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Messages - Roni
1
« pada: Januari 29, 2025, 04:30:13 PM »
\section{Mekanika Kuantum yang Tidak Mengistimewakan Partikel Tertentu}
Dalam fisika atom, kita mempelajari bagaimana elektron-elektron bersifat probabilistik yang berwujud gelombang probabilistik awan-awan elektron terhadap tenaga potensial listrik Coulomb dengan inti atom sebagai sumber potensial listrik Coulomb. Gerak dari gelombang probabilistik awan-awan elektron tersebut diatur oleh persamaan gerak gelombang Schr\"odinger. Ini dapat dibenarkan, tetapi ini masih mengistimewakan inti atom yang terletak pada posisi yang bersifat pasti (tidak probabilistik), serta masih mengistimewakan elektron yang terletak pada posisi yang bersifat probabilistik (tidak pasti). Bagaimana apabila kita ingin membangun mekanika kuantum yang tidak mengistimewakan partikel tertentu? Mungkinkah? Ini tentu saja dapat dilakukan. Contohnya adalah sebagai berikut.
Andaikan di ruang hampa $\mathbb{R}^3$ hanya ada dua partikel bermuatan listrik $q_1, q_2 \in \mathbb{R}$ yang berturut-turut bermassa $m_1, m_2 \in \mathbb{R}^+$ yang berturut-turut terletak di posisi probabilistik $\vec{r}_1, \vec{r}_2 \in \mathbb{R}^3$. Kedua partikel ini berinteraksi listrik Coulomb. Bagaimana persamaan gelombang kebolehjadian dari kedua partikel tersebut? Peluang keberadaan kedua partikel tersebut di ruang hampa $\mathbb{R}^3$ tersebut diwakili oleh fungsi gelombang kebolehjadian
\[ \Psi \,:\, \mathbb{R}^3\times\mathbb{R}^3\times\mathbb{R} \to \mathbb{C} \,:\, (\vec{r}_1, \vec{r}_2, t) \mapsto \Psi(\vec{r}_1, \vec{r}_2, t) \]
yang memenuhi persamaan Schr\"odinger
\[ -\frac{1}{2}\hbar^2\left( \frac{1}{m_1}\nabla_1^2 + \frac{1}{m_2}\nabla_2^2 \right)\Psi(\vec{r}_1, \vec{r}_2, t) + \frac{q_1 q_2}{2\pi\epsilon_0|\vec{r}_1 - \vec{r}_2|}\Psi(\vec{r}_1, \vec{r}_2, t) = i\hbar\frac{\partial}{\partial t}\Psi(\vec{r}_1, \vec{r}_2, t) \]
dengan $\nabla_1 := \partial/\partial\vec{r}_1$ dan $\nabla_2 := \partial/\partial\vec{r}_2$ serta $t \in \mathbb{R}$ adalah waktu. Di sini, $\epsilon_0$ adalah permitivitas listrik di ruang hampa. Penyelesaian dari persamaan Schr\"odinger tersebut menghasilkan $\Psi(\vec{r}_1, \vec{r}_2, t)$ yang memuat segala informasi fisis terkait segala besaran-besaran fisis yang dimiliki oleh kedua partikel tersebut.
2
« pada: Desember 26, 2024, 06:33:20 PM »
Scary Sounds (1) (Alternative Title: Haunted Bell Tower)In Minomartani Village there is a Catholic church called the Church of St. Peter and Paul, which is located not far from the Gremeng Cemetery. This church has a bell tower. The bell tower is quite tall, and is used to mark when a holy mass or eucharist celebration will be held. Around May 1994, the bell tower was still under construction, so the tower had not been blessed. At that time, children in the housing complex, around the area, really liked to climb the bell tower. However, they were afraid that Darsono, the guard of the church area, would find out that they were climbing the tower. Darsono would certainly be furious if he found out. Therefore, the children immediately came down from the tower when they saw Darsono from above. On one night of Eid al-Fitr ( Takbiran), the children did not show any fear. This time, Dika (5), Roni (9), Toni (7), Vendi (6), and Yudhis ( climbed the bell tower. The five children were indeed trained at heights. Then, Roni said to his friends, "Let's climb to the top, yo!". The boys started climbing nimbly. After reaching the top, they looked at the atmosphere below with satisfaction. After being on the tower for a while, Roni said, "Friends, let's go down first, yo," Roni suggested, "Mr. Darsono will be angry with us, you!" Then, they decided to go down. They walked around their housing complex. On the way, they met Erick (11). Erick was a visitor who was going on a pilgrimage. He was in the pick-up car waiting for his classmates. Then, Roni and his friends invited Erick to join them in climbing the bell tower like before. Erick agreed to their invitation. He quickly got out of the pick-up car and followed the five children. Now, there were six of them. After arriving at the bell tower, the six of them immediately climbed the tower. Erick, who was climbing the bell tower for the first time, was initially overwhelmed in doing so. However, not long after, he immediately became good at climbing. He only climbed up to the 2nd floor. "So that I know if the driver calls me." That was Erick's reason for not wanting to climb up to the 3rd floor. After they had been on the tower for a while, Erick said goodbye to his friends that he would leave them because he had to continue his journey for a pilgrimage. After saying goodbye, Erick immediately got back into the pick-up car. Now, there were five of them again. However, a few moments later, Gunari, Dika's mother called him to go to the rosary prayer. Because he was afraid of his mother, he immediately came down from the tower and followed her to the place where the rosary prayer was being held. Now, there were four of them. However, a few moments later, Toni and Vendi (who were Muslims) remembered that there was a Takbiran that night. They both had to attend the event. So, they rushed down from the tower and went to the mosque with Udin, their younger brother. After the two children left, only Roni and Yudhis were left in the tower. Yudhis invited Roni to sit between the stairs of the tower. While sitting, they chatted to get rid of their fear. After chatting for quite a while, they felt something strange. Suddenly, the atmosphere turned silent. Then, a very scary sound was heard from the top floor of the tower, " HUAHH!" They became scared and ran away from the tower through the church terrace. Strangely, they ran in the opposite direction. After that, they both told their friends, including those who had climbed earlier. The next day, in the morning (around 05:30), Roni, Yegar ( 8 ), and Yudhis, climbed the bell tower. When the three of them arrived at the top floor, they saw a hat, black trousers, a collared shirt, and cloth shoes, all of which were in tatters. They were very surprised. However, it might have something to do with last night's incident.
3
« pada: Desember 26, 2024, 06:21:17 PM »
\section{Christmas Holiday 1999 and Eid Holiday 2000} During the second quarter of grade III of junior high school in 1999, in order to welcome the fasting month of Ramadhan, this time our school, SLTP Sanata Dharma Depok Yogyakarta, increased the holiday quota from the original one week to three weeks plus three days, adjusting to public schools that were closed for five weeks. In fact, this fasting and Eid holiday passed the Christmas and New Year holidays of the Millennium III. Our school was closed from Thursday, December 23, 1999 to Sunday, January 16, 2000. We went back to school on Monday, January 17, 2000. Our holiday experience began from the days before the holiday began. At that time, the fasting month of Ramadhan had begun, but our school had not yet closed. At that time, I always woke up very early in the morning around five in the morning to study a little to memorize school notes, after that I watched a little television which happened to be playing classical acoustic guitar music whose notes I still memorize to this day. After that, I usually go out of the house to see the river near my house which is slightly overflowing due to the heavy rain last night, with my friend, Oni. Usually, very early in the morning, every fasting month, the sound of \textit{lem bumbung} is heard, a term used by Oni. At that time, it was a very happy day, because soon it would be the time for the Ramadan, Christmas, New Year's Day, and Lebaran holidays, so the \textit{suit-suit} was getting louder, accompanied by a song with the lyrics "Ya ya ya, Christmas Day bla bla bla. Uuuuuu." from the radio that always accompanied my studies and always rang in my ears. The days went by happily. On December 18, 1999 which fell on a Saturday, in the afternoon, Dodo and I, my cousin and friend, agreed to hold a recording of our own songs at my house, namely the album "Kujaga". We only had an acoustic nylon guitar and some cans and jars and two ballpoint pens as a substitute for drums, and of course a recording device in the form of a radio tip equipped with two microphones. At that time, we recorded happily considering the long holiday that was approaching. The atmosphere at that time was clearly very pleasant. During the recording, we sang 12 songs of our own creation, namely (1) Adik, (2) Berkhayal, (3) Reformasi, (4) Kisah, (5) Padang Pasir, (6) Kujaga, (7) Lebih Baik Sakit, ( Makan, (9) Kapan Budhalmu, (10) Sepak Bola, (11) Harus Kujalani Hidup (H.K.H.), and (12) Kucingku. Songs number (1) to number ( we had sung in July 1999 during the class promotion holiday. Finally, it became a simple album on one small cassette containing 12 short songs. After finishing working on that one album, the two of us made avocado juice and drank it while relaxing and listening to the small cassette. On Monday, Tuesday, and Wednesday, during our last days of school, we were very excited to welcome the holidays that were coming soon. On Wednesday afternoon, after returning from school on the last day before the holidays, Dodo and I rode a motorbike around the villages that were quite far away, namely in the Ngemplak and Cangkringan sub-districts. We passed fish ponds and the foot of the mountain where the air was cool and quite cold. After we were satisfied riding the motorbike, we returned to Minomartani, where we lived. Before going home to my house, the two of us stopped for a moment to buy meatballs at a meatball stall in our village. At that time, we saw a man eating meatballs. Dodo said to me, "\textit{My fathers must be religious, whether they are Christian, Catholic, Hindu, Buddhist.}", considering that it was still daytime during the fasting month. In the afternoon, we both agreed to record again like last Saturday afternoon. This time, we worked on songs that were popular at that time among young people and teenagers. At that time, we worked on the songs (1) Sheila on 7 - Dan, (2) Sheila on 7 - Kita, (3) Sheila on 7 - J.A.P., (4) Sheila on 7 - Anugerah Terindah yang Pernah Kumiliki, (5) Boomerang - Bawalah Aku, (6) Boomerang - Kisah, (7) SlanK - tidak mau Percaya, ( SlanK - Bela Diri, (9) SlanK - Siapa yang Salah, (10) dOt - Jangan-Jangan, and (11) Tipe-X - Genit. Our second recording took place very lively and was very enjoyable. Finally, we managed to finish half of the larger cassette for these songs. Dodo himself even borrowed the cassette because the recording results were so good. The next day, Thursday, December 23, 1999, we started our holiday. Dodo and I had agreed to play several songs from our 12 songs at the MBS Condongcatur studio. Therefore, at around 9 am, we both left our respective homes to the Mino terminal to take the Kopades bus to Condongcatur. We got off somewhere in Condongcatur, then walked to the MBS Studio. After arriving at the studio, we immediately booked our entry time with the studio officer. When asked by the studio officer what the name of the \textit{band} was, Dodo spontaneously answered, "Kalender". After that, we both entered the studio room. In the room, I held an electric guitar, while Dodo held the \textit{drums}. We tried to play several songs of our own, although they were not recorded. First, we played the song "Sepak Bola" because it was a new song of ours that was really fun to play. After that, we played the song "Kujaga", because it was the song we planned to be the \textit{top hit} of the 12 songs on the album. Next, we played other songs we had written until the studio rental hours were over. In the afternoon, Dodo and I agreed to record again, and hoped that it would be as lively as the previous recording. However, for some reason, the atmosphere this time was so quiet and not very lively. Even so, we still forced ourselves to record. This time we worked on three songs, namely (1) Busku, (2) Yogyanira, and (3) Dua Satu, with arrangements that were still spontaneous and simple. This time Dodo did not want to borrow the cassette of the recording. At that time it was the day of preparation for Christmas and Aunt Rosaline's silver anniversary which would be held on Tuesday, December 28, 1999. At that time, Dodo and I were very happy, but suddenly the atmosphere became tense and gloomy when my mother said, "Auntie, Sister wants to fly." At that time, what I had in mind was, in the afternoon in Semarang, precisely on the veranda of Elisabeth Hospital, Aunt Suster and all the nieces and nephews and relatives had gathered, after that Aunt Suster said goodbye and then flew into the sky in front of the nieces and relatives who were present there, while being accompanied by two different versions of the song, namely "Bagai Rajawali" and "Padi - Seperti Kekasihku". On Friday night, December 24, 1999, during the Christmas Eve mass at St. Peter and Paul Minomartani church, several of our relatives came to spend the night at our house, for example Aunt Ning and Nana, also attending the Christmas Eve mass at our church. At that time, the "Millennium Cave" had been made, and Yogi, our friend, became the altar server carrying the wiruk. The opening song was "Angkatkanlah Kepalamu", and there was a song that had never been sung at Christmas Eve masses in previous years, namely "Tuhan Datang di Malam Ram" which was quite cool. After mass, our parish priest, Father Yere, announced that small plastic bottles of "Bee Jelly" branded drinks had been provided in front of the church. After church, I invited Dodo to stay overnight at my house, while there were some of my relatives who were also staying overnight at my house. Before going to bed, the two of us recorded again. This time, we did not work on a song, but instead worked on a very scary story about death. However, Dodo ended up not staying overnight, and went home after staying overnight. In the morning, Saturday, December 25, 1999, we went to church. Incidentally, Dodo was on altar server duty. More of my relatives came to my house, for example Uda Leven. The next day, Sunday, December 26, 1999, my father and mother along with Aunt Ning, Nana, and so on left for Semarang, because it happened that there would be a collective silver jubilee for the sisters, one of whom was Budhe Suster Rosaline, in the form of a mass that coincided with the Feast of the Holy Family. When we returned home, only my father and mother returned home, while Aunt Ning, Nana, and so on, had already stayed overnight at the Elisabeth Hospital in Semarang. On Monday, December 27, 1999, in the afternoon, I, Dodo, my father and mother, Evi, Uncle Dodo, and Aunt Dodo, left for Semarang by car. On the way, we played the cassette of the album "Kujaga" that we had worked on a few days ago. In my mind at that time, I imagined that we were on the veranda of the Elisabeth Hospital in Semarang in the late afternoon, accompanied by the song "Sheila on 7 - Terlintas Dua Kata".
4
« pada: November 21, 2023, 04:45:28 PM »
\[ _{11}^{15}\text{Na}^{3-} \]
5
« pada: September 29, 2023, 06:42:44 PM »
Jarak Euclidean Titik, Garis, dan Bidang di $\mathbb{R}^3$ Sistem Koordinat Cartesian
Jarak antara titik $(a_x,a_y,a_z)$ dan titik $(b_x,b_y,b_z)$ adalah
\[ d_{00}=\sqrt{(a_x-b_x)^2+(a_y-b_y)^2+(a_z-b_z)^2}. \]
Jarak antara titik $(a_x,a_y,a_z)$ dan garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ adalah
\[ d_{01}=\sqrt{\frac{[(a_y-y_0)v_z-(a_z-z_0)v_y]^2+[(a_z-z_0)v_x-(a_x-x_0)v_z]^2+[(a_x-x_0)v_y-(a_y-y_0)v_x]^2}{{v_x}^2+{v_y}^2+{v_z}^2}}. \]
Jarak antara titik $(a_x,a_y,a_z)$ dan bidang $N_xx+N_yy+N_zz+C=0$ adalah
\[ d_{02}=\frac{|a_xN_x+a_yN_y+a_zN_z+C|}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}}. \]
Jarak antara garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ dan garis $\frac{x-x_1}{w_x}=\frac{y-y_1}{w_y}=\frac{z-z_1}{w_z}$ adalah
\[ d_{11}=\frac{|(x_0-x_1)(v_yw_z-v_zw_y)+(y_0-y_1)(v_zw_x-v_xw_z)+(z_0-z_1)(v_xw_y-v_yw_x)|}{\sqrt{(v_yw_z-v_zw_y)^2+(v_zw_x-v_xw_z)^2+(v_xw_y-v_yw_x)^2}} \]
apabila $v_yw_z\neq{v_zw_y}$ atau $v_zw_x\neq{v_xw_z}$ atau $v_xw_y\neq{v_yw_x}$.
Apabila $v_yw_z=v_zw_y$ dan $v_zw_x=v_xw_z$ dan $v_xw_y=v_yw_x$, maka
\[ d_{11}=\sqrt{\frac{[(y_0-y_1)v_z-(z_0-z_1)v_y]^2+[(z_0-z_1)v_x-(x_0-x_1)v_z]^2+[(x_0-x_1)v_y-(y_0-y_1)v_x]^2}{{v_x}^2+{v_y}^2+{v_z}^2}}. \]
Jarak antara garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ dan bidang $N_xx+N_yy+N_zz+C=0$ adalah
\[ d_{12}=\frac{|x_0N_x+y_0N_y+z_0N_z+C|}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}} \]
apabila $N_xv_x+N_yv_y+N_zv_z=0$.
Apabila $N_xv_x+N_yv_y+N_zv_z\neq0$, maka $d_{12}=0$.
Jarak antara bidang $N_xx+N_yy+N_zz+C=0$ dan bidang $kN_xx+kN_yy+kN_zz+C^\prime=0$ adalah
\[ d_{22}=\frac{C-(C^\prime/k)}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}}. \]
Jarak antara bidang $N_xx+N_yy+N_zz+C=0$ dan bidang $M_xx+M_yy+M_zz+C^\prime=0$ adalah
\[ d_{22}=0 \]
apabila $N_yM_z\neq{N_zM_y}$ atau $N_zM_x\neq{N_xM_z}$ atau $N_xM_y\neq{N_yM_x}$.
6
« pada: Februari 25, 2022, 11:10:42 AM »
7
« pada: Februari 24, 2022, 03:58:15 PM »
8
« pada: April 05, 2021, 06:11:11 PM »
Bertahun-tahun, hidup saya sangat sering menderita sengsara. Saya sering hidup menderita lahir dan batin. Hidup saya sering berada dalam era transisi antara hidup an mati. Saya sering mendapat gangguan lahir dan batin selama bertahun-tahun. Oleh karena itu, mulai sekarang saya tidak ingin hidup saya menderita lagi. Mulai sekarang, saya ingin selalu berbahagia lahir dan batin, jasmani dan rohani, untuk selama-lamanya, minimal (paling tidak) hidup yang wajar-wajar saja tanpa gangguan dari pihak manapun. Semoga hal ini terwujud agar saya selalu bahagia lahir dan batin, jasmani dan rohani. Semoga segala gangguan dari pihak manapun agar segera lenyap sampai tak berbekas agar hidup saya menjadi tentram, damai, dan bahagia selama-lamanya. Amin.
9
« pada: Maret 10, 2021, 08:45:00 AM »
\[ S = \sum_{\text{$i, j$ \\ $i \neq j$}} a_{ij} \]
10
« pada: Januari 02, 2021, 12:50:47 PM »
\begin{align}
x_\pm := \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{align}
\begin{align}
x_\pm := \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{align}
11
« pada: Desember 17, 2020, 11:47:02 AM »
12
« pada: Juli 19, 2020, 12:44:43 PM »
\[ \int_a^b f(x) dx = \lim_{n\to\infty}\sum_{j=0}^n f\left(a + j\frac{b - a}{n}\right)\frac{b - a}{n} \]
13
« pada: Juli 12, 2020, 03:28:08 PM »
Mengapa dipindahkan . . ?
14
« pada: Juni 22, 2020, 05:39:42 PM »
\section{Bayangan Titik akibat Pencerminan oleh Cermin Berbentuk Permukaan Bola}
Andaikan di ruang $\mathbb{R}^3$, ada sebuah cermin berbentuk permukaan bola, yaitu
\[ S^2(\vec{r}_0, R) := \{ \vec{r} \in \mathbb{R}^3 ~|~ |\vec{r} - \vec{r}_0| = R \} \]
di mana $\vec{r}_0 \in \mathbb{R}^3$ adalah pusat dari $S^2(\vec{r}_0, R)$, serta $R \in \mathbb{R}^+$ adalah jari-jari dari $S^2(\vec{r}_0, R)$.
Selanjutnya, titik $\vec{r} \in \mathbb{R}^3$ akan dicerminkan oleh $S^2(\vec{r}_0, R)$, sehingga menghasilkan dua buah bayangan, yaitu $\vec{r}'_1, \vec{r}'_2 \in \mathbb{R}^3$.
\[ \vec{r}'_1 = \vec{r}_0 + (R + s'_1)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ s'_1 := \frac{s_1f_1}{s_1 - f_1}, ~~~~~ s_1 := |\vec{r} - \vec{r}_0| - R, ~~~~~ f_1 := -\frac{1}{2}R. \]
\[ \vec{r}'_1 = \vec{r}_0 + \left(R + \frac{s_1f_1}{s_1 - f_1}\right)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_1 = \vec{r}_0 + \left(R + \frac{(|\vec{r} - \vec{r}_0| - R)(-R/2)}{|\vec{r} - \vec{r}_0| - R/2}\right)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_2 = \vec{r}_0 + (R - s'_2)\frac{\vec{r}_0 - \vec{r}}{|\vec{r}_0 - \vec{r}|}. \]
\[ \vec{r}'_2 = \vec{r}_0 + (s'_2 - R)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ s'_2 := \frac{s_2f_2}{s_2 - f_2}, ~~~~~ s_2 := |\vec{r} - \vec{r}_0| + R, ~~~~~ f_2 := \frac{1}{2}R. \]
\[ \vec{r}'_2 = \vec{r}_0 + \left(\frac{s_2f_2}{s_2 - f_2} - R\right)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_2 = \vec{r}_0 + \left(\frac{(|\vec{r} - \vec{r}_0| + R)R/2}{|\vec{r} - \vec{r}_0| + R/2} - R\right)\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_1 = \vec{r}_0 + \frac{R(|\vec{r} - \vec{r}_0| - R/2) + (|\vec{r} - \vec{r}_0| - R)(-R/2)}{|\vec{r} - \vec{r}_0| - R/2}\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_1 = \vec{r}_0 + \frac{R|\vec{r} - \vec{r}_0|/2}{|\vec{r} - \vec{r}_0| - R/2}\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_1 = \vec{r}_0 + R\frac{\vec{r} - \vec{r}_0}{2|\vec{r} - \vec{r}_0| - R}. \]
\[ \vec{r}'_2 = \vec{r}_0 + \frac{(|\vec{r} - \vec{r}_0| + R)R/2 - R(|\vec{r} - \vec{r}_0| + R/2)}{|\vec{r} - \vec{r}_0| + R/2}\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_2 = \vec{r}_0 + \frac{(-R/2)|\vec{r} - \vec{r}_0|}{|\vec{r} - \vec{r}_0| + R/2}\frac{\vec{r} - \vec{r}_0}{|\vec{r} - \vec{r}_0|}. \]
\[ \vec{r}'_2 = \vec{r}_0 - R\frac{\vec{r} - \vec{r}_0}{2|\vec{r} - \vec{r}_0| + R}. \]
Jadi, bayangan dari titik $\vec{r}$ akibat pencerminan oleh cermin berbentuk permukaan bola $S^2(\vec{r}_0, R)$ adalah
\[ \vec{r}' = \vec{r}'_\pm = \vec{r}_0 \pm R\frac{\vec{r} - \vec{r}_0}{2|\vec{r} - \vec{r}_0| \mp R}. \]
Bayangannya ada dua, yaitu $\vec{r}'_+$ dan $\vec{r}'_-$.
15
« pada: Februari 11, 2020, 07:12:01 PM »
Terhitung sejak awal Februari 2020, saya resmi sudah merdeka. Saya sudah 6 tahun bekerja di UKRIM (Universitas Kristen Immanuel) Yogyakarta sejak awal Februari 2014. Selama bekerja di UKRIM, begitu banyak suka dan duka yang saya alami. Saya berjumpa dengan rekan-rekan sekantor yang sangat menyenangkan. Saya juga berjumpa dengan para karyawan UKRIM dan mahasiswa UKRIM yang sangat menginspirasi hidup saya. Dalam kitab Taurat, tertulis bahwa barangsiapa sudah bekerja 6 tahun lamanya, maka ia dikatakan sudah merdeka. Mulai sekarang, saya resmi sudah merdeka dari perbudakan setan. Oleh karena itu, pada kesempatan ini, perkenankan saya memproklamasikan kemerdekaan saya, yaitu merdeka dalam Kristus Yesus, Juru Selamat-ku yang sangat baik hati kepada saya. Sekali merdeka tetap merdeka selamanya. Salam kemerdekaan. Merdeka!!!
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