Calculator usage: The ENG function on the Casio fx-260solar

The tutor explains his recent understanding of a function he’s wondered about.

I’ve noticed the ENG function on more than one calculator, but have never used it. I’ve always assumed it means “engineering”; since I’m not one, it makes sense that I’m unfamiliar with it.

Yesterday my curiosity finally focused on this mysterious ENG function. You access it by SHIFT ÷ on the Casio fx-260solar. If you’re in COMP mode (I haven’t tried it with other modes), it seems to change the entered number to the highest power of 103 for which the number will be > 1. Examples:

0.056 SHIFT ÷ gives 56×10-3

0.000362 SHIFT ÷ gives 362×10-6

12037059.1 SHIFT ÷ gives 12.0370591×106

While I’m not an engineer, this notation is familiar to me. I know that in electronics, it’s common to refer to 0.056A as 56mA. Similarly, 0.000178A will likely by referred to as 178µA, also known as 178×10-6A. 12400000Ω would likely be referred to as 12.4MΩ (M=Mega=106).

I have more to say about the ENG function:)


Casio fx-260solar operation manual. London: Casio Electronics Co., Ltd.

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

Math: trigonometry: reference angles

The tutor offers a couple of illustrations of an important concept from trigonometry.

When an angle is drawn in standard position, it opens counterclockwise from the positive x axis.

Example 1: Show the angle 160° in standard position, along with its reference angle. Also label the quadrants.

The reference angle is always thought to be positive and is always measured from the x axis to where the angle finishes.

Example 2: Draw the angle in Quadrant III whose reference angle is 35°.

We see that the QIII angle with reference 35° has actual measure 215°.

The QIV angle with reference 35° is 325°.



Travers, Kenneth J et al. Using Advanced Algebra. Toronto: Doubleday Canada, 1977.

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=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:


Entering the expression straight into a forward-entry calculator gives


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:)


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

Thanks to

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

Modern manufacturing: brandless products

The tutor asks: Is this a modern phenomenon?

During 2005-2010, I’d occasionally go to Future Shop just to see what was new. Ironically, I’d usually end up buying something “old” – aka, outdated – that was offered for cheap because it would soon be obsolete.

Back then, my kids were young. I hadn’t time to research new trends or products, so didn’t know when something sitting new on the shelf was already passé. Technology was improving so quickly, things that seemed hard for me to imagine were already on the bargain table. When I saw such a thing there that seemed useful to me, I bought it.

One such purchase was a 60gb (I know: you’re laughing) usb external hard drive. It’s not a pen drive; rather, it’s about 8″ by 5″ by 1″ and probably weighs over a pound. I’d estimate I bought it around 2009, long before a 64gb pen drive seemed a consideration. For the capacity, the drive seemed cheap; it might have been 50$. Thinking I might need the storage someday, I picked it up.

At home, I got the drive working and got familiar with it. It’s as simple to use as a pen drive anyway; not much to learn. I didn’t need it just then, so in a corner it went, and collected dust for about six years.

Recently I retrieved the drive in order to back up some files. I was immediately very pleased with its speed: since it’s formatted ntfs, moving stuff from Windows onto it is very convenient. I don’t know whether, when I got it, I formatted it ntfs, or it just came that way. Whichever the case, it works great for me.

I’d planned to write this post about what a great little rig that external hard drive is. Surprisingly, I can’t identify it to you; the drive has absolutely no brand markings on it anywhere. When, under Properties, I search its manufacturer, Windows classifies it as Standard disk drives. Years ago I threw out the product documentation. I have no way of identifying this external drive that sits on my desktop.

Before the new millennium, manufacturers all seemed to want us to know, without any doubt, who they where. Electronics manufacturers seemed especially proud. After all, the new products they made were often so impressive. The companies didn’t just make those products for profit; perhaps more importantly, they made them to impress us.

Nowadays, apparently, we have factories making quite good products anonymously. I wonder why they didn’t put a brand name on the drive. Possibly, the factory only produced it for a few months before switching to a different product. They likely knew the drive itself would be obsolete in a short time, with new technology soon to arrive. Why put your name on something that will just be “old” in a few months?

Whoever made the external drive, I’m happy with it. I trust that, whatever that factory is making now, it’s likely worth buying. I wonder how many workers who helped produce my drive, are still there today?

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

Calculator usage: finding the derivative with the Sharp EL-520W

The tutor shares how to find the derivative with the Sharp EL-520W.

To my knowledge, the Sharp EL-520W won’t give the symbolic derivative. Rather (as you’d likely expect anyway), it evaluates a function’s derivative at the x value the user provides. For instance:

Example 1: Find the value of the derivative of 5x3 – 2x when x=7.


  1. Press ON/C to clear the calculator.
  2. Enter the function by keying 5 ALPHA RCL x3 – 2 ALPHA RCL
  3. Key in 2ndF ∫dx
  4. The calculator responds with X? For this case, we key in 7, then =
  5. The calculator now asks the size of dx. I just press = again.
  6. Hopefully d/dx= 733 appears.

I think you’ll agree that calculating a derivative is easy with the SHARP EL-520W.

Make sure, if you’re evaluating a trig derivative, you’re set to rads! (2nd . to change trig mode:)

I’ll be expanding on this topic in future posts:)


Sharp Scientific Calculator Model EL-520W Operation Manual.

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

Spreadsheets: LibreOffice Calc: the determinant of a matrix

The tutor shares a feature of LibreOffice Calc that’s very convenient.

I don’t evaluate determinants very often, but in the past I’ve done it a few times. I find it’s a process that requires care.

LibreOffice Calc will evaluate the determinant for you, as follows:

Let’s imagine you insert the matrix entries into cells a1 through c3. In a cell that’s detached (I use d5), type in


Hopefully you’re rewarded with the determinant of the matrix that spans a1 to c3.

I’ll be sharing more hints about LibreOffice Calc in future posts:)

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

Easter eggs: the factor command

Here, the tutor is happy to report, Easter comes early.

An easter egg is a feature not reported. To become aware of it, the user must either stumble upon it, or else find out from research.

Reading about Linux terminal commands, I’ve recently become aware of the factor command. For example,

factor 24

will yield its prime factorization as follows:

24: 2 2 2 3

(Of course, 24=2x2x2x3.)

The command works identically from the Windows command prompt, even though when you type help, the factor command is absent from the list.

Neat, huh?


McGrath, Mike. Linux in easy steps. Southam: Computer Step, 2008.

Wikipedia (easter egg)

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.

Tree identification: black locust, continued

The tutor brings another finding about the beloved black locust tree.

The black locust is a tree I remember from my childhood, back in Nova Scotia’s Annapolis Valley (see my post here). This summer I became aware that black locust trees live on Vancouver Island – specifically, in Nanaimo (see my post here).

Nanaimo is 150km south of here; I know of at least one tree I see down there, but not here. I wondered if the black locust is such a tree.

The balmy fall mornings find me walking home after dropping off the car at my wife’s work. On those walks I’ve noticed no fewer than six black locust trees, one of which lives only a few doors down.

Black locust trees are easy to spot right now, because their leaves are turning yellow. Most of the other trees’ leaves are turning orange, red, or brown. I first noticed one near my wife’s work; now I see them everywhere.

The black locusts I see up here are not big like the ones I recall from the Annapolis Valley; obviously they’ve been planted more recently. I’d guess they’re 20-35 years old.

Often, it seems, you need to see something in a different place before you can notice it where you live. Anyhow, I happily walk by these black locust trees on my way home each morning, wondering how many other people appreciate them:)


Brockman, Frank, Rebecca Merrilees and Herbert Zim. Trees of North America.
   New York: Golden Press, 1968.

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

Physics: projectile motion: maximum height

Continuing about projectiles, the tutor finds the maximum height of the golf ball.

My post from Oct 16 sets the premise: a golf ball is struck at 55m/s at 27° elevation. The velocity is resolved thus:



To find the maximum height, we focus on vy. Specifically, when vy=0, the ball is at max height.

We can use the formula


in which vf is the final velocity; vi , the initial; a, the acceleration due to gravity; d, the displacement (in this case, the vertical displacement: the height).


0=625 -19.6d



The golf ball reaches max height of 32m.



Giancoli, Douglas C. Physics. New Jersey: Prentice Hall, 1998.

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