sometimes the difference between a right and wrong answer is how you plug it into your calculator. You won't make these kinds of mistakes since you will see how Shaun Dychko made the calculation.

College Physics Answers offers screencast video solutions to end of chapter problems in the textbooks published by OpenStax titled "College Physics" and "College Physics for AP Courses". These textbooks are available for free by following the links below. Both the PDF and printed versions of these textbooks contain the same problems. The only difference is that "College Physics" omits the "Test Prep for AP Courses" section found only in the "College Physics for AP Courses" text, but otherwise the end of chapter problems are identical.

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Submitted by marievillafuerte on Tue, 06/12/2018 - 21:57

In the problem of part b you have 8/3 in the square root, but in your calculator you have 5. Is that an error?

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on Wed, 06/13/2018 - 07:30

Nice catch marievillafuerte! Yes, that was an error. I've corrected it by uploading an updated calculator screenshot and changed the final written answer.

Thanks again, and best wishes with your studies,

Shaun

In reply to In the problem of part b you… by marievillafuerte

Submitted by marievillafuerte on Tue, 06/12/2018 - 20:20

On my table 5.1 Steele on ice for static friction is 0.40

Also, because she is initially stationary doesn't that mean she is not moving. Meaning that her acceleration would be zero?

Submitted by ShaunDychko on Tue, 06/12/2018 - 20:32

Teach debugging

In the fall of 2000, I took my first engineering class: Carolbar Womens Solid Color Cute Bow Block Heel Lovely Court Shoes White rK9eWq4Mnu
, an entry-level digital design class for first-year computer engineers. It was standing room only, filled with waitlisted students who would find seats later in the semester as people dropped out. We had been warned in orientation that half of us wouldn't survive the year. In class, We were warned again that half of us were doomed to fail, and that ECE 352 was the weed-out class that would be responsible for much of the damage.

The class moved briskly. The first lecture wasted little time on matters of the syllabus, quickly diving into the real course material. Subsequent lectures built on previous lectures; anyone who couldn't grasp one had no chance at the next. Projects began after two weeks, and also built upon their predecessors; anyone who didn't finish one had no hope of doing the next.

A friend of mine and I couldn't understand why some people were having so much trouble; the material seemed like common sense. The Feynman Method was the only tool we needed.

The Feynman Method failed us on the last project: the design of a divider , a real-world-scale project an order of magnitude more complex than anything we'd been asked to tackle before. On the day he assigned the project, the professor exhorted us to begin early. Over the next few weeks, we heard rumors that some of our classmates worked day and night without making progress.

But until 6pm the night before the project was due, my friend and I ignored all this evidence. It didn't surprise us that people were struggling because half the class had trouble with all of the assignments. We were in the half that breezed through everything. We thought we'd start the evening before the deadline and finish up in time for dinner.

We were wrong.

An hour after we thought we'd be done, we'd barely started; neither of us had a working design. Our failures were different enough that we couldn't productively compare notes. The lab, packed with people who had been laboring for weeks alongside those of us who waited until the last minute, was full of bad news: a handful of people had managed to produce a working division unit on the first try, but no one had figured how to convert an incorrect design into something that could do third-grade arithmetic.

I proceeded to apply the only tool I had: thinking really hard. That method, previously infallible, now yielded nothing but confusion because the project was too complex to visualize in its entirety. I tried thinking about the parts of the design separately, but that only revealed that the problem was in some interaction between the parts; I could see nothing wrong with each individual component. Thinking about the relationship between pieces was an exercise in frustration, a continual feeling that the solution was just out of reach, as concentrating on one part would push some other critical piece of knowledge out of my head. The following semester I would acquire enough experience in managing complexity and thinking about collections of components as black-box abstractions that I could reason about a design another order of magnitude more complicated without problems -- but that was three long winter months of practice away, and this night I was at a loss for how to proceed.

"Be yourself. Everyone else is already taken." — Oscar Wilde