Monday, November 17, 2008

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Kochanowski was born in 1530 in Sycyna, died of a heart attack in 1584 at the age Lublinie.Żył Renesansu.Był great fame poet, playwright and tłumaczem.Pochodził for middle-class noble family . Educated at the University of Krakow, in Padua and Królewcu.Posiadał extensive knowledge of ancient literature, especially Greek and historii.Pełnił secretary at the court of Sigismund Augusta.Interesował polityką.Towarzyszył then the king during the signing of the Union of Lublin (1569). He accepted lower ordained to the priesthood, and won title proboszcza.Zrezygnowal of these goods, however, and left for Dorothy Podlodowska, with whom he settled in Czarnolesie.Rodzinne lucky disrupted deaths of his daughters and Hanny.W Urszulka Uli saw great talent poetycki.Po her death, wrote a series of Threnodies XII, in which he expresses his pain over the loss of her beloved dziecka.Pisał songs like Greek lyric poetry, referred to the Horacego.Stworzył over 300 epigrams, which describes the topics of the daily life of ordinary ludzi.Pisał-translation of the psalms of the Old Testamentu.Stworzył first Polish drama "Greek Members Allowances ". premiere drama took place in the wedding 1577roku podkanclerze Jan Zamoyski the daughter of John Radziwill-Krystyną.Twórczość Czarnolas enriched with a nave of Polish literature genres plow contributed to the development of modern Polish language.

Saturday, November 15, 2008

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ADAM-biography-biography MICKIEWICZ


Adam was born on 24 December 1798r. in the farm Zaolzie Nowogrodek. Shortly after the birth of Adam Mickiewicz, the state moved to Nowogródek where his father was a defender of the future poet court. Adam is also enrolled in a school run by the Dominicans. In 1815. after graduating from high school in Nowogrodek went to Vilnius where he studied at the university, started them on the faculty of natural science but after the first half of the faculty changed teaching gzie got a government scholarship. During his studies he joined the Society philomaths, and wrote poems problematic for the company before. in 1818. line: "Even with the serene skies evaluate." In 1819 when fulfilled, a discharge Mickiewicz had to take a job as a teacher at the school to make up for a scholarship Kaunas. During Kaunas wrote, "Ballads and Romances," which became part of volume of poetry published in 1822r.W 1823r.władze fell on the track of the Tsarist secret organizations not only in Vilnius, but also throughout Lithuania, the situation became so threatening that Adam Czartoryski stepped down as trustee in his place came Novosiltsov senator who initiated an investigation into the secret of youth organizations. In connection with the investigation Mickiewicz and many others, was arrested and convicted of 1824. Adam was sent into exile to Russia. From Vilnius, he went to St. Petersburg and Odessa and Moscow, there came into contact with writers conspirators and participated in the Decembrist uprising which upadło.Pod time trip to the Crimea (in the summer of 1825.) had a chance to know oriental culture. After this trip he wrote "Crimean Sonnets" 1826r.W Russian period, he wrote: "Forefathers' Eve" part. II and IV and "Grazyna" 1823., And Konrad Wallenrod 1828. In 1829r. Poet managed to leave Russia. Mickiewicz traveled via Hamburg, Berlin, Prague, Czech etc. across Europe was in Rome and there in 1830. came the news of the uprising. Mickiewicz, he returned to his homeland but failed to reach the inception and, together with the refugees got to Dresden, and there wrote "Dziady part. III," 1832. At the time traveling in Europe wrote "Pan Tadeusz" came from Dresden to Paris 1834. orzenił the daughter of Polish pianist Szymanowska Cline, who bore him children sześćoro. The 1839-1840 academic year, he moved to Lausanne in Switzerland where he became a professor of literature łaćskiej, here also wrote a series of poems called Lozajniskimi. However, there was interrupted by work in a job 1840r.objoć słowistyki professor at the College de France in Paris and worked for four years. During the Spring of the People (1848r.) Mickiewicz went to Rome of Italy exactly where he wanted to create a Polish Legion, however, not convinced by this opinion of the Pope or the rich parts of the Polish emigration. But few persons under the leadership of the poet's legion marched from Rome to Milan, where he was subordinated to the sovereignty of Lombardy and the years he fought with Austria. After returning to Paris he founded the Tribune people ", but had to withdraw from the editors and then by his views had been taken under the supervision of the police and eventually released from a professor at the College de France. And in 1852 he managed to occupy the position of librarian of the Paris Arsenal Library. His patriotic hopes tied with Napoleon III and the war that began in 1855. between France, England and Russia. After the death of his wife left to Constantinople in 1855. leaving the minor children in Paris. Mickiewicz wanted to support his authority created here Cossack troops to fight with Rosie. Mentally tired political struggles for power in the legion and gave a tired physically attack the disease. He died on 26 November 1885. His death caused deep mourning among the Poles, and more.

Wednesday, November 12, 2008

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Zadanie nr14

Broken calculator does not display the number 1 For example, if you type the number 3131, it shows the number 33 without any spaces between numbers. Michael wrote on this a number of six-digit calculator calculator and the display appears the number 2007. For how many numbers could happen?
A) 12
B) 13
C) 14
D) 15
E) 16 Solution

tasks:

need to add two number ones in 2007. Depending on where it is written from left to first number one, do a head count if it is possible to write the second jedynki.Pierwsza number one is:
* before 2007, we have 5 possible
* before 007, we have four possibilities,
* before 2007, we have 3 opportunities
* before 7, we have two possibilities,
* at the end, we have an opportunity. So

in total we have 1 +2 +3 +4 +5 = 15 possibilities.

Golf Cart Manufacturers

Zadanie 13 with

Fuel Concern raised twice in one week the price of gasoline, the first time
by 10%, and the second time by 5%. After two increases of one liter of gasoline, produced by
this group, it costs 4.62 zł. Calculate the price of one liter of gasoline in question before
increases.

denoted by x the price of one liter of gasoline before the hikes;
1.1 x-price of a liter of gasoline after the first rise;
* 1.1 x 1.05 - the price of a liter of gasoline after two increases.
I record the equation: 1.05 * 1.1 x = 4.62

1.155 x = 4.62
The solution of the equation is x = 4;
price of one liter of gasoline before the increases were equal to 4 zł.

Tuesday, November 11, 2008

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Zadanie nr12 nr11

Where is the error?
a + b = c / + a + b
2a 2 b = a + b + c /
2a-2c 2 b-2c = a + bc
2 (a + bc) = a + bc / (a \u200b\u200b+ bc) 2 = 1

Solution:
All the transformations of the equation a + b = c are correct, but the latter transformation is disallowed.
Why?
simple answer: a + bc is equal to zero, and how well we do not divide by zero.

Monday, November 10, 2008

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Zadanie

Find the lowest four consecutive odd integers whose sum is divisible by 15.


solution to the problem:
four consecutive odd numbers is: 2k-3, 2k-1, 2k +1, 2k +3, where k> 1 to N
knalezy sum of these numbers is: 2k-3 +2 k-1 + 2k +1 +2 +3 = 8k k
smallest number of the form 8k 15 is divisible by 8 * 15 = 120, k = 15

Answer searched numbers satisfying conditions of the problem are: 27, 29, 31, 33

Sunday, November 9, 2008

Build Single Seater Aircraft

Zadanie NR10

Find all pairs of natural numbers whose sum is equal to 192, and the greatest common divisor 24th

solution to the problem: We will contact

pairs of numbers that satisfy the first condition, that is, their sum is 192, and they are divisible by 24:24, 16848, 14472, 12096, 96
greatest common divisor of these numbers are: 24, 168> 2448, 144> 4872, 120> 2496, 96> 96
Answer: The numbers 24 and 168 and 72 and 120 meet the conditions of the problem.

Saturday, November 8, 2008

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Zadanie nr9

For which values \u200b\u200bof a and b, the number of the same seven digits 213a54b is divisible by 45?

solution to the problem:
number is divisible by 45, if it is divisible by 9 and features 5.Z number divisible by 9 (the number is divisible by 9 if the sum of its digits creates a number divisible by 9) we obtain the condition: the number of 2 +1 + 3 + 4 + 5 and b = a + b is 15 9.Z divisible by the number of features divisible by 5 (the number is divisible by 5 if its last digit is 0 or 5) indicates that b = 0 or b = 5
For b = 0 we obtain a 15 is divisible by 9, and? <0;9>, the numbers in the range <0+15;9+15>? <15;24> number divisible by 9 is the number 18, ie a = 3
For b = 5 we get: a 20 is divisible by 9, the numbers in the range <0+20;9+20>? <20;29> number divisible by 9 is the number 27, ie a = 7
Answer: For a = 3 b = 0 and a = 7 and b = 5 as the number is divisible by 213a54b 45th

Friday, November 7, 2008

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Zadanie nr8

Dana is a simple y = 2x + m
a). Determine the number of points in common straight line y = 2x + m parabola
y = x2-2x-3 depending on the parameter m.
b). On the line y = 2x + m, where m = 1
selected segment AB where A length of the interval (1, 3). Set point B.
c). Solve the system of equations:
{kx-2y = 3x + 3
ky = 2
For which values \u200b\u200bof the parameter k a simple cross in the second quadrant of the coordinate system


solution to the problem:
a). Number of points in common and simple parabola is equal to the number of solutions
system of equations:
{y = 2x + y = m
x2-2x-3
number of solutions is equal to the number of solutions
equation: 2x + m = x2-2x-3
ie x2-4x-3-m = 0
This equation is quadratic equation and the number of solutions depends on distinguishing

= 16-4 (3-m) = 16 12 4 28 m = 4m
If> 0 <=> 4m 28> 0 <=> m> -7, this equation, and thus
system has two solutions
<=> If = 0 m = 7, then the system has a solution
If <0> m <7, to układ nie ma rozwiązań
Re. For m> 7 parabola and straight are two common points
For m = 7 parabola and straight to a point in common
For m <7 parabola i prosta nie mają punktów wspólnych
b). On the line y = 2x a selected segment AB. Point A = (1, 3),
point B lies on a straight line y = 2x +1 in the distance from point A, ie, AB =

Let B = (x, y) y = 2x +1 (since point B lies on a straight line) so
B = (x, 2x +1)
AB =
=
is: (x-1) 2 + (2x-2) 2 = 45 x 2-2x
a 4 x 2-8x +4 = 45
5x2-10x-40 = 0 /: 5
x2 2x-8 = 0
= 4 32 = 36 => x = (2-6) / 2 = 2 or x = (2 +6) / 2 = 4
Hence: B = (-2, 2ŮÚ (-2 ) 1) or B = (4, 2ŮÚ4 +1)
or
resp. B = (-2, -3) and B = (4, 9)
c). We solve the system of equations:
{kx-2y = 3 / k 0 iMN
3x + ky = 2 / ŮÚ2 (by opposing factors
we determine x) {
k2x-2ky
6x = 3k 2 ky = 4
________________+
x (k2 +6) = 3k
Since k2 4 6 0 for k R,
We set y by opposing factors
{ KX-2y = 3 / uu (-3)
3x + ky = 2 / k 0 iMN
For k = 0
{0x-2y = 3
0 y = 3x 2
{x = 2 / 3 y =-
3 / 2 This solution does not satisfy the condition
point belonging to the second quarter. Solution


and to appoint a point from the second quarter
, ie x 0, ie

Thursday, November 6, 2008

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Zadanie NR6 NR7

Circle C and k are defined simple equations x2 + y2-4 * x-1 = 0 and 2 * x-y + 1 = 0.a) Prove that the line k is tangent to the circle Cb) Determine the equation of the image circle C in the symmetry line near


solution to the problem:
a) When a line is tangent to the circle is the circle has only one common point. So I must resolve the following equations to see if solutions of this system.
{x2 + y2-4 * x-1 = 0 {y = 2 * x +1
x2 + (2 * x +1) 2-4 * x-1 = 0x2 4 * x2 +4 * x +1 4 * x-1 = 05 * x2 = 0
{x = 0 {y = 1
Re. The system of equations has a solution, so simple is tangent to the circle at the point (0, 1).
b) It
calculate the center of the circle cx2 + y2-4 * x-1 = 0x2-2 * 2 * x 22 + y 2-1-22 = 0 (x-2) 2 + (y 0) 2 = 5
center circle has coordinates S (2, 0)
point of contact straight to the district calculated under a) has the coordinates P (0, 1)
Calculate Now the coordinates of the vector PS.PS = [Px-Sx, Py-Sy] = [0-2, 1 -0] PS = [-2, 1]
Now move the point S by a vector of PS and get the coordinates of the center of the circle symmetric prostej.S '= P + PS = (0,1) + [-2.1] S' = [-2, 2]
The general formula substitutes the district received coordinates of the center and radius, which is the same as the circle C.
r2 = 5S '= (-2, 2)
(x +2) 2 + (y-2) 2 = 5
x2 + y2 +4 * x-4 * y +3 = 0
Re . Balanced equation of the circle at line k has the form x2 + y2 +4 * x-4 * y +3 = 0

Wednesday, November 5, 2008

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Zadanie

The house lights went out. Mom found four candles, which lit a match daddy. How much time will clear the house, where a single candle burns in 11 minutes?

Solution tasks: Light will
11 minutes, because all the smoke at the same time (have been lit at the same time and go out in that same time).

Tuesday, November 4, 2008

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Zadanie no.5

after crash current Rysiek lit four candles. The first candle lit two minutes after the lights went out. Another candle lit every 5 minutes. When the last candle went out, back lit light. How much time took power failure when a candle burns in 7 minutes?

Solution tasks:
time from ignition to ignite the first candle lit świeczkiZanim last quarter, 4 candle has been 5 * 3 = 15 (minutes), because the four candles lit - an interval of five minutes between each inflammation. A total of 3 intervals every 5 minutes or 15 minutes from inflammation of a candle to ignite four candles. Duration
awarii4 candle burned a total of 7 minutes so persistent failure: Time to ignite the first candle to ignite + Time + Time fourth candle burning four candles which is 2 + 15 + 7 = 24 (minutes)
Answer: The failure lasted for 24 minutes