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Shome mishtake shurely? This doesn't seem to me to be about reaction rates. pKa relates to the equilibrium constant for dissociation of an acid. I would think -RTlnK = ΔG = ΔH - TΔS would be where the first equation comes from, wouldn't it? Regarding "f", seeing pH and pKa subtracted from each other reminds me of the Henderson-Hasselbalch equation. Perhaps our friend can take things from there......... (On past form this may be some kind of homework, so I'm not going to get enmeshed in the algebra myself.)

Tell you what. Why not taking it further still? Zoroaster didn't die, so he was immortal. He became Jesus, who became Mohammed. That works better, I think. Covers more history, and explains monotheism as a logical continuity. IOW, The funny thing about religious thinking is you can make up just about anything. It all seems to work in your mind, under the utterly permissive protocol of coming up with a convenient just-so story, which is what characterises religions of any kind.

Other than his ability to think well outside the common decency box, and care nothing about anyone but himself, he's no genius either. He's played himself. Or in the words of Mrs. Gump..."Stupid is as stupid does".

Unless his goal is destabilization across the planet, of course. Loss of Ukrainian wheat leading to starvation across Africa and the Middle East. Leading all of Europe to fear nuclear fallout from taking over Chernobyl, threatening tactical nuke usage, and more. Other nations using this “distraction” as a perfect time to ratchet up ballistic missile tests (N.Korea), to shift leaders (Iran), to consider taking Taiwan (China), and to split democracies more broadly in South America. If Putins goal is to weaken the seams stitching together a cohesive global society, perhaps he’s perfectly hitting his target and chewing exactly the amount he wants.

https://mars.nasa.gov/resources/26616/perseverance-looks-toward-santa-cruz/ February 14, 2022 Engineers at NASA’s Jet Propulsion Laboratory performed tests on rocks such as this one to understand why the first attempt by the agency’s Perseverance rover resulted in a powderized sample. A duplicate of the rover’s drill attempted to create cores from crumbly rocks. A key objective for Perseverance’s mission on Mars is astrobiology, including the search for signs of ancient microbial life. The rover will characterize the planet’s geology and past climate, pave the way for human exploration of the Red Planet, and be the first mission to collect and cache Martian rock and regolith (broken rock and dust). Subsequent NASA missions, in cooperation with ESA (European Space Agency), would send spacecraft to Mars to collect these sealed samples from the surface and return them to Earth for in-depth analysis. The Mars 2020 Perseverance mission is part of NASA’s Moon to Mars exploration approach, which includes Artemis missions to the Moon that will help prepare for human exploration of the Red Planet. JPL, which is managed for NASA by Caltech in Pasadena, California, built and manages operations of the Perseverance rover. For more about Perseverance: mars.nasa.gov/mars2020/ nasa.gov/perseverance March 01, 2022 Smaller than a penny, the flower-like rock artifact on the left was imaged by NASA’s Curiosity Mars rover using its Mars Hand Lens Imager (MAHLI) camera on the end of its robotic arm. The image was taken on Feb. 24, 2022, the 3,396th Martian day, or sol, of the mission. The “flower,” along with the spherical rock artifacts seen to the right, were made in the ancient past when minerals carried by water cemented the rock. Figure A shows a tighter view of the flower-like feature. Clouds can be seen drifting across the Martian sky in an 8-frame movie made using images from a navigation camera aboard NASA’s Curiosity rover. Shadows from these clouds can be seen drifting across the terrain. These images were taken on Dec. 12, 2021, the 3,325th Martian day, or sol, of the mission. A second 8-frame movie, taken using the same navigation camera, is included here as Figure A. These images show the clouds as they were seen drifting directly above Curiosity. Scientists can calculate how fast the clouds are moving – and how high they are in the sky – by comparing the two perspectives. These clouds are very high, nearly 50 miles (80 kilometers) above the surface. It’s extremely cold at that height, which suggests these clouds are composed of carbon dioxide ice as opposed to water ice clouds, which are typically found at lower altitude. Martian clouds are very faint in the atmosphere, so special imaging techniques are needed to see them. Multiple images are taken to be able to get a clear, static background. That allows anything else moving within the image (like clouds or shadows) to become visible after subtracting this static background from each individual image. https://mars.nasa.gov/resources/26557/curiosity-captures-drifting-clouds-on-dec-12-2021/

The point Confucius is trying to make is, if we just hate instead of trying to understand; then we all lose...

In the theorem's case, it's important to realise that, \[D=\frac{\partial^{2}f}{\partial x^{2}}\frac{\partial^{2}f}{\partial y^{2}}-\left(\frac{\partial^{2}f}{\partial x\partial y}\right)^{2}=\left|\begin{array}{cc} \frac{\partial^{2}f}{\partial x^{2}} & \frac{\partial^{2}f}{\partial x\partial y}\\ \frac{\partial^{2}f}{\partial y\partial x} & \frac{\partial^{2}f}{\partial y^{2}} \end{array}\right| \] In the case you propose, \[ \left|\begin{array}{ccc} \frac{\partial^{2}f}{\partial x^{2}} & \frac{\partial^{2}f}{\partial x\partial y} & \frac{\partial^{2}f}{\partial x\partial z}\\ \frac{\partial^{2}f}{\partial y\partial x} & \frac{\partial^{2}f}{\partial y^{2}} & \frac{\partial^{2}f}{\partial y\partial z}\\ \frac{\partial^{2}f}{\partial z\partial x} & \frac{\partial^{2}f}{\partial z\partial y} & \frac{\partial^{2}f}{\partial z^{2}} \end{array}\right| \] The condition that these 2nd-order determinants not being zero amount to being able to invert the relation that gives you the second-order derivatives and ascertaining the nature of your critical point. The determinant being zero amounts to second-order equations not being solvable, and therefore the method being inconclusive. There's an elegant method to solve this kind of problem which is the method of Lagrange multipliers. And there's the method that @Genady proposes too.

x+y+z=10. You can express z by x and y. Then, you can substitute this expression for z in the given function, and it becomes a function of two variables. You can apply the theorem 2.6 as is to this function.

Another APOD photo.................... Milky Way over Devils Tower Image Credit & Copyright: MaryBeth Kiczenski Explanation: What created Devils Tower? The origin of this extraordinary rock monolith in Wyoming, USA is still debated, with a leading hypothesis holding that it is a hardened lava plume that never reached the surface to become a volcano. In this theory, the lighter rock that once surrounded the dense volcanic neck has now eroded away, leaving the dramatic tower. Known by Native Americans by names including Bear's Lodge and Great Gray Horn, the dense rock includes the longest hexagonal columns known, some over 180-meters tall. High above, the central band of the Milky Way galaxy arches across the sky. Many notable sky objects are visible, including dark strands of the Pipe Nebula and the reddish Lagoon Nebula to the tower's right. Green grass and trees line the foreground, while clouds appear near the horizon to the tower's left. Unlike many other international landmarks, mountaineers are permitted to climb Devils Tower. ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Presumably the same Devil's Tower made famous in the movie "Close Encounters of the Third Kind" ? A solitary Masai giraffe is showered by light in a magnificent sun burst at Masai Mara National Reserve, Kenya. This image was selected out of more than 20,000 photo entries from nature photographers in 50 countries and displayed in the “Nature’s Best Photography Windland Smith Rice International Awards” exhibition on view at the Smithsonian’s National Museum of Natural History through April 20, 2015.

Yep, and that argument was specious, unfounded, and plainly wrong, too. Lol. You should worship Frankenstein, not Jesus or Mo

Which god(s)?

Yes ?? I said a lot of stuff about it, that was just one thing, it was related, part of the topic's question