Friday, September 07, 2018

Summer Recap, Part 1

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(C)Copyright 2018, C. Burke.

Someone has to be the last to know.

This was supposed to be Wednesday's comic, and today's comic will hopefully appear Monday. Yeah, school started again.




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Monday, September 03, 2018

Annulus

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(C)Copyright 2018, C. Burke.

I prefer let no one 'put us under', but no one catches that when I say it out loud.




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Saturday, September 01, 2018

Dec Savage: The Polar Measure

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(C)Copyright 2018, C. Burke.

Would a polar bear be a 'bear north'? Like a compass? Would it live in a concave?

Oddly, I enjoyed the titular pun because it could refer to an actual measurement, or what actions Dec and the team undertake!

The Polar Treasure was both the fourth pulp adventure and the fourth Bantam paperback.




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Wednesday, August 29, 2018

SPF 360

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(C)Copyright 2018, C. Burke.

The design flaw is the bottoms of your feet. You don't want to get burned down to your soles.

Yes, I feel like a heel for telling that joke.




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Tuesday, August 28, 2018

SPF 60?

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(C)Copyright 2018, C. Burke.

If I had to hypothesize, I'd go with 30*ln(x), where x is the number of coats.

Or just wear coats for the Sun can't get to you. But you might pass out from the heat that way.




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Saturday, August 25, 2018

Dec Savage: The Quest of the 8-Sider

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(C)Copyright 2018, C. Burke.

Even as I type "8-sider", I'm thinking "octahedron" not "octagon".

I haven't read Quest for the Spider yet, and I didn't know that it was so early in the series because it wasn't reprinted as a Bantam paperback until #68.




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Summer Limits

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(C)Copyright 2018, C. Burke.

The limit is on the allowed amount of fun.

The bigger joke is that people think Mike is a stand-in for me, but Mike has never raised his voice to express himself.

Once again, this comic is semi-autobiographical. I can invoke Murphy's here because I've been saying that due to all the rain this summer, I haven't had to top off the pool (or water the garden as much), so the water bill should go down. And now there's a week of Sun ahead of us, and I'm topping off the pool. With cold water. That likely won't warm up too quickly.




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Wednesday, August 22, 2018

Blnx

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(C)Copyright 2018, C. Burke.

Don't try to steal it! It's already taken!

So this happened:

A Twitter colleague, Taylor Grant, @teachbarefoot, announced his new blog

Captain’s ln(x): A Fresh Start
https://teachbarefoot.wordpress.com/2018/08/21/captains-lnx-a-fresh-start/

To which I replied, Now that is a great name for a bln(x)!

Taylor liked my pun better, and re-christened his bln(x) to include the "b".

Obviously, I'm not stealing his idea because a) I suggested the "b", and b) I skipped the parentheses to save space.

Enjoy his blog. My blog will remain the usual comics, test questions and answers, and the occasional mathematical insights, which are hopefully my own and not someone else's restated in (mostly) my own words.




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Tuesday, August 21, 2018

Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


13. A student studying public policy created a model for the population of Detroit, where the population decreased 25% over a decade. He used the model P = 714(0.75)d, where P is the population, in thousands, d decades after 2010. Another student, Suzanne, wants to use a model that would predict the population after y years. Suzanne’s model is best represented by
Which explanation is appropriate for Miles and his dad to make?
1) P = 714(0.6500)y
2) P = 714(0.8500)y
3) P = 714(0.9716)y
4) P = 714(0.9750)y

Answer: 3) P = 714(0.9716)y
There are 10 years to 1 decade, so d = 10y
So P = 714(0.75)d = 714(0.75)10y = 714(0.7510)y
And P = 714(0.9716)y





14. The probability that Gary and Jane have a child with blue eyes is 0.25, and the probability that they have a child with blond hair is 0.5. The probability that they have a child with both blue eyes and blond hair is 0.125. Given this information, the events blue eyes and blond hair are

I: dependent
II: independent
III: mutually exclusive

1) I, only
2) II, only
3) I and III
4) II and III

Answer: (2) II, only
They are independent because P(A and B) = P(A) * P(B). That is 0.125 = 0.5 * 0.25.
This eliminates choices 1 and 3.
The events are not mutually exclusive, because P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.5 - 0.125 = 0.625, but 0.625 =/= 0.5 + 0.25.





15. Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x) = 23.914sin(0.508x - 2.116) + 55.300. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) = 20.238sin(0.525x - 2.148) + 86.729.
Which statement can not be concluded based on the average monthly temperature models x months after starting data collection?
1) The average monthly temperature variation is more in Bar Harbor than in Phoenix.
2) The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix.
3) The maximum average monthly temperature for Bar Harbor is 79° F, to the nearest degree.
4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.

Answer: 4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.
If you graph both of these functions you will find the following information:
For Bar Harbor: the minimum value is 31.39, the midline 55.3, the maximum is 79.21 and the range is 47.83.
For Phoenix, min is 66.49, mid is 86.73, max is 106.97 and range is 40.48.
Choices 1, 2, and 3 can be seen in the data. Choice 4 is incorrect, the minimum average monthly temperature for Phoenix is approximately 66° F, to the nearest degree.



Comments and questions welcome.

More Algebra 2 problems.

Monday, August 20, 2018

Palindrome Week

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(C)Copyright 2018, C. Burke.

Dammit, I'm mad.

I guess that was, you know, "palindrome weak".




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Saturday, August 18, 2018

Dec Savage: The Plane of Terror

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(C)Copyright 2018, C. Burke.

Are the odds stacked against Dec?

I'm still decided on the format. I'll probably use the pulp order (or publication order) but parody the Bantam covers.

I fiddled with the logo, and I made the image taller so I could include a "cover blurb", which makes up for the lack of dialogue. Also, the blurb means people who see the image away from the blog or the comic page will see that text and not miss the joke. Without context, it's just an odd image.




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Friday, August 17, 2018

Pleased as Punch

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(C)Copyright 2018, C. Burke.

Historically, the expression is *pleased as Punch & Judy*.

And Ken is the puppet master.

I had more exposition, but it was just a recap of last week's comic and blog notes. Who needs that, right? what we really need is a wacky Wikipedia link!




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Wednesday, August 15, 2018

(x, why?) School Life #6: The Next Level

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(C)Copyright 2018, C. Burke.

When you beat bosses together, it's getting serious.

My intent had been to have more updates this week, but this one took a lot longer than anticipated, even in black and white.




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Monday, August 13, 2018

(x, why?) School Life #5: At The Beach

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(C)Copyright 2018, C. Burke.

Well, someone's got to get these two together, right?

Debated whether or not to do "School Life" in the summer, and then whether or not this strip would fall into that category. (For one thing, it's in color, not black and white.) That's what I get for starting so many sub-series within the main series. Why am I even numbering these things?

How should things work out for Vanessa and Sven? Or Missy and Vaughn? Or the green-haired kid whom I don't think I created a name for...




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Saturday, August 11, 2018

Dec Savage: The Shape of Bronze

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(C)Copyright 2018, C. Burke.

''Doc? Are we going to Widow's Peak?'' ''No!''

Something old becomes something new. I had a bit of debate with myself about how to do this. Just the covers? Do I need dialogue? If so, where to add it? Maybe underneath, or just the "alt" text. I don't know.

If it's just the covers, with no dialogue, then I spent too much time -- including a Twitter poll -- deciding on the supporting characters. We'll see as time moves on.

Also, if anyone knows how to *easily* remove the shadows from WordArt, or knows a similar program to produce the titles, that would be great.

By the way, the alternate title was going to be Dec Visage, to remove it further from the original, but I thought that that might be too far. "Visage", of course, is a word refering to a face, which 3-D objects, like prisms and pyramids, have.




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Friday, August 10, 2018

Logical Progression

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(C)Copyright 2018, C. Burke.

ObMath: The mean age of the guys should equal the mean age of the girls. And other mean stuff going on.

The dialogue for this comic was originally wordier, trying to get it where it needed to go (and even included, sort of, a reference to the above fact, giving their relative ages). Judy and Chuck have been together almost as long as Ken and Michele (possibly longer, but I'm only going by first mentions).

Stranger fact: even though Chuck has been mentioned a few times, I don't think he's appeared since comic #321 on the Fourth of July in 2009. NINE YEARS! He was supposed to be shown at the wedding, but I simplified that strip as much as I could, so none of the +1's were shown.




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Wednesday, August 08, 2018

(x, why?) Mini: Viscous

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(C)Copyright 2018, C. Burke.

Stand back. You don't to get into the thick of it!




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Monday, August 06, 2018

(x, why?) Mini: Changin' Sines

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(C)Copyright 2018, C. Burke.

Don't stand in the amplitude. Don't block the wave.

Yeah, that's about all I had. That's why this became a "mini". For what it's worth, this looks like the 100th Mini I've done.
I say "looks like" because my count has been off once before due to mislabeling a file. But this is the 100th entry that has the Mini tag.




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Saturday, August 04, 2018

The Casebook of Sherlock Pi: The Adventures of the Cardboard Box

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(C)Copyright 2018, C. Burke.

Doctor Woo Hoo and his Companion. Or Doctor Cutey and her Companion.




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Wednesday, August 01, 2018

Angles in the Night

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(C)Copyright 2018, C. Burke.

They were complementary, and it turned out so right.




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Monday, July 30, 2018

Old Blue Eyes

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(C)Copyright 2018, C. Burke.

Don't be the negative one here. That's his job.

I can't believe I haven't done this before. And there may be more of this to come.




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Saturday, July 28, 2018

The Casebook of Sherlock Pi: The Noble Bachelor

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(C)Copyright 2018, C. Burke.

He is happy just as He is. Say what you want, you won't get a reaction.




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Friday, July 27, 2018

Togetherness

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(C)Copyright 2018, C. Burke.

Mr. & Mrs. Wayne will pop up any time now.

I wanted a Ken-and-Michele-are-back comic, and then I left them out of it.

I also left out the math -- probability that two people would capsize the chair was approximately 1.0.

I also figured that they would have gone out with Judy and Chuck first, but where's the math in that? Other than figuring the tip? (Chuck might be the least mature of the group, but I didn't want him to be a dweeb or anything.)




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Thursday, July 26, 2018

Parallel vs. Perpendicular vs. Skew: Getting Shiggy edition

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(C)Copyright 2018, C. Burke.

It's only skew if the dancer *misses* the pole. But that wouldn't be as funny!
Don't try this at home. Or on the road.

Don't get ''shiggy'' with it.






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Wednesday, July 25, 2018

(x, why?) Mini: 10 to the -6th Aggressions

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(C)Copyright 2018, C. Burke.

I had a couple different ideas, but thise was the quicker one to do after my day off.






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Monday, July 23, 2018

June 2018 Common Core Geometry Regents, Parts III and IV

The following are some of the multiple questions from the recent June 2018 New York State Common Core Geometry Regents exam.
The answers to Part I can be found here
The answers to Part II can be found here

June 2018 Geometry, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.


32. Triangle ABC has vertices with coordinates A(-1,-1), B(4,0), and C(0,4). Prove that ABC is an isosceles triangle but not an equilateral triangle. [The use of the set of axes below is optional.]

Answer:
If it is isosceles, then at least two legs have the same length. If it is not equilateral, then the third leg will have a different length.
Looking at the coordinates of the points, it should be obvious that AB and AC are congruent because you'll be using the same numbers in the calculations.
AB = SQRT ( (-1 - 4)2 + (-1 - 0)2 ) = SQRT(26)
AC = SQRT ( (-1 - 0)2 + (-1 - 4)2 ) = SQRT(26)
BC = SQRT ( (4 - 0)2 + (0 - 4)2 ) = SQRT(32)
There is no need to simplify because you're only looking for equality or inequality.
AB is the same length as AC but not the same as BC. Only two sides are congruent, so ABC is isosceles but not equilateral.


33. The map of a campground is shown below. Campsite C, first aid station F, and supply station S lie along a straight path. The path from the supply station to the tower, T, is perpendicular to the path from the supply station to the campsite. The length of path FS is 400 feet. The angle formed by path TF and path FS is 72°. The angle formed by path TC and path CS is 55°.


Determine and state, to the nearest foot, the distance from the campsite to the tower.

Answer:
We can find the length of TS by using the tangent function with triangle TSF.
Once we know TS, we can use the sine function with triangle TSC to find the length of CT, the distance from the campsite to the tower.
Make sure your calculator is in Degree mode.

Tan 72 = x / 400
x = 400 * tan 72 = 1231.07...

Sin 55 = 1231.07 / y
y = 1231.07 / sin 55 = 1502.85897... = 1503 feet.
The distance from the campsite to the tower is 1503 feet.

Note that you could have skipped the intermediary skip and used (x / 400) in the last equation. Finding the length of TS was not required for the problem.


34. Shae has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The total weight of the bag, pole, and unfilled base is 270 pounds. The cylindrical base is 18 inches tall with a diameter of 20 inches. The dry sand used to fill the base weighs 95.46 lbs per cubic foot.


To the nearest pound, determine and state the total weight of the training equipment if the base is filled to 85% of its capacity.

Answer:
Find the Volume of the Base in cubic feet (not cubic inches). Multiply that by .85 to find 85% of the Volume. Multiply that by 95.46 to find the weight of the sand in the base. Then add 270 pounds for the bag, pole and unfilled base.
Remember that the radius is half the diameter: 20 / 2 = 10 inches, which is 10/12 of a foot. The height is 18 inches, which is 18/12 feet.
V = pi * r2 * h = (3.141592...)(10/12)2 * 18/12 = 3.27249
.85V = .85 * 3.27249 = 2.7816 cubic feet.
The weight of the sand = 2.7816 * 95.46 = 265.53 pounds.
Total weight = 265.53 + 270 = 535.53 or 536 pounds.


End of Part III

Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.


35. Parallelogram ABCD, BF ⊥ AFD, and DE ⊥ BEC.


Prove: BEDF is a rectangle

Answer:
BEDF is a rectangle if it is a parallelogram as has a right angle. You need not prove the length of the opposite sides are congruent.
1. ABCD is a parallelogram, BF ⊥ AFD, DE ⊥ BEC: Given
2. BC || AD: Opposite sides of a parallelogram are parallel.
3. BE || DE: Parts of parallel lines are parallel.
4. BF || DE: Two lines that are perpendicular to the same line are parallel.
5. BEDF is a parallelogram: A quadrilateral with two pairs of parallel sides is a parallelogram.
6. Angle DEB is a right angle: Perpendicular lines form right angles.
Note: Line 6 wasn't actually *Given*, even though the boxes for right angles are shown in the diagram. Whatever reason you give, the fact that it is a right angle is important and must be stated!
7. BEDF is a rectangle: A parallelogram with a right angles is a rectangle.

End of Part IV

How did you do?

Questions, comments and corrections welcome.