This week in PreCalc 11 we started Trigonometry. The mistake I chose to focus on for this week was the mistake I made when finding the reference angle. I chose this mistake because I did it multiple times. When finding the reference angle you take the rotational angle and either subtract or add it to the closest x-axis. When doing this I would so often subtract or add it to the number from the y-axis.
This week in math ten we started graphing quadratics. I liked graphing last year so i was more so excited for this unit but it’s been difficult then i thought. What was difficult for me this week was remembering the difference between stretch, reflection and vertex. I didn’t understand how they all related and it was making me very confused when we began graphing using these numbers
This week in learning factoring, my favorite mistake was more of a silly mistake. When doing factoring I forgot that when doing a difference of square with two binomials that there is no middle term, and you can just solve with x² and the last term.
One mistake I made this week in the Adding and Subtracting Radicals unit was not knowing that with the same base underneath the radical sign you can just add or subtract the coefficients on the outside of the radical symbol, keeping the bas the same and get the right answer. I was under the impression I would have to convert the mixed radical to a entire radical to properly solve the equation, however I was overcomplicating it.
For example:
7√3 + 5√3 = 12√3
7√3 – 5√3 = 2√3
As shown above you can just add/subtract the coefficients/numbers in front of the radical sign when you have the same base under the radical symbol, and you get the right answer.
What are black holes and how do they come about/affect their environment?
Why did I choose this question?
Why did I choose the question “what are black holes and how do they come about/affect their environment”? Since I learned what a black hole was, I thought I knew what it was in theory but never took a second to understand it in its entirety.I have always been curious about celestial bodies such stars and planets as well as black holes. For that reason, I chose to answer my long unanswered wondering “What are black holes and how do they come about/affect their environment?”
What are black holes and how do they come about?
What are Black Holes? Black Holes, having been studied for years, have been determined by scientists to be celestial bodies containing such gravity and dense mass, even light’s energy cannot escape from its pull. Black holes contain a death zone, determined by the mass being the point within it that nothing can escape from, and then after that having the “event horizon” in which the perception of time changes and due to the gravity, the thing that entered at this point has no chance of return. Spaghettification is a term used to refer to the event that happens in a black hole when the object is stretched so thin referring to a spaghetti noodle when it gets too close to a black hole. In an article published by N.A.S.A titled “What Happens When Something Gets ‘Too Close’ to a Black Hole?”scientist talk about how the “tidal forces” emitted from a black hole can cause “Spaghettification” due to the black holes gravitational pull. In space, black holes are hard to identify but can be spotted by their presence in space, which swallows and engulfs other celestial bodies such as planets, stars and space junk. Now, how do they come about? Black holes are all originally stars, specifically a “Massive star”, containing 20 solar masses or more. They have the normal life of a star, however when it comes time to die have one of two paths to go down. They can either become a neutron star or in turn a black hole. Now how is this determined? This is determined by the final mass/size of the star. Throughout its lifetime stars endure many things causing it to lose its mass in its core such as supernova explosions, winds, and mass transfers etc. The core of the star must be large enough to become a black hole or it therefore turns into a neutron star.
Black holes and their effect on planets and stars:
Black holes have quite an effect on the environment around them in space. Being something with such power and place in space, they can swallow even planets and stars. During a process referred to as “feeding” they take in tons of space junk and other things including at times stars or even planets. An example of this happened previously when an occurrence came about that NASA caught titled a “Tidal disruption” according to an article published by ‘CBS News’ titled “NASA captures black hole ripping and swallowing star the size of our sun”. It proceeds to explain how this phenomenon is quite rare, only occurring every 10,000 to 100,000 years.
Theories:
Black hole.
While researching this topic multiple theories came about. One of which in particular resonated with me. This theory talked about how white holes could be the other half of a black hole. This could be considered a wormhole according to Einstein’s“Rosen bridge theory” but to simplify his studies, he talks about how mathematically it’s proven that a black hole has another side. The other side being the white hole would lead to a parallel universe where time moves backwards and instead of attracting objects like a black hole the white hole expels. This would be impossible to prove as it would take an infinite amount of time to get to the other side, but I still thought this theory was fascinating and gave me a better idea of different theories involving black holes.
This week in math 10 I learned about Domain and Range.
Domain: Domain has all the possibilities for input that can be taken by a function. Ex: if you have the function that gives the cost of pencils the domain would be the number of possible pencils you could buy.
Range: Range is the possibilities for output that can possibly be produced by said function. Ex: Range is the possible costs for pencils you can be subject to.
