Cooking: the found recipe

Tutoring high school subjects, you learn about teenagers. The tutor tells a story about a recipe he found.

On a late-July day in 2013, walking around Robron Centre with my kids, I saw a photocopy lying on the deserted pavement. I knew at once it was a kid’s assignment, cast off with the school year that had ended a month earlier. I picked it up.

I guess there hadn’t been much rain since school had let out. The photocopy was in good condition, somewhat browned from the sun. It was a recipe, likely from a foods class. The title – Apple Coffee Cake – led into a description of the muffin method. The page had neither date nor name. In neat pen, much neater than my writing ever was, the student had answered all the questions following the recipe.

I decided to keep the recipe; I told my kids we’d make it at home. Not immediately, but sometime that fall, when school was already back in, we did. I’ve made it a few times since; my family likes it. The recipe is pinned to the fridge.

I’ve always wondered why the student, having completed that assignment, never handed it in. Likely, by now, they’ve either graduated or are just about to. Do they recall that recipe, that day in foods class, at all?

A teenager’s life is often more complex than an adult’s. Priorities can change invisibly, hour by hour. That’s how you end up with a carefully completed assignment, deserted in a school parking lot, never having earned any credit.

Let’s get those completed assignments in, people:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Lifestyle: toy repair with J-B Weld, part II

The tutor continues about a toy repair, with some reinforcement ideas.

While we were repairing the toy a few nights ago (see my previous post), my father-in-law suggested that, after the first repair cured, a second application should be considered around the outside. Such reinforcement, he commented, would give the repair its best chance of holding.

I considered his counsel from an engineering point of view: how much extra strength could we anticipate from application of J-B Weld around the outside of the repair site?

Let’s imagine the shear force to be straight forward. The strength of a reinforcement can be, generally, proportional to its left-right length multiplied by its height, then by the square of its forward length. Assuming the J-B Weld works as an integral piece after drying, I imagined an outside application along each side plane. The application would be about 20 times the height of the original shear, then its same forward length, but only about 1/30 of its left-right length. Compared with the first repair reuniting the two sheared surfaces, the reinforcement strength per side might be 20(1/30) or 2/3. Both sides together could offer reinforcement strength of 2(2/3)=4/3 or 1.33 times the strength of the original repair, more than doubling its shear resistance.

With these numbers in mind, I took my father-in-law’s advice and made the reinforcement application about 24 hours ago. The repair should be ready right now.

I’ll be sharing more about this fascinating toy repair:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Lifestyle: toy repair w/ J-B Weld

The tutor wonders about a pending toy repair.

My younger son has a toy he really loves that broke. Specifically, a pot metal part sheared off. It’s a toy out of production, so can’t be replaced.

Looking at the breakage, a repair seemed unlikely to work. I went to the hardware store and explained the situation. The man handed me J-B Weld: “If anything could work, this will.”

The J-B Weld label suggests a tensile strength of 3960 psi. The tensile strength of pot metal might be around 40 000 psi. In the toy, the strain on the metal part is not tensile, but rather shear. The shear strength of pot metal is around 75% of its tensile; if the same for the repair, it might be around 3000 psi.

I estimate the surface of the repair to be about 1/64, or 0.015625, inch2, suggesting a repair strength of 3000(0.015625) = 47 pounds.

The pot metal part stretches an elastic. Stretching the same elastic even further by a hanging mass, I’ve determined that the toy’s pulling force is less than 2.5 lbs. With estimated strength of 47 pounds, the repair should hold.

J-B Weld needs 24 hours to cure; the repair has had about 36. I guess we’ll know soon if it works. I’ll keep you posted:)

Source:

wikipedia

sciencedaily.com

jbweld.com

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Spreadsheets: Excel circular reference: recursive deduction calculation

The tutor shows how to use a spreadsheet (Excel) to compute a recursive deduction rate using a circular reference.

In yesterday’s post I brought up an example in which a deduction depends upon the income minus that same deduction. It’s a recursive situation: to calculate the deduction, it seems, you must already have subtracted it from the income; therefore, you must already know it. As I showed in yesterday’s post, algebra handles the calculation of the deduction nicely.

For those not keen on using algebra, there is a spreadsheet method, as well, to calculate the deduction. Let’s revisit the problem, then solve it the spreadsheet way:

An employer offers a health plan that costs 6% of net income. The company’s definition of net income is gross pay minus the health plan deduction. Find the monthly health premium of an employee whose gross monthly pay is 2500.

Solution:

On a spreadsheet, we solve the problem by naming a few cells, then defining a couple of formulas. Of course, you can use whichever cells you want. Let’s imagine you start with cell B6 and name it Income. To name it, just right-click while it’s selected, then click Name a Range… A text box will appear in which you can type the name, then click OK.

It’s easy to forget which cell you actually named. I highlight the ones I use by clicking the down arrow next to the Fill icon (which is a bucket of paint spilling, found with the font change icons). I click the shade I want, then the cell is highlighted that color.

Now I select another cell – let’s say it’s D6. I’ll name it Net_Income (names can’t have spaces), then type, inside it, the formula

=Income – Health_Premium

Next, I highlight that cell so I can see where it is.

Yet another cell needs to be selected. It will be named Health_Premium. Inside that cell will be typed the formula

=0.06*Net_Income

Of course, * means multiply.

Now, depending on how Excel is set up, a blue line might appear between the Net_Income and Health_Premium cells. In addition, you might see a pop-up: Circular Reference Warning. It explains that a circular reference is a formula that depends on its own result. If offers more information if you click OK; we do so.

In the ensuing write-up about circular references, the first option mentioned is to withdraw the circular reference. Down further, it tells how to enable the circular reference:

  1. Click the top left button (the round one with the four coloured squares), then click Excel Options.
  2. In the next menu that appears click Formulas.
  3. To the right, under calculation options, click the box Enable Iterative Calculation. Then, at the bottom, click OK.

When you return to the spreadsheet, the blue line between the Net_Income and Health_Premium cells will be gone.

If you type the value 2500 into the Income cell, 2358.49 will appear in the Net_Income cell, and 141.51 in the Health_Premium cell. Those values are the same from yesterday’s post.

I think you’ll agree that the spreadsheet solution is appealing. However, the user needs to grasp the problem very well in order to define the cells and the formulas they must contain. It truly is a case of telling the computer the problem to solve, then having the computer solve it.

I’ll be talking more about spreadsheets in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Math: Deduction rates: a recursive example

Sometimes, deduction rates can be tricky. The tutor offers an example of a “circular argument.”

Let’s imagine a benevolent employer offers a health plan that costs 6% of the employee’s net income. The company’s definition of net income is gross pay minus the health plan deduction. Find the monthly health premium of an employee whose gross monthly pay is 2500.

Solution:

Let p be the premium amount.

    \[p=0.06(2500 - p)\]

Expanding, we get

    \[p=150 - 0.06p\]

Adding 0.06p to both sides, we get

    \[1.06p=150\]

Dividing both sides by 1.06, we arrive at

    \[p=\frac{150}{1.06}\]

Finally,

    \[p=141.51\]

Apparently, the health premium for a gross income of 2500 is 141.51. Let’s check:

    \[2500 - 141.51 = 2358.49\]

If our premium is correct, it should be 6% of 2358.49:

    \[0.06(2358.49)=141.51\]

Algebra allows for circular arguments because the same variable can occur on both sides.

HTH:)

Thanks to quicklatex

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Spreadsheets: using names in formulas

The tutor shows an example of naming items in a spreadsheet for use in a formula.

This post focuses on Microsoft Excel; hopefully I’ll do a similar one for a generic spreadsheet soon.

Let’s imagine Jones faces two tax rates: one for capital gains (15%) and the other for working (26%). Furthermore, they’re both flat rates: no special deductions.

A spreadsheet can easily be created to handle Jones’s situation. For the user’s convenience, they might want to type Capital Gains and Work Income at the tops of two columns, with a few columns in between for easy reading.

Let’s imagine “Capital Gains” is in cell A1. Then, depending on how many entries the user might expect, they can select the range (by dragging the mouse) from, for instance, A3 to A20.

Very conveniently, that selected range can be named by right-clicking it (while still selected), then clicking Name a Range… from the pop-up menu. Name a Range… appears near the bottom of the menu. When you click it, it provides a text box in which to type the name. Just type the name and hit enter: for the case of Jones, the range from A3 to A20 might be called Capital_Gains. (My understanding is that you can’t have a space in a name, so I use an underscore.)

Now let’s imagine Work Income is typed in C1. The range from C3 to C20 (denoted C3:C20) can be selected by dragging the mouse. Next, the user can right-click, then click Name a Range…. Of course, you might call it Work_Income.

In the cells A3:A20 the user can enter the various amounts that are capital gains. C3:C20 will contain entries of work income.

In Jones’s case, the formula for tax owed is 0.15*sum(Capital_Gains) + 0.26*sum(Work_Income). You can type that formula, starting with the = sign, in any unused cell. The tax owed will appear after you leave that cell.

The fact that you can name cells, as well as ranges of cells, really boosts the spreadsheet’s power: using names in a formula makes clear what’s being done.

I’ll be talking more about using spreadsheets:)

Source:

Microsoft Excel User’s Guide. Microsoft: 1993-94.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Math: ounces to pounds and ounces

The tutor shows a conversion from early Math 10 Pre-Calc.

Herein, I use the abbreviations oz for ounce and lb for pound.

Example: Convert 1013 ounces to pounds and ounces.

Solution:

  1. Realize that 16 oz=1 lb.
  2. Divide 1013 by 16 to get how many whole pounds you have.
  3. On a calculator, you’ll get the answer 63.3125. Keep the 63, but discard the decimal.
  4. The 63 means 63 pounds. You just need to find the number of ounces left over.
  5. Multiply 63 by 16; you’ll get 1008.
  6. The number of ounces left over is 1013-1008, or 5 ounces.
  7. Realize the meaning of the answer: 1013 oz is 63 lb, 5 oz.
  8. Check your answer: 63×16+5=1013:)

There are other ways to do this conversion, but this way seems the neatest that doesn’t use the fraction button.

I’ll be discussing unit conversions in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Lifestyle: the Hydro bill

The tutor investigates higher household usage over last year.

For Nov11-Jan11, our daily household usage this year was 6kWh above last year. My wife points to the new electric fireplace downstairs as the culprit. More specifically, she means that it’s been left on while people weren’t in the room. (The people who left it on would be the culprits.)

To be sure, late December through early January was cold: the first week back to school, snow still lay around from December 23. Around here, cold temperatures sustaining that long are rare.

The heat from the electric fireplace was needed anyway. The fan, however, doesn’t produce heat, but just circulates it. I’ve looked around and suspect, from hearth.com, that the fan might use 120W (0.12kW). Left on 14 hours per day, it would use 0.12kWx14h=1.68kWh. That’s more than 25% of the 6kWh per day over what we used last year.

Where the other three quarters went, I’ll continue to investigate:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Financial math: can time be negative?

The tutor answers a question that brought someone to his site.

These days, Oracle Tutoring gets between 5000 and 6000 distinct visitors per month. Looking over the raw log entries of how some visitors arrived, I saw an inquiry yesterday that I’m sad to say may have gone unsatisfied. The literal query:

financial math can time be negative?

It’s a great question, but I don’t think I’ve covered it specifically – until now. In honour of that brave inquirer, here’s my response:

Let’s consider the compound interest formula

A=P(1+i)t

where

A=accumulated amount after time t

P=principal amount (amount today)

i=annual interest rate

t=time in years

In this context, negative t can represent years previous.

Example 1: Using negative time, find the amount that would have been invested three years ago, at 3.2% compounded annually, to be worth 5000 today.

Solution: In this case, A will represent the amount needed back then to give 5000 now; P will be 5000, the amount today. The interest rate 3.2% must be written in decimal form 0.032:

A=5000(1+0.032)-3

Entering the expression straight into a forward-entry calculator gives

A=4549.16

Using negative time, we have back-valued today’s principal of 5000 to what it would have been, in that account, three years ago.

I love raw, straightforward questions like that. HTH:)

Source:

Tan, Soo Tang. Applied Finite Mathematics. Boston: PWS-KENT, 1990.

Thanks to w3schools.com

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

The handyman role: reconnecting the barbecue

The tutor shares an adventure in his handyman-lite role.

For big jobs, I call in professionals with crews, etc. (It’s amazing what those guys know and can do.) The smaller jobs I try to handle myself.

Even a small job takes me much longer than it would a tradesman; I lack the wrist strength and the dexterity that they take for granted. However, my understanding of the basic principles is decent. Over the years I’ve done a fair amount of research about carpentry, plumbing, etc.

Following the departure of some contractors (who did a beautiful job, I’m happy to say), I had to reconnect the barbecue to the gas feed at the wall. There shouldn’t have been a problem; it’s a quick connect. However, I just couldn’t get the line end to click back into the wall fitting.

I pulled up the shield around the wall fitting and noticed the ball bearings around it. They obviously pop out as the line end is being removed, then pop back in around it when it’s replaced. However, they were stuck in the way, so the fitting couldn’t push in past them. I just ran my finger around the inside, pushing them outwards. Then, when I tried again to insert the line end, it worked.

I was concerned that the ball bearings may not clamp around the line fitting, since they weren’t moving easily. However, when I tried to pull it back out (without releasing the shield), the wall fitting wouldn’t release it. Good enough, I guess:)

Finally, I replaced the plastic box around the gas fitting.

I’ll be sharing more of my handyman experiences as they arise:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.