This comic is for Sunday, June 30, 2019. It was completed on Monday, July 1, 2019 and the entry for the date was updated.
(C)Copyright 2019, C. Burke.
The Arc of the Great Circle sounds like a future Trigonometry Jones series ... Not saying it would be one, but it sounds like one.
A Great Circle is the circle on the plane that divides the sphere into two hemispheres. The equator would be an example.
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This comic is for Friday, June 28, 2019. It was completed on Monday, July 1, 2019 and the entry for the date was updated.
(C)Copyright 2019, C. Burke.
Tau Day will never be A Thing in schools because we'll be on our way out the door if we aren't there already.
A few years back, I referred to Tau as "the Betamax of transcendental numbers". I stand by that description. You may find it better to use, and superior in every way, but VHS still won the VCR wars.
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This comic is for Wednesday, June 26, 2019. It was completed on Monday, July 1, 2019 and the entry for the date was updated.
(C)Copyright 2019, C. Burke.
Issues aside, there's so much truth to this comic.
The female principal and female APs reminded the staff at a meeting in June -- as well as reminding students -- about the dress code. One item was bare midriffs. (Thankfully, I was working at a school where sagging pants are not an overwhelming problem.)
But another part of this is that guidance counselors will loan out shirts (usually extra gym shirts), which the students dislike wearing. However, it's not uncommon that the students have extra clothes in their backpacks -- and that those clothes are what their parents think that they are wearing.
So while you can make an argument for students being able to express themselves through their clothes (and I will REPEAT: you can make it, but it doesn't mean I'll entertain an argument, especially if you're rude, but even if you aren't), some of these arguments get underminded by the fact that they couldn't leave their houses dressed like that because their own parents didn't approve of it. And they are aware of this fact.
Honestly, despite the math pun, I nearly skipped doing this one. But once the last line came to me, I couldn't not use it just because it is a typical thing for a student to say.
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Wait until Mr. Wayne signs it.
Comics have been late because of Real Life, so I may have some school comics despite it being summer time.
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More Algebra 2 problems.
January 2017, Part I
All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.
4. If sin2(32°) + cos2(M) = 1, then M equals
1) 32°
2) 58°
3) 68°
4) 72°
Answer: 1) 32°
The identify is: sin2 x + cos2 x = 1, so the two angles must be the same.
5. What is the solution to the system of equations y = 3x - 2 and
y = g(x) where g(x) is defined by the function below?
1) {(0,-2)}
2) {(0,-2), (1,6)}
3) {(1,6)}
4) {(1,6), (6,16)}
Answer: 4) {(1,6), (6,16)}
First, notice that the graph of g(x) does not go through the point (0, -2), so choices (1) and (2) are incorrect.
Similarly, you can see that (1, 6) is not on the graph. So choice (3) is out.
Choice (4) is the only possible choice.
Point (1, 1) is part of g(x) and (1) = 3(1) - 2 is a true statement.
How do you know that (6, 16) is part of g(x)? You can tell from points (0, 4), (1, 1) and (2, 0) that g(x) is a quadratic function, which in vertex form is y = (x - 2)2. Substitute 6 for x and you will get y = 16.
6. Which statement about statistical analysis is false?
1) Experiments can suggest patterns and relationships in data.
2) Experiments can determine cause and effect relationships.
3) Observational studies can determine cause and effect relationships.
4) Observational studies can suggest patterns and relationships in data.
Answer: 3) Observational studies can determine cause and effect relationships.
Observational studies can investigate an associations between two variables.
Experiment can determine cause and effect relationships.
Comments and questions welcome.
More Algebra 2 problems.
You can't have Testing without Sting.
And in New York today, there is state testing going on.
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Life's been a little crazy, which is why you didn't get a Friday update (which has already been written), nor has one been posted yet for today.
Somehow, I've managed to keep creating Mothers Day and Fathers Day comics, even after losing each of my parents during the years of writing this webcomic. I don't wish to stop now.
So watch this space, a Fathers Day comic will appear soon. I hope. But if not soon, then probably not at all because it will just back me up for everything else. The way it goes I guess.
Update:
Blame the older sibling! It's always the older sibling!
But if he were closing in on the Big Five-0, we (being from Brooklyn) might've called him "Yo Fat" ... or we might not have ...
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More Algebra 2 problems.
January 2017, Part I
All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.
1. Relative to the graph of y = 3 sin x, what is the shift of the graph of y = 3 sin(x + π/3)?
1) π/3 right
2) π/3 left
3) π/3 up
4) π/3 down
Answer: 2) π/3 left
This is the same as it was with functions in Algebra 1. If the change is inside the parentheses, the shift occurs to the left (if there is a plus sign) or right (if there is a minus sign). Outside of the parentheses, the shift occurs up (plus) or down (minus).
By adding to the x value, you are getting y values sooner than you would have with the original function, so the shift is to the left.
2. A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t) is the population of rabbits with respect to time, about how many rabbits will there be in 98 days?
1) 56
2) 152
3) 3668
4) 81,920
Answer: 1) 56
Change 98 days to 14 weeks (divide by 7). The population doubles every 4 weeks, so divide 14 by 4 and get 3.5.
The rabbit population doubles "three and a half" times.
At this point, you can estimate an answer, if you wanted to:
5 doubles once to 10, twice to 20, three times to 40 and four times to 80.
There is only one choice between 40 and 80 and that's Choice (1) 56.
Mathematically, enter the following into the calculator:
5*23.5 = 56.56854... Even though this would round to 57, the only possible choice is 56.
Also, you could have just entered 5*2(98/28), just remember the parentheses if you have an older operating system. The only reason I don't like doing this is that it relies completely on the calculator, and my "Number Sense" probably won't alert me that I made a mistake entering the equation unless it's a completely ridiculous answer. I can picture what doubling three and a half times might mean.
3. When factored completely, m5 + m3 - 6m is equivalent to
1) (m + 3)(m - 2)
2) (m3 + 3m)(m2 - 2)
3) m(m4 + m2 - 6)
4) m(m2 + 3)(m2 - 2)
Answer: 4) m(m2 + 3)(m2 - 2)
Each term has a factor of m, so there must be a factor of m in the answer. This eliminates Choices (1) and (2). Choice (3) can be factored further, so it wasn't "factored completely".
Comments and questions welcome.
More Algebra 2 problems.
Not now. I just 8.
This version of the comic was posted on Twitter on Monday, June 10:
Another topic to cover.
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More Algebra 2 problems.
January 2019, Part IV
The Question in Part IV is worth 6 credits. Partial credit can be earned.
Write a function, A(t), to represent the amount of money that will be in his account in t years.
Graph A(t) where 0 ≤ t ≤ 20 on the set of axes below.
Tony’s goal is to save $1,000,000. Determine algebraically, to the nearest year, how many years it
will take for him to achieve his goal.
Explain how your graph of A(t) confirms your answer.
37.Tony is evaluating his retirement savings. He currently has $318,000 in his account, which earns
an interest rate of 7% compounded annually. He wants to determine how much he will have in the account in the future, even if he makes no additional contributions to the account.
Answer:
A(t) = 318000(1.07)t
Put the equation into a graphing calculator and get the table of values. Plot the points.
Tony's goal is $1,000,000. We can see from the Table of Values and the graph that this will happen between years 16 and 17. However, we need to solve this algebraically. But if we don't get an answer between 16 and 17, we know that a mistake was made and can check our work.
Substitute 1000000 for A(t) and solve for t.
Explain: On the graph A(17) is approximately $1,000,000. This confirms the answer we found.
Comments and questions welcome.
More Algebra 2 problems.
He has the round base. He got the pointy top.
I say: One and one and one is three.
He makes the bad puns and doesn't know when to stop.
If I'm gonna steal, I'll do it math'matically!
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More Algebra 2 problems.
January 2019, Part III
All Questions in Part I are worth 4 credits. Partial credit can be earned.
A simulation was run 1000 times based upon the results of the survey. The results of the
simulation appear below.
Based on the simulation results, is the claim that commuters listen to the station on average
30 minutes plausible? Explain your response including an interval containing the middle 95% of
the data, rounded to the nearest hundredth.
35.A radio station claims to its advertisers that the mean number of minutes commuters listen to the
station is 30. The station conducted a survey of 500 of their listeners who commute. The sample
statistics are shown below.
Answer:
The mean is 29.101. The middle 95% is two standard deviations above and below the mean.
29.101 - 2(0.934) = 27.233
29.101 + 2(0.934) = 30.969
The interval is 27.23 - 30.97
Yes, 30 falls within the interval so the claim is plausible.
36.Solve the given equation algebraically for all values of x.
Answer:
Isolate the radical term by adding 2x to both sides. Then square both sides and solve the quadratic equation.
Discard any negative results because of the radical. (x cannot be less than 0.)
Check for extraneous results
Check: 3 (6.25).5 - 2(6.25) = 3(2.5) - 12.5 = 7.5 - 12.5 = -5 (check)
3 (1).5 - 2(.5) = 3(1) - 1 = 3 - 1 = 2 =/= -5 (reject)
x = 6.25.
Comments and questions welcome.
More Algebra 2 problems.
The rain has to stop at some point, right?
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