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Section 6 WeBWorK

These exercises demonstrate some WeBWorK features.
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Checkpoint 6.1. Answer Type Variety.

This problem demonstrates that WeBWorK can process many kinds of answers.
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Consider the function \(f\) defined by \(f(x)={\sqrt{x}}\text{.}\)
  1. The exact value of \(f(12)\) is and a decimal approximation for this is .
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  2. The domain of this function, in interval notation, is .
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  3. The graph of \(y={\sqrt{x}}\) intersects the graph of \(y=6-x\) at .
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  4. \(\frac{d}{dx}{\sqrt{x}}={}\) .
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  5. The formula for \(f(x)^2\text{,}\) including its restricted domain, is .
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  6. \(f\) is a
    function.
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  7. Which is true of the word “radical”?
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    • It shares ancestry with "radius", as in the radius of a circle.
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    • It shares ancestry with "radish", a vegetable.
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    • It shares ancestry with "radler", a mixture of beer and grapefruit soda.
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Answer 1.
\(2\sqrt{3}\)
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Answer 2.
\(3.4641\)
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Answer 3.
\(\left[0,\infty \right)\)
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Answer 4.
\(\left(4,2\right)\)
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Answer 5.
\(\frac{1}{2\sqrt{x}}\)
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Answer 6.
\(x, x\ge 0\)
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Answer 7.
\(\text{power}\)
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Answer 8.
\(\text{Choice 2}\)
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Checkpoint 6.2. Special Feedback.

Try multiplying the exponents to see what feedback you get. Also, try something no one should get credit for, like x^2*x^5.
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Simplify the expression \({x^{2}x^{5}}\text{.}\)
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Hint.
Add the exponents.
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Answer.
\(x^{7}\)
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Solution.
To simplify the product of two powers of the same base, add the exponents.
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\begin{equation*} \begin{aligned} {x^{2}x^{5}}\amp=x^{2+5}\\ \amp={x^{7}} \end{aligned} \end{equation*}
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Checkpoint 6.3. String Answers.

Spelling counts, but not capitalization or spaces.
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This Venn Diagram groups animals by certain characteristics.
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epspdfpngsvgtex
Name an animal that belongs in the center region. Spelling counts!
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Answer.
\({\text{platypus}}\)
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Checkpoint 6.4. Open Problem Library.

WeBWorK has an Open Problem Library with over 40,000 exercises. One of them is this exercise, with file path Library/PCC/BasicAlgebra/NumberBasics/FactorInteger10.pg
 1 
github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/PCC/BasicAlgebra/NumberBasics/FactorInteger10.pg
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Find the prime factorization of \(35\text{.}\)
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\(35={}\)
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Answer.
\(5\cdot 7\)
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Solution.
After checking to see if small prime numbers divide \(35\text{,}\) we find that \(5\) is one divisor. So \(35=5\cdot7\text{.}\)
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Since both \(5\) and \(7\) are prime, the prime factorization of \(35\) is \(5\cdot7\text{.}\)
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Checkpoint 6.5. Structured with Tasks.

This problem has multiple parts that must be completed in order. Try answering the second part with various things you might expect a user to enter.
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(a) Identify Coefficients.

Consider the equation
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\begin{equation*} {2x^{2}-7x-15} = 0 \end{equation*}
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Identify the coefficients for the quadratic equation using the standard form from Subsection 1.1.
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\(a=\) , \(b=\) , \(c=\)
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Answer 1.
\(2\)
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Answer 2.
\(-7\)
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Answer 3.
\(-15\)
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Solution.
Take the coefficient of \(x^2\) for the value of \(a\text{,}\) the coefficient of \(x\) for \(b\text{,}\) and the constant for \(c\text{.}\) In this case, they are \(a = 2\text{,}\) \(b = -7\text{,}\) \(c = -15\text{.}\)
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(b) Use the Quadratic Formula.

Use the quadratic formula to find the solution set to
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\begin{equation*} {2x^{2}-7x-15}=0 \end{equation*}
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Answer.
\(\frac{-3}{2}, 5\)
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Solution.
Recall that the quadratic formula is given in Subsection 1.1.
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You already identified \(a = 2\text{,}\) \(b = -7\text{,}\) and \(c = -15\text{,}\) and the results from using these in the quadratic formula are \(-\frac{3}{2}\) and \(5\text{.}\)
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Checkpoint 6.6. Units in Answers.

The answers in this exercise require that units be used.
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  1. The average cost of gasoline in the United States in 2010 was $2.78 per gallon. How much gasoline would $20 get you in 2010, on average?
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  2. In 2011, the average cost was $3.52 per gallon. What percent increase was that from 2010?
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  3. In 2012, the cost had risen 2.8% from the 2011 cost. What was the cost of a gallon of gasoline in 2012?
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Answer 1.
\(7.19424\ {\rm gal}\)
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Answer 2.
\(26.6\%\)
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Answer 3.
\(\$3.62\)
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