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PreTeXt Sample Book Abstract Algebra (SAMPLE ONLY)

Section 5.28 SPLICE Integration

SPLICE is a project to supply documentation and infrastructure to help with adopting shared standards, protocols, and tools for web-based learning tools. The project has designed a protocol for an embedded iframe to communicate with its host page.
One aspect is the ability of an iframe to ask for a new size. Below is a test of that capability.
These are examples that use the SPLICE protocol for communicating with a server, such as Runestone. They are all integrated into this PreTeXt book as an <interactive> that uses an @iframe attribute to embed an iframe from some other server.
This first sample tests the ability of an iframe to ask for a new size.
The next uses CodeCheck.
Figure 5.28.1. CodeCheck iframe
And the remaing four are from the OpenDSA project.
Figure 5.28.2. Stack pop slideshow
Figure 5.28.3. A List Insertion Exercise
Figure 5.28.4. A Binary Search Exercise
Figure 5.28.5. Dijkstra’s Algorithm Exercise
(2025-11-05) The following two exercises are strictly EXPERIMENTAL. Do not incorporate them into your projects as they are likely to change dramatically.

Checkpoint 5.28.6. Finding the average velocity of a moving object from data (dual, Doenet).

Consider a car whose position \(s\) (in feet) at time \(t\) (in seconds) is given by the table:
\(t\) (sec) \(0\) \(0.3\) \(0.6\) \(0.9\) \(1.2\) \(1.5\)
\(s\) (feet) \(0\) \(0.117\) \(0.468\) \(1.053\) \(1.872\) \(2.925\)

(a)

What are the units on the average velocity of the car?
Hint.
Consider possibilities such as β€œfeet”, β€œseconds”, β€œfeet per second”, or β€œseconds per foot”.
Answer.
feet per second

(b)

Find the average velocity of the car on the interval \(0 \le t \le 0.9\text{.}\)
Hint.
Recall that average velocity is β€œchange in position divided by change in time”.
Answer.
The average velocity of the car on the interval \(0 \le t \le 0.9\) is \(1.17\) feet per second.

(c)

Find the average velocity of the car on the interval \([0.9, 1.5]\text{.}\)
Answer.
The average velocity of the car on the interval \([0.9,1.5]\) is \(3.12\) feet per second.
Source on GitHub

Checkpoint 5.28.7. OpenDSA List Insertion (Dual).

Work this following problem. Note that this is really just a test to see if additional text (beyond an <interactive>) will show up.
An exercise about array-based list insertion goes here.
Source on GitHub
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