(x, why?) Mini: Hot and Cold

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(C)Copyright 2016, C. Burke.

Sitting next to a four-year-old on long trips really can run hot and cold.

We did visit a coal mine in West Virginia, by the way.




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(x, why?) Mini: Under the Sci...

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(C)Copyright 2016, C. Burke.

I prefer to apply Sturgeon's Law to all webcomics, not just to the 1100+ I've written.

By the way, I was just at a Sweet 16 party with an "Under the Sea" theme for the daughter of a couple of friends who go back to my Brooklyn College Science Fiction Society days, which may have played a role and bringing this back to the forefront of my brain.




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Hypersphere

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(C)Copyright 2016, C. Burke.

RIP2-D2

I was considering this months ago, but because I wanted to do it in a classroom setting and didn't have time before the end of the year, I was saving it for the fall.

However, with the passing of Kenny Baker, the man inside the droid we were looking for, I moved it up and reworked it.

For the record, the Volume inside a 4D hypersphere would be 1/2 * pi^2 * r^4.

Edit Wayne's first dialogue balloon is messed up. Two sentences were combined by accident. It will be corrected as time permits. Oopsie!




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(x, why?) Mini: Kites

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(C)Copyright 2016, C. Burke.

Actually, we went South on vacation, not North.

Throwback Thursday: I used a PC with Windows XP and Paint 5.1 to create this one. You use the tools you have not the tools you wish you have.

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(x, why?) Mini: Slugger

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(C)Copyright 2016, C. Burke.

It's all a matter of momentum and position and energy and ... stuff.

Okay, so, no, I'm really not sure how to explain it, so I'll recommend that you check out a wiki page on Liouville equations.

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Daily Regents: Similar Triangles are Proportional (August 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

Geometry, August 2015, Question 27

27. To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.

Use the surveyor’s information to determine and state the distance from point B to point C, to the nearest yard

There are two right triangles. Right angles are congruent.
Both triangles contain angle A. Reflexive Property says angle A is congruent to itself.
Therefore, triangle ABC ~ ADE
If the triangles are similar, then their corresponding sides are proportional.

AE = 230, AC = 230 + 85 = 315. DE = 120. BC corresponds to DE.

Set up a proportion: AE / DE = AC / BC
230/120 = (230 + 85) / x
230 x = (120)(315)
230 x = 37800
x = 164.3478...
x = 164 yards

The distance from point B to point C is 164 yards.

Prove You're Not a Robot

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(C)Copyright 2016, C. Burke.

When we have to bow down to our Computer Overlords, someone will have to answer for this!

Click for other appearances of Tomorrow's Teachers of Tomorrow.




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(x, why?) Mini: Now Playing . . .

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(C)Copyright 2016, C. Burke.

They're here to restore Order to your Operations!

But are some operations too powerful?




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Daily Regents: Volume and Density (August 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

Geometry, August 2015, Question 25

25. A wooden cube has an edge length of 6 centimeters and a mass of 137.8 grams. Determine the density of the cube, to the nearest thousandth.
State which type of wood the cube is made of, using the density table below.

Density is defined as Mass divided by Volume. (d = m/V). You are given the length of one edge of a cube. The volume of the rectangular prism = length times width times height (V = L * W * H). However, with a cube, all three values are the same, so V = s³.

Density = mass / Volume. Volume of a cube = (edge length)³.
If you substitute the values that we know, we find that Density = mass / (edge)³ = 137.8 / (6)³ = 0.63796..., which rounds to 0.638.

According to the table, the approximate value of Ash wood is 0.638.
The wood is Ash.

Note: Don't forget to identify the wood after finding the density, even if you just circle the correct answer.

Also: If you get "Ash" without showing any work, you will NOT score a point.

Daily Regents: Right Triangle Altitude Theorem (June 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

Geometry, June 2015, Question 34

34. In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular.

If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard chair.

Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer.

First part: PLC is a right triangle. This means that you can find the missing side using the Pythagorean Theorem.
So (PL)² + (LC)² = (LC)²
x² + .25² = .55²
x² + .0625 = .3025
x² = .24
x = 0.48989794855 = 0.49 to the nearest hundredth mile.

The second part of the question wants to know, essentially, what is the length of FC. We already know the length of LC, so we need to find the length of FL. We can do this using the Right Triangle Altitude Theorem.
(PL)² = (FL) * (LC) Remember, we found that x² = .24. Do NOT square 0.49
.24 = FL * .25
.24 / .25 = FL
FL = .96
FC = FL + LC = .96 + .25 = 1.21
Gerald is incorrect. The distance is shorter than 1.5 miles.

Alternate Solution

All three right triangles in the diagram are similar triangles, so their corresponding sides are proportional.
Therefore, the proportion (base1) / (hypontenuse1) = (base2) / (hypontenuse2) must be a true statement.

Fill in the information we know: .25 / .55 = .55 / FC
Cross-multiply: .25 FC = (.55)²
.25 FC = .3025
FC = .3025 / .25 = 1.21, which is less than 1.5

Dewfall

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(C)Copyright 2016, C. Burke.

You gotta dew what you gotta dew.




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Henways & Wormdoos

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(C)Copyright 2016, C. Burke.

Sometimes a good pun is just lost on them. And this math man would prefer to go a-whiskey.




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