# The tutor gives a nontechnical explanation of how a metal detector functions.

Watching Curse of Oak Island on the History channel, you see them use metal detectors.

How does a metal detector work? A basic explanation is this:

1. The search coil has electricity passing through it so that it emits a magnetic field.
2. A characteristic of metals (as opposed to nonmetals) is that their electrons are moved by a magnetic field.
3. As the metal object’s electrons move, they change the electromagnetic environment. It’s a kind of “rebound” effect.
4. The detector has a detection coil that senses the electromagnetic rebound broadcast from the movement of the metal’s electrons.

Source:

electronics.howstuffworks.com

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

# The tutor shares an observation about the concat() function.

The concat() function is used to join one or more strings to the end of another:

var strng0 = “This string, “;
var strng1 = “then this one”
var strng2 = “:)”
var strng3 = strng0.concat(strng1,strng2);
document.getElementById(“output”).innerHTML = strng3;

will display

This string, then this one:)

In my experience, a literal string can also be used at the front:

var strng_a = “then this one”
var strng_b = “:)”
var strng_c = “This string, “.concat(strng_a,strng_b);
document.getElementById(“output”).innerHTML = strng_c;

will also display

This string, then this one:)

Source:

www.w3schools.com

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

# The tutor shows how to get a best-fit line with the HP-10B.

Imagine the following data:

 x y 3 10.1 4 14.7 9 32.5 12 47.1

To get a best-fit line for it of form y=mx+b, here are the steps:

1. First, clear the stat registers of the HP-10B by pressing _ →M.
2. Key 3, then INPUT, then 10.1, then Σ+.
3. Key in the other data pairs similarly.
4. In y=mx+b, you get b by pressing 0 _ 5.
5. Now, get m by pressing _ K.

For this example, b=-1.9, while m=4. The best-fit line is y=4x-1.9

HTH:)

Source:

HP-10B Business Calculator Owner’s Manual. Corvallis: Hewlett-Packard Co., 1988.

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

# The tutor compares the fat content of white and dark turkey meat.

Apparently, cooked turkey thigh (dark meat) is about 5.9% fat, whereas cooked turkey breast (white meat) is about 1.2% fat. Lean roast beef, by comparison, is about 6.4% fat.

Happy holidays!

Source:

www.ohpoultry.org

www.weightlossresources.co.uk

www.metric-conversions.org

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

# The tutor shares some experience about investigating a computer that is running fast.

When no-one is using a computer, and it’s not meant to be doing anything in particular, it might be expected to be idle. Sometimes, however, the Windows 7 computer I use runs fast anyway.

Today I opened the Task Manager from the Search box in the Windows Start menu. In the Performance pane I clicked Resource Monitor. The CPU pane lists the programs using CPU resources, in descending order.

A program called audiodg.exe figured prominently; I looked it up and found it to be associated with the Windows Audio service. At the time, no audio was playing. Perhaps, however, a memory leak can happen with it.

To stop audiodg.exe from using resources when no audio is being used, a suggestion I inferred from Microsoft is to restart the Windows Audio service (AudioSrv). In the Resource Monitor, below the CPU pane, the Services pane can be selected. Within, AudioSrv can be selected, then right-clicked, revealing Restart Service as an option. It seems to have worked for me.

Source:

support.microsoft.com

support.microsoft.com

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

# The tutor shows the derivative of arcsin, the inverse of sin.

In yesterday’s post I explained the formula for the derivative of an inverse function

(m-1(x))’ = 1/m'(m-1(x))

Today, I’ll use it to find the derivative of “inverse sin(x)”, aka sin-1(x), aka arcsin(x).

arcsin'(x) = 1/cos(arcsin(x))

Now, behold:

We see, in the illustration, that arcsin(x) = θ. The formula becomes

arcsin'(x) = 1/cos(θ)

Once again, from the illustration: cos(θ) =

So we have

arcsin'(x) = 1/

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, 3rd ed. Toronto: D C Heath and Company, 1989.

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

# The tutor shows the development of a formula for the derivative of an inverse.

Let’s imagine m(x) is a function with inverse m-1(x). Then

m(m-1(x)) = x

By implicit differentiation,

[m(m-1(x))]’ = 1

By the chain rule,

[m(m-1(x))]’ = m'(m-1(x))*(m-1(x))’

Therefore,

m'(m-1(x))*(m-1(x))’ = 1

Dividing both sides by m'(m-1(x)) yields

(m-1(x))’ = 1/m'(m-1(x))

In a coming post I’ll show an example of using this formula to find the derivative of a specific inverse function.

HTH:)

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, 3rd ed. Toronto: D C Heath and Company, 1989.

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

# The tutor shows the example ∫dx/(x2+6)

∫dx/(x2+1) = arctanx + C

The related integral

∫dx/(x2+6)

must be put in the form, as follows:

∫dx/(x2+6) = ∫dx/(6(x2/6+1)) = 1/6 ∫dx/(x2/6 + 1)

=1/6 ∫dx/((x/√6)2+1) = (√6)/6∫(dx(1/√6))/((x/√6)2 + 1)

Next it becomes

1/√6∫(dx(1/√6))/((x/√6)2 + 1)

which can be integrated:

1/√6 ∫(dx(1/√6))/((x/√6)2 + 1)=(1/√6)arctan(x/√6) + C

HTH:)

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, 3rd ed. Toronto: D C Heath and Company, 1989.

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

# The tutor looks at forming a Taylor polynomial with the example of square root 31.

A transcendental function is one there is no operation for. Rather, it’s represented by a series of expressions. Square root and sin are two examples.

The Taylor polynomial for a function is defined as

P(x)=f(c) + f'(c)(x-c) + f”(c)(x-c)2/2! + f”'(c)(x-c)3/3! + ….

For presentation purposes, we note that square root c = c0.5. In general,

Following the form of the Taylor polynomial gives, for square root,

P(x) = (c)0.5 + 0.5c-0.5(x-c) -0.25c-1.5(x-c)2/2! + 0.375c-2.5(x-c)3/3! – 0.9375c-3.5(x-c)4/4! + ….

The meaning of c

In the Taylor polynomial above, c is an “anchor value” at which you already know the output. Preferably it’s the closest value [to the one being evaluated] for which the exact answer is known.

Example: Evaluate square root 31 using a Taylor polynomial.

Solution: closest to 31 is 36, so c=36. Then

P(31) = 360.5 + 0.5(36)-0.5(31-36) – 0.25(36)-1.5(31-36)2/2! + 0.375(36)-2.5(31-36)3/3! – 0.9375(36)-3.5(31-36)4/4! + ….

which becomes

6 + (0.5/6)(-5) – (0.25/216)(-5)2/2! + (0.375/7776)(-5)3/3! – (0.9375/279936)(-5)4/4! + ….

and then

6 – 0.416666667 – 0.014467592 – 0.00100469393 – 0.00008721301476

=5.567773835

According to the calculator,

310.5 = 5.567765363

The difference between the values is 0.00000947215. Perhaps each term in the series gives an additional decimal place of accuracy.

HTH:)

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, 3rd ed. Toronto: DC Heath and Company, 1989.

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

# The tutor shares a nice function that seems to work the same in Excel or LibreOffice Calc.

The frequency() function tells, from an array of values and another of categories, the frequency in each category. A potential use is to make a histogram.

Example: Organize the following values into categories:

49,55,81,63,99,48,77,37,86,93,88,97,73,78,65,67,71,60,90,55

Solution:

1. Enter the values into a range: let’s imagine you use b1:b20
2. Decide the categories you want. In this case, six might make sense: 0-49, 50-59, 60-69, 70-79, 80-89, 90-100
3. To the frequency() function, a category is an upper limit. Your category array, perhaps entered in range c1:c6, could be as follows:

49 59 69 79 89 >90

4. With the values entered in b1:b20, and the categories entered in c1:c6, you might select the range e1:e6.
5. Type =frequency(b1:b20,c1:c6) but don’t press Enter!
6. frequency() is an array function; you must press Ctrl+Shift+Enter.
7. Hopefully you receive, in e1:e6, the array 3 2 4 4 3 4

Btw: In LibreOffice Calc, the frequency() function is under ARRAY functions. In Excel, it’s a Statistical function (under More Functions).

HTH:)

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