March, 2008

Problem 5

The sum of two positive numbers is 2. Find the smallest value possible for the sum of the cube of one number and the square of the other.

Solution 5
Let
x and y = the numbers
x + y = 2 —Equation (1)
1 + y’ = 0
y’ = –1

z = x³ + y² —Equation (2)
dz/dx = 3x² + 2y y’ = 0
3x² + 2y(–1) = 0
y = 3/2 x²

From Equation (1)
x + 3/2 x² = 2
2x + 3x² = 4
3x² + 2x - 4 = 0

By Quadratic Formula

x = 0.8685 & –1.5352

use x = 0.8685

y = 3/2 (0.8685)²
y = 1.1315

z = 0.8685³ + 1.1315²
z = 1.9354

Problem 1

What number exceeds its square by the maximum amount?

Solution 1
Let
x = the number and
x² = the square of the number
y = their difference

y = x – x²
y’ = 1 – 2x = 0
x = ½

Problem 2

What positive number added to its reciprocal gives the minimum sum?

Graph of the Function y = f(x)

The graph of a function y = f(x) may be plotted using Differential Calculus. Consider the graph shown below.

As x increases, the curve rises if the slope is positive, as of arc AB; it falls if the slope is negative, as of arc BC.

Calculus is a branch of mathematics which uses derivative to analyze the way in which the values of a function vary. Developed on 17th century, Calculus has now applications almost in all areas of human endeavor: engineering, physics, business, economics, astronomy, chemistry, biology, psychology, sociology, etc.

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I really like this Honda advertisement, so I post it here. It reminds me of Tom and Jerry but this is a little different because all works here are calculated and highly engineered. It is said that it took 37 attempts before it get right. Some said it is only an animation rendered with Cinema 4D. What ever it is, for me this ad is great.

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Problem
A train moving with constant acceleration travels 24 ft during the 10^th sec of its motion and 18 ft during the 12^th sec of its motion. Find its initial velocity and its constant acceleration.

Solution
Let v_o = the required initial velocity
Let v₁ = velocity after 10 seconds = 24 ft/sec
Let v₂ = velocity after 12 seconds = 18 ft/sec

PROBLEM

On a certain stretch of track, trains run at 60 mph. How far back of a stopped train should be a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 2 ft/sec².

SOLUTION
Use the formula
v_f = v_i² + 2as

where:
v_f = final velocity (ft/sec)
v_i = initial velocity (ft/sec)
a = acceleration (ft/sec²)
s = distance (ft)

A brokenhearted man Auctions all that he has on eBay. You’re reading it right; it’s a life for sale. The bid start at A$1 (1 Australian Dollar). The A$1 starting bid is for the following...

Car: 1989 Mazda 929

Motorbike: 1996 Kawasaki Ninja ZX6R

Jet Ski: 1995 Kawasaki 650SX

....It always feels good to write something about how you consider your existence in this crazy but enjoyable place called Earth. It makes sense to me thinking that we're all but travelers who never retire journeying and trying to unveil the unfathomable secrets destined to be kept as they are for all eternity. We're constantly mobile trying to explore the extremities of the boundless space that encapsulates our existence and even tends to sprawl the more we feel we're getting nearer to the brink.

base from my observation, lot of people like this anime! (naruto shippuden)..
naruto naruto naruto ... amo nala ton perme tak nababatian danay kada adlaw ...
its so cool ... by the way i borrowed jarvin's (lim) dvd just to watch it completely ..
im addicted to it! ...
all characters are brilliant with their own
ninja skills and abilities! ...
if you want to watch it just click the link below ...
www.aninaruto.com ....

hello ... hmmmm.. *speechless**lolz
by the way, blog blog blog ... making blog quite difficult ... lol
but it enhance our vocabulary..tama ba??? heheh
it seems so hot this day! (maupay nala ton kaysa it nauran! anu?!)
no direct topic ... wa kasi ako mabuhat!
cge la friendster ...
add nalang ko!
cumlanajwhirlyjan@yahoo.com ...
hehehe
view me at www.friendster.com/cumlanajwhirlyjan

till next time! ...

Stone Going Upward
Use the formula
v_f = v_i + at

where
v_f = final velocity
v_i = initial velocity
a = acceleration
t = time

v_f = v_h = 0
v_i = v_o
a = -g = -9.81 m/sec²
t = 5 sec

0 = v_o – 9.81(5)
v_o = 49.05 m/sec

Its ANNOYING, I think this is the disadvantage of becoming an engineer. Your neighbors will call you engineer. You church mates that called you brother or bro or brod, now they call you engineer. The workers will call you engineer. The guy in the phone will look for the engineer; my college professors called me engineer, my classmates-we called each other engineer, my relatives called me engineer.

Determine the equation of the curve such that the sum of the distances of any point on the curve from two points whose coordinates are (–3, 0) and (3, 0) is always equal to 8.

By Philippine Information Agency, PIA Regional Office 8
March 11, 2008

TACLOBAN CITY, Leyte – Eastern Samar Governor strongly opposed the imposition of 124% increase in power rate being charged by the Eastern Samar Electric Cooperative (ESAMELCO).

In separate interviews with the local radio stations in Tacloban, Governor Evardone said that the increase is exorbitant especially at this time when the people of Eastern Samar are still reeling from the damages of the recent flash floods.