PTXSC WeBWorK

Section 6 WeBWorK

These exercises demonstrate some WeBWorK features.

Checkpoint 6.1. Answer Type Variety.

This problem demonstrates that WeBWorK can process many kinds of answers.

Consider the function $f$ defined by $f(x)={\sqrt{x}}\text{.}$

The exact value of $f(12)$ is and a decimal approximation for this is .
The domain of this function, in interval notation, is .
The graph of $y={\sqrt{x}}$ intersects the graph of $y=6-x$ at .
$\frac{d}{dx}{\sqrt{x}}={}$ .
The formula for $f(x)^2\text{,}$ including its restricted domain, is .
$f$ is a
- power
- exponential
- linear
- quadratic
function.
Which is true of the word “radical”?
- It shares ancestry with "radius", as in the radius of a circle.
- It shares ancestry with "radish", a vegetable.
- It shares ancestry with "radler", a mixture of beer and grapefruit soda.

Answer 1.

$2\sqrt{3}$

Answer 2.

$3.4641$

Answer 3.

$\left[0,\infty \right)$

Answer 4.

$\left(4,2\right)$

Answer 5.

$\frac{1}{2\sqrt{x}}$

Answer 6.

$x, x\ge 0$

Answer 7.

$\text{power}$

Answer 8.

$\text{Choice 2}$

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.

Simplify the expression ${x^{2}x^{5}}\text{.}$

Hint.

Add the exponents.

Answer.

$x^{7}$

Solution.

To simplify the product of two powers of the same base, add the exponents.

\begin{equation*} \begin{aligned} {x^{2}x^{5}}\amp=x^{2+5}\\ \amp={x^{7}} \end{aligned} \end{equation*}

Checkpoint 6.3. String Answers.

Spelling counts, but not capitalization or spaces.

This Venn Diagram groups animals by certain characteristics.

eps pdf png svg tex

Name an animal that belongs in the center region. Spelling counts!

Answer.

${\text{platypus}}$

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

github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/PCC/BasicAlgebra/NumberBasics/FactorInteger10.pg

Find the prime factorization of $35\text{.}$

$35={}$

Answer.

$5\cdot 7$

Solution.

After checking to see if small prime numbers divide $35\text{,}$ we find that $5$ is one divisor. So $35=5\cdot7\text{.}$

Since both $5$ and $7$ are prime, the prime factorization of $35$ is $5\cdot7\text{.}$

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.

(a) Identify Coefficients.

Consider the equation

\begin{equation*} {2x^{2}-7x-15} = 0 \end{equation*}

Identify the coefficients for the quadratic equation using the standard form from Subsection 1.1.

$a=$ , $b=$ , $c=$

Answer 1.

$2$

Answer 2.

$-7$

Answer 3.

$-15$

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 $a = 2\text{,}$ $b = -7\text{,}$ $c = -15\text{.}$

(b) Use the Quadratic Formula.

Use the quadratic formula to find the solution set to

\begin{equation*} {2x^{2}-7x-15}=0 \end{equation*}

Answer.

$\frac{-3}{2}, 5$

Solution.

Recall that the quadratic formula is given in Subsection 1.1.

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 $5\text{.}$

Checkpoint 6.6. Units in Answers.

The answers in this exercise require that units be used.

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?
In 2011, the average cost was $3.52 per gallon. What percent increase was that from 2010?
In 2012, the cost had risen 2.8% from the 2011 cost. What was the cost of a gallon of gasoline in 2012?

Answer 1.

$7.19424\ {\rm gal}$

Answer 2.

$26.6\%$

Answer 3.

$\$3.62$

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