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      "body": "<div class=\"text-justify\"> \n\n# Dear Steemian friends,\nAt first, take my cordial salam. This is @nahiansajid from #bangladesh. It's hoped that all of you are well by the grace of omni-merciful ALLAH. I am also great by the grace of almighty ALLAH. \n\n\nToday, I'm going to take part in a contest in Steem For Pakistan community. The contest is titled ***\"One Picture And One Story Week #69\"***. It is organized by honorable @suboohi mam. I hope that all of you will enjoy my writing, as, this is written about a great mystery of physics.\n\n--- \n\n## <center>One Picture And One Story Week #69</center>\n\n\n---\n\n\n![nasa-hubble-space-telescope-TZIorZKAXYo-unsplash.jpg](https://cdn.steemitimages.com/DQmXGx63hy5EdEwcZnJ7rqdSfVvwGzXwyDkd4CAJo7yEkzo/nasa-hubble-space-telescope-TZIorZKAXYo-unsplash.jpg)\n[Source](https://unsplash.com/photos/an-image-of-a-very-large-and-colorful-object-in-the-sky-TZIorZKAXYo)\n\n\n--- \n\n## <center><div class=\"phishy\">Dark Matter</div> </center>\n\n\n---\n\nDark matter is one of the most mysterious and noteworthy constituents of the Universe. It is a type of matter which is completely opaque and can only be detected due to its gravitational influence. Despite being quite elusive, scientists believe that dark matter makes up about two-thirds 27% of the total mass-energy content of the Universe and far surpassing visible matter 5%. The remaining 68% is dark energy, an unknown force responsible for the expansion of the universe, which already accelerated. \n\n--- \n\n## <center><div class=\"phishy\">The Evidence for Dark Matter </div> </center>\n\n\n---\n\nThe concept of dark matter emerged in the early 20th century when astronomers observed gravitational anomalies that could not be explained by visible matter alone. One of the earliest pieces of evidence came from Fritz Zwicky in 1933, who studied galaxy clusters in the Coma Cluster. He further found that the observed mass of galaxies was insufficient to account for gravitational force that holds galaxies together. He coined the word \"dark matter\" for this (non)sensate mass. \n\nDuring the 1970s, Vera Rubin and Kent Ford also provided more convincing evidence analyzing the rotation curves of the spiral galaxies. They pointed out that stars at the galaxy outskirts were rotating much faster than one would expect. According to Newtonian physics, however, their velocities should be reduced to compensate for their increasing radial distance from the center of the galactic system, where most of the apparent mass resides. However, the rotation curves remained flat, implying the presence of an unseen mass—dark matter—that extends well beyond the visible galaxy. \n\n--- \n\n## <center><div class=\"phishy\">Properties of Dark Matter</div> </center>\n\n\n---\n\nDark matter has no interaction, effect on electromagnetic (EM) forces, so it cannot emit or absorb light. It communicates mainly via gravity and, perhaps, via weak subatomic forces, which makes it extremely difficult to notice. Its definitive structure is not established yet but physical scientists imagine that it may or not include a set of theoretical entities such as axions, WIMPs (Weakly Interacting Massive Particles) and sterile neutrinos. \n\n--- \n\n## <center><div class=\"phishy\">Role in The Universe</div> </center>\n\n\n---\n\nDark matter plays a critical role in the formation and evolution of the universe. Gravitational fields at that epoch of the universe retained the gravitationally bound visible matter and formed galaxies and other large-scale structures. The universe would be, without dark matter, very different with smaller and fewer galaxies. \n\nFurther, CDM has effects on gravitational lensing with the bending of the radiation emanating from distant objects by the matter concentrations of the order of the galaxy cluster. Observing these effects, scientists have been able to delineate the distribution of the dark matter and it has been discovered to be in the shape of large, unimpeded (non-looping) structures that encase the entire space. \n\n--- \n\n## <center><div class=\"phishy\">Challenges and Ongoing Research</div> </center>\n\n\n---\n\nIn spite of its importance, dark matter is still one of the most persistent unsolved mysteries in the physics. Experiment has been conducted for direct detection of dark matter relics, such as Large Hadron Collider (LHC) and underground detectors, e.g., LUX-ZEPLIN. However, no conclusive evidence has been found. \n\nTheoretical physicists are also looking at alternative proposals such as, e.g., Modified Newtonian Dynamics (MOND) or other versions of the theory about gravity. However, those theories are limited-range in how they are used to explain the overall structure of the universe and the dark matter hypothesis to reasonable accuracy. \n\n--- \n\n## <center><div class=\"phishy\">Conclusion</div> </center>\n\n\n---\n\nDark matter is the mysterious, unexplained majority of the universe that challenges our view of fundamental physics, and our view of the universe. Although the nature is unknown, the gravitation pull obtained from it is undeniable proof of its existence. Continuous advances in observational methods and theory place us at the brink of the following cosmic puzzle. UNVEILING THE TRUE NATURE OF THE DARK MATTER, would open the door to entirely new branches of physics and a new perspective on the cosmos.\n\n\n![20250102_084127.png](https://cdn.steemitimages.com/DQmXHjxfrKUvU5UqN53ejAHpmZbrVpykHMG1h8koKBGTQaf/20250102_084127.png) \n\n@suboohi\n\n\n|No|My invited steemit friends|\n|-|-|\n|1|@kalidsyfulla|\n|2|@mdpolasmia|\n|3|@mahadisalim| \n\n\n\n|<center>***Thank you so much for reading my article with patience***</center>|\n|-| \n\n|<div class=\"phishy\"><center>Hafez-a-kallah</center></div>|\n|-| \n\n</div>",
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      "body": "<div class=\"text-justify\"> \n\n# Dear Steemian friends,\nAt first, take my cordial salam. This is @nahiansajid from #bangladesh. It's hoped that all of you are well by the grace of omni-merciful ALLAH. I am also great by the grace of almighty ALLAH. Today, I'm going to take part in \"SLC-S22W4//Linear and Quadratic equations equations\". \n\n\n![Black Green and White Typographic and Modern Maths Themed Youtube Thumbnail.jpg](https://cdn.steemitimages.com/DQmRxYACVzgYFN2itqo19AMJkDJU9DUiLAE3px4KEXj4gwx/Black%20Green%20and%20White%20Typographic%20and%20Modern%20Maths%20Themed%20Youtube%20Thumbnail.jpg)\n[Source](https://www.canva.com/design/DAGbkzdDQKk/Rv4xQTKNvAy75mfYgSYbCg/edit?ui=eyJEIjp7IlEiOnsiQSI6dHJ1ZX19fQ)\n\n\n\n![20250108_112236.jpg](https://cdn.steemitimages.com/DQmTSH3XvMqbG2sXnzpvGF5vYVFqNNoiRFY6PVGEWJ6jjwA/20250108_112236.jpg)\n\n--- \n\n## <center>Explain difference between linear and quadratic equations. Provide examples of each type of system of equation and describe their general forms. </center>\n\n\n---\n\n- Definition of Linear Equation :- \n\nA linear equation is an algebraic equation in which the highest power of the variable(s) is 1. It represents a straight line when plotted on a graph. \n\n- Definition of Quadratic Equation :- \n\nA quadratic equation is an algebraic equation in which the highest power of the variable is 2. It represents a parabola when plotted on a graph. \n\n### Difference between Linear Equation and Quadratic Equation :- \n\n|Feature|Linear Equation|Quadratic Equation|\n|-|-|-|\n|Definition|An equation where the highest power of the variable is 1.|An equation where the highest power of the variable is 2.|\n|General Form| ax + by = 1 (single variable) or, ax + by + c = 0 (two variables)| ax^2 + bx + c = 0, where a is equal not 0|\n|Graph|It represents a straight line in 2D space.|It represents a parabola in 2D space.|\n|Solutions|Linear equations have a single solution, but in some case, it can have no solution (parallel lines) or infinitely many (in systems)|Quadratic equation can have two, one, or no real solutions, depending on the discriminant (b^2 - 4ac)|\n\n\n### <center>Examples of Systems of Equation</center>\n\n- Linear System Example : \n\n1. x + y = 6\n2. x - y = 2 \n\nThis system can be solved to find x = 4 and y = 2 \n\n- Quadratic System Example : \n\n1. y = x^2 + 3x + 2\n2. y = 2x + 1 \n\nThese equations intersect at two points. This system can be solved to find \nx = -3, y = -5 \nand\nx = -1, y = -1 .\n\n\n### <center>General Froms</center>\n\n- General forms of linear equation : \n\nThe general form of linear equation in one variable is:\n\nax + b = c \n\n> a is not equal 0 \n\n> a, b and c are real numbers. \n\nThe general form of quadratic equation is :\n\naz^2 + bx + c = 0 \n\n> a is not equal 0 \n\n> b is the coefficient of x \n\n> c is a constant \n\n\n![20250108_112251.jpg](https://cdn.steemitimages.com/DQmPnhFdFKjwQchULMKphPEgV8SEGTEz8whQibGVq7iDMiP/20250108_112251.jpg)\n\n\n\n--- \n\n## <center>Describe methods for solving quadratic equations and share pros and cons for each method. </center>\n\n\n---\n\nThere are several methods for solving quadratic equations. I'm going to share the common methods. \n\n## <center>1. Factoring</center>\n\n- Process :- \n\nFirst of all, we have to express the quadratic equation as two binomials, like,\nax^2 + bx + c =0, and it can be solved factoring into (px + q)(rx + s) = 0, then, we can easily find out the value of x. \n\n- Pros :- \n\nWhen it works, it's simple to solve and it provides the roots quickly. \n\n- Cons :- \n\nThe main demerit is that it doesn't always work because all equations can not be factored. Sometimes, it becomes so complex to get the equation factored.\n\n\n## <center>2. Quadratic Formula</center>\n\n- Process :- \n\nThe general solution for a quadratic equation is given by :- \n\n> x = (-b ± √(b^2 - 4ac))/2a \n\n- Pros :- \n\nIn this method, there doesn't matter whether the quadratic equation is factorable or not factorable. \n\n- Cons :- \n\nSometimes, it provides complex solutions if the discriminant is negative. It needs to remember the formula. Some teachers don't prefer it when the equation can be solved through factoring method. \n\n## <center>3. Graphing</center>\n\n- Process :- \n\nIt needs to graph the quadratic function, \ny = ax^2 + bx + c, then, we can easily find out the value of x where it crosses the x-axis. \n\n- Pros :- \n\nIt is visible method, and helpful in understanding the behaviour of quadratic function. \n\n- Cons :- \n\nThis method may not be effective for large values. It needs graph paper or external software. \n\n\n![20250108_112320.jpg](https://cdn.steemitimages.com/DQmYiEAJ3uB7MwDTDriDET7V2i4cjNzV4cVdyRaMyyoH85S/20250108_112320.jpg)\n\nStep by step process to solve the linear equation (3x + 2 = 11) is following :-\n\n![20250107_202148.jpg](https://cdn.steemitimages.com/DQmSoqZZYc4PyVkPeSYRUeA1cPWQnmTgm147sNGbb2i2Kcr/20250107_202148.jpg)\n\n\n\nStep by step process to solve the quadratic equation (x^2 + 2x - 6 = 0) is following :- \n\n![20250107_202202.jpg](https://cdn.steemitimages.com/DQmUCjgixxB9mA1vvocxeH3upxHwUNb24NajnFSQf9FtPLg/20250107_202202.jpg)\n\n\n\n![20250108_112345.jpg](https://cdn.steemitimages.com/DQmbwzbTdDsVAyQgL4KDwM5U2teNJvVBfRYP5TpfNvhznem/20250108_112345.jpg)\n\n\n## Solution for the real life scenario number 1: \n\n\n![20250107_202129.jpg](https://cdn.steemitimages.com/DQmUhg7TJH3uiY27TCkLXZ9pLe67UTeEyrhBQMfyqMZk5vK/20250107_202129.jpg)\n\n\n### <center>Given Equation</center>\n\nx + 3 = 15\nx = 15 - 3\nx = 12 \n\nSo, the value of x is 12. It means, Ali has left 12$. \n\n## Solution for real life scenario number 2 \n\n\n![20250107_202109.jpg](https://cdn.steemitimages.com/DQmYReSix6MHNacMNjRm2XTU5NnLVGnR8q2XGAW68RhsWyT/20250107_202109.jpg)\n\n\n### <center>Given Equation</center>\n\nh(t) = -5t^2 + 20t \n\nWe have to find out the maximum height (h). So, at first, we have to identify the value of t when the ball reaches at the maximum height. \n\nWe have to use the formula for the vertex of parabola. \n\nt = -b / 2a \n\nHere, a = -5 and b = 20 \n\nt = -20 / 2×(-5)\nt = -20 / -10\nt = 2 \n\nSo, the value of t is 2 seconds. \n\nNow, we can easily find out the maximum height. \n\nh(t) = -5t^2 + 20t\nh(2) = -5×(2)^2 + 20×(2)\nh(2) = -5×4 + 40\nh(2) = -20 + 40\nh(2) = 20 \n\nSo the maximum height that the ball can reach is 20 meters.\n\n![20250102_084127.png](https://cdn.steemitimages.com/DQmXHjxfrKUvU5UqN53ejAHpmZbrVpykHMG1h8koKBGTQaf/20250102_084127.png)\n\n\n\n@khursheedanwar\n\n\n|No|My invited steemit friends|\n|-|-|\n|1|@kalidsyfulla|\n|2|@mdpolasmia|\n|3|@mahadisalim| \n\n\n|<center>***Thank you so much for reading my article with patience***</center>|\n|-| \n\n|<div class=\"phishy\"><center>Hafez-a-kallah</center></div>|\n|-| \n\n</div>",
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