*Its All about Pj Problem Strings (S _{i}P_{j}A_{jk}) -
7 Spaces Of Interest (S_{i}) and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (A_{jk})*

WiseBites * - Chew And Swallow*

My **Brain** Is **Stringed** - Iremisan Adegiga : I became a *TECian* (a person or any other *being* that sees the Universe through the *TECTechnics Prism*) about two years ago after ... more

While **Africa Slumbered** - O. A. Asemota:
The African Story to date, is bittersweet. Volumes have been written about the first continent. Also, there have been many movies (fictions and nonfictions) about Africa. The *Black Panther* is an example of a recent fictional movie about Africa. I saw the movie, *The Black Panther*. The cinematography, costumes and cast are excellent. However, after all the pageantry, I was reminded that... more

**Jealousy** The **Green-Eyed Monster** - Iremisan Adegiga :
Human imperfection with respect to existential living is an existential reality. As humans live day by day, they fall short of the marks they set for themselves, or that societies set for them; or that their religion set for them; etc. I am definitely a member of the group of imperfect humans. However, there is .. more

The **Simplicity** Of **Nature's Infinite Intelligence**: *Nature* has dual meanings in this presentation: (a) the totality of the *being* of the physical Universe ... more

Why **Greatness** Eludes Nigeria - O.A. Asemota: While contemplating the title of this article, two thoughts came to mind ... more

The **Animal** In Humans: the domestication of humans began centuries ago as humans became smarter than their fellow animals in the jungle. Civilization after... more

**Great Concepts** From Africa: Africans established human existence on Earth. There is no human accomplishment greater than this. In addition to pioneering human existence on Earth, Africans gave humanity the following great concepts ... more

**Hi-story** - Iremisan Adegiga: I called my parents at the end of my freshman year in college to inform them about my decision to major in history instead of economics as... more

Political **Thieves** Within Nigeria: The Implication - O. A. Asemota: *Stealing* is the *taking* of property without permission from the owner of the property. A *thief* is one who *steals*... more

A **Grain** Of **Faith** In The Scientific Method...more

**Genesis Chapter One** (KJV) -Reconciling Creation With Facts: Belief in the creation account in Genesis Chapter one, is mostly *faith-based*. Nonetheless, there is...more

**War**. Lessons **Unlearned**: *Cognitive beings* defend *being* and space when faced with existential threats ...more

**Denatured Conquest**: The ability to *conquer* (defeat or overwhelm) was incorporated into the *being* of *cognitive beings* at their creation because ...more

Many **Kingdoms** Within Nigeria's **Democracy** - O. A. Asemota: There were sophisticated political systems in the space now called Nigeria prior to the coming of the white men... more

**Bloom** - Kimberlee June Benart: My momma said to me, “*Don’t hide your light under* ... more

**Leaders** And **Leaders-Makers**: Human political systems did not fall from the sky. They are consequences of gradual political evolutions that... more

**Policing** The **Pursuit** Of **Knowledge** : *Policing* is the enforcement of the system of laws of a space. The *police* are ... more

**Spiritual** But Not **Religious** - Kimberlee J. Benart : I saw the title of the blog and took the time to read it, but how it saddened me to see it full of harsh unkindness ... more

**Mis-Information** As A **Weapon** - The Larger Issue: *Information* is *shared knowledge*. The knowledge shared does not have to be accurate...more

**I Charlie** - A Farmer At **Heart**: From growing up on a farm in America to pioneering and working in Africa...more

**One** Nation Under **What?**: A nation is a group of individuals with different identities... more

**Selective Freedom**: *Freedom* is the condition of not being controlled by another. The implication here is not that a person is ... more

**Ultimate Reality**: the awareness of *being* establishes *reality* ... more

**All** is Mathematics: *Nature only speaks mathematics* within the context of 7 universal concepts (Pj problems). This language is uniform everywhere in the Universe and is ... more

**Good** Walls **Bad** Walls: A *wall* is a barrier that encloses a space. A wall does not have to be visible to the naked eye. The structure of a wall... more

"I have reduced physics to mathematics" - **Descartes**.

Strings (S_{i}P_{j}A_{jk}) reduce all knowledge to mathematics.

Determine the approximate volume of the barrel in figure 5.1, if the sides are bent to the arc of a parabola and D = 60 inches, d= 50 inches, and h = 120 inches

→ Solution: the strings and the math.

Suppose a grocer sells 2 apples for 5 cents and 3 oranges for 5 cents. He surmises that the simple arithmetic of selling 5 fruits for 10 cents results in the same average price. In other words, according to him, a sale of 2 apples and 3 oranges have the same average price as a sale of any 5 pieces of fruits for 10 cents.

Is the grocer right? What is the correct average price ?

→ Solution: the strings and the math.

The population of town A is 10,0000 and is increasing by 600 each year. The population of town B is 20,000 and is increasing by 400 each year. After how many years will the two towns have the same population?

→ Solution: the strings and the math.

A publisher finds that the cost of preparing a book for printing and of making the plates is $5000. Each set of 1000 printed copies costs $1000. He can sell the books at $5 per copy. How many copies must he sell to at least recover his costs?

→ Solution: the strings and the math.

Radeen examined figure 1.1 and posited the following premises and deductive conclusion:

All college students are clever. All young boys are clever. Therefore All college students are young boys.

Evadin examined figure 1.1 and posited the following premises and deductive conclusion:

All college students are clever. All young boys are clever. Some clever college students are young boys.

Who has the correct deductive conclusion base on figure 1.1. Radeen or Evadin?

→ Solution: the strings and the math.

A wolf, a goat, and a cabbage are to be rowed across a river in a boat holding only one of these three objects besides the oarsman. How should he carry them across so that the goat should not eat the cabbage or the wolf devour the goat?

→ Solution: the strings and the math.

Container *A*, contains 7 apples. Container *B*, contains 7 peaches. You are asked to select a fruit from each of the following spaces formed by containers *A* and *B*:

(a) A ∪ (A ∩ B)

(b) A ∩ (A ∪ B)

(c) (A - B) ∪ B

What is the maximum number of apples you can select? What is the maximum number of peaches you can select?

Hint: simplify expressions before selecting. A ∪ B (fig. 7.87a) means the set of elements in A or in B or in both (if in both, counted only once). A ∩ B ( fig. 7.87b) means the set of elements in A and in B (elements common to both A and B). A - B (fig. 7.87c) means the set of elements in A but not in B.

→ Solution: the strings and the math.

A ditch-digger can dig a ditch in 2 days and another ditch-digger can dig the same ditch in 3 days. What is their average rate of ditch-digging per day?

→ Solution: the strings and the math.

Figure 16.2 shows the i - λ characteristics of an iron-core inductor:

(a) Calculate the energy and incremental inductance for i = 1 A.

(b) Given that the sinusoidal current i(t) = 0.5sin2πt and coil resistance is 2Ω, calculate the
voltage across the terminals of the inductor.

→ Solution: the strings and the math.

A coil having 100 turns is immersed in a magnetic field that is varing uniformly from 80 mWb (milliWeber) to 30 mWb in 2 seconds. Determine the induced voltage in the coil.

→ Solution: the strings and the math.

Figure 1.2 shows a charge *q* moving with velocity **u** (a vector) in a magnetic field with magnetic flux density **B** (a vector). Assuming that the field is a scalar field (i.e, it is spatially unidirectional).

(a) Express the vector force **f** in terms of the charge q, and the vectors **u** and **B**.

(b) What is the magnitude of **f** If **u** makes an angle θ with the magnetic field?

(c) Suppose the magnetic flux lines are perpendicular to a cross sectional area *A* (fig1.3). Express the magnetic flux ψ, of the field in terms of the flux density **B**.

(d) State Faraday's Law that relate magnetic flux φ to eletromotive force (emf), *e*.

→ Solution: the strings and the math.

Figure 8.56 is a *Wye* (or *Y*) configuration of a Balanced three phase AC circuit. Show that:

(a) The magnitude of the line voltages is equal to √3 times the magnitude of the phase voltages.

(b) No conducting wire is needed to connect nodes *n* and *n ^{'}*.

(c) If the 3 balanced load impedances are replaced with 3 equal resistances

→ Solution: the strings and the math.

Figure 8.14 shows a simple AC circuit. Figure 8.14(a) is the time domain circuit while figure 8.14(b) is its power triangle. Given that
v(t) = 16cosωt; i(t) = 4cos(ωt - π/6); and ω 377 rad/sec. Determine:

(a) The power factor, *pf*.

(b) The values of the real power P, the reactive power Q and the apparent power S of the power triangle.

→ Solution: the strings and the math.

Figure 8.7 shows a simple AC circuit. Figure 8.7(a) is the time domain circuit while figure 8.7(b) is its phasor form.

Given that the sinusoidal voltage and current of the circuit are as follows:

v(t) = Vcos(ωt);
i(t) = Icos(ωt - θ); Determine:

(a) The average power of the circuit in the time domain

(b) The average power of the circuit in the frequency domain.

→ Solution: the strings and the math.

Figure 8.42 shows a center-tapped Transformer. The following information is given about the transformer:

Voltages and current are rms values.

Primary voltage = 4,800 V

Secondary voltage of 240 V is split (because transformer is center tap) into two voltages:

V_{2} = 120 V; V_{3} = 120 V.

Three resistive loads (R_{1}, R_{2}, R_{3}) are connected to the transformer (connection not shown in figure 8.42).

R_{1} is connected to the 240 V line.

R_{2} and R_{3} are connected to each of the 120 V lines.

Determine the power absorbed by each of the loads, if:

Power absorbed by R_{2} = P_{2}

Power absorbed by R_{1} = 5P_{2}

Power absorbed by R_{3} = 1.5P_{2}

Ccurrent through primary coil, I_{1} = 1.5625 A.

→ Solution: the strings and the math.

Figure 8.35 shows an Ideal Transformer. Show that:
The apparent power of the primary coil equals the apparent power of the secondary coil.

→ Solution: the strings and the math.

Figure 7.56 shows a circuit of a simple RLC filter. Determine:

(a) The frequency response of the RLC filter in terms of the *natural* or *resonant* frequency.

(b) The *bandwidth* in terms of the *natural* or *resonant* frequency and the *quality factor*.

→ Solution: the strings and the math.

Figure 7.50 shows a circuit of a simple RC filter. Determine:

(a) The phasor form of the frequency response, *H(jω)* in terms of ω, R and C.

(b) The cutoff frequency of the RC filter.

→ Solution: the strings and the math.

Figure 7.49 shows a circuit of a simple RC filter. Determine:

(a) The phasor form of the frequency response, *H(jω)* in terms of ω, R and C.

(b) The cutoff frequency of the RC filter.

→ Solution: the strings and the math.

Figure 8.25 shows the sum V_{s}(t) of the sinusoidal voltage signals V_{1}(t) and V_{2}(t).

Determine the phasor form of V_{s} given the following information:

V_{1}(t): amplitude = 15; frequency = 377; phase angle = 45^{o}.

V_{1}(t): amplitude = 15; frequency = 377; phase angle = 30^{o}.

→ Solution: the strings and the math.

Figure 6.11 shows a circuit of the given elements. Determine the behavior of the frequency response of the voltage V_{0} at extremely high and low frequencies.

→ Solution: the strings and the math.

The signal *v(t)* from a voltage source is a binary waveform: it is either 0.5 V or -0.5 V.

The sign change has a 50-50 chance of occurrence within the interval of 1 μs. In other words, *v(t)* has an equal chance for positive or negative values within this interval.

What is the average and effective values of *v(t)* over a period of 5 secs?

→ Solution: the strings and the math.

Signaling is a ubiquitious phenomenon in the societies of cognitive beings.

(a) What is a signal?

(b) What is a periodic signal?

(c) Identify the following periodic waveforms:

(i)

(ii)

(iii)

→ Solution: the strings and the math.

Figure 7.13 shows two periodic signals (blue and red). Which of the signals is an even function and which is an odd function.

→ Solution: the strings and the math.

Mind Warm Ups

The Universe is composed of *matter* and *radiant energy*. *Matter* is any *mass-energy* that travels with velocities less than the velocity of light. *Radiant energy* is any *mass-energy* that travels with the velocity of light.

The *point* "**.**" is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Rocket Work Take That Load Up

Cable Work Bring That Load Up

Friction Work Bring That Moving Object To Stop

Escape Velocity

Signals From Mars

Speed Of A Satellite In An Orbit

Acceleration Of Object In Circular Motion With Constant Speed

Object Thrown Up From The Roof

Maximum Height Of A Projectile

Maximum Range Of A Projectile

Direction Of A Projectile

Difference Between Matter And Radiant Energy

Difference Between Mass And Weight

Einsteins Energy Formula Applied To Uranium-235 Detonation

Water At Bottom Of A Water Fall Warmer Than Water At Top

Air Plane In Flight-Head Wind Tail Wind

Couples In Equilibrium

Sound Travel In An Iron

Shell Fired At An Angle

Range Of A Projectile

How Deep Is The Well

Slow And Steady Average Speed Of Auto

Kings An Aces

Inclined Plane

Car Choices

Free Falling Pebble-2

Free Falling Pebble

Meridian Travel

Row Your Boat

Composition Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Structure Of Matter

Bond Length Bond Angle

Valence Shell Electron Pair Repulsion

Molecular Shape Orbital Hybridization

Sigma Bonds Pi Bonds

Non ABn Molecules

Molecular Orbital Theory