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For Problem 11 on the WeBWorK I did the division correctly as my quotient was right, but my remainder was wrong. I got 14 as my remainder.
What is the polynomial you are dividing and the polynomial divisor?
The polynomial is \(x^5-x^4+4x^3-4x^2+5x-9\), the divisor being \(x-1.\)
Below you will find two animations showing the steps you would take using synthetic and long division:
For WeBWorK 10 Problem 2, how do I get the last root of the function off the graph? I have the first three, but I need one more given the function is a 4th degree.
Assuming the graph has zeros \(x=1,-1,\) and \(0\), then the equation for the function should be of the following form:
$$
f(x) = k(x-1)(x+1)x
$$
where \(k\) is some constant to be determined. In addition, you have one other point \((2,-1)\) which the function must pass through. Therefore, substituting in this ordered pair into our equation, we obtain the value of \(k\):
$$
-1 = k(2-1)(2+1)2
$$
or that \(k = -1/6.\)
So, the equation which has the given graph is given by
$$
f(x) = \frac{-1}{6} (x-1)(x+1)x.
$$
I got 8/63 as my value for k, but it was wrong. So I set the problem up like so: -8=k(1-8)(1+8)1. Simplifying this gives you -63k=-8. Divide by -63 and you get 8/63.
What are the given conditions that have to be satisfied?
Professor Nevo, for Problem 1 on WeBWorK 10 I’m getting x^4-4x^3-19x^2+46x-24 as my answer. It’s wrong, but I don’t know why. How do I account for the y intercept at (0,12)?
Take a look at the solution to question 2 that I provided below. A similar argument should be used for problem 1.
But then 0=12 which is false, no?
This message comes up when I try to put in the answer for Problem 8 Set 9
Warning — there may be something wrong with this question. Please inform your instructor including the warning messages below.
WeBWorK error
An error occured while processing your request. For help, please send mail to this site’s webmaster (webmaster@localhost), including all of the following information as well as what what you were doing when the error occured.
Wed Jun 12 16:41:19 2013
Warning messages
Processing of this PG problem was not completed. Probably because of a syntax error. The translator died prematurely and no PG warning messages were transmitted. at /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/Problem.pm line 752.
Error messages
Can’t use an undefined value as an ARRAY reference at /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/Problem.pm line 215.
Call stack
The information below can help locate the source of the problem.
in WeBWorK::ContentGenerator::Problem::attemptResults called at line 1400 of /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/Problem.pm
in WeBWorK::ContentGenerator::Problem::output_summary called at line 152 of /opt/webwork/webwork2/lib/WeBWorK/Template.pm
in WeBWorK::Template::template called at line 496 of /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator.pm
in WeBWorK::ContentGenerator::content called at line 477 of /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/Problem.pm
in WeBWorK::ContentGenerator::Problem::content called at line 200 of /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator.pm
in WeBWorK::ContentGenerator::go called at line 371 of /opt/webwork/webwork2/lib/WeBWorK.pm
Request information
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For Problem 8 on WeBWorK how would I find the other two numbers where the company breaks even? I have the first one.
Break-even occurs when revenue equals cost or, equivalently, when profit equals zero. That is, if P(x) is the profit function, then break-even is a solution to P(x) = 0.
Professor Nevo, for Problems 12 & 13, I’m not sure how to input my answers. I have a list of x values, but the problem is asking for an inequality. Why is this?
This question has already been raised by another student. Take a look at the older comments.
For Problem 2 on thze Homework how would you find all real zeros of the function?
Try factor-by-grouping.
Professor Nevo, how would you find two different polynomial functions given their zeros?
Here is an example: Suppose you want to find two different polynomials that have zeros \(x = 0\) and \(x = -2\). Then certainly \(f(x) = x(x+2)\) and \(g(x) = 3x(x+2)\) satisfy the given conditions.
How do I type in infinity on the webwork
Use INF and -INF for infinity and negative infinity, respectively.
For WebWork9 I don’t understand why the answers of problems 12 and 13 have to be inequalities? The final factored forms are \(3x^2(x+4)(x-4)\) and \(4x(x+4)(x-3)\) respectively leaving the roots to be 0,4,-4 and 0,-4,3, I believe; how do I enter this as an inequality?
WeBWorK wants the input to be in the form “x = 0 or x = 4 or x = -4” in whatever order you like. The main thing is to list the solutions as “x = a”, where “a” is a solution, separated by “or”.