This past week in Pre Calculus 11 we finished unit 3: Solving Quadratic Equations. We learned how to determine the discriminant and what the purpose of finding it is. The discriminant tells me how many roots each equation has. You use the formula b^2 -4ac=0 and solve.
This past week in Pre-Calculus I learned that when a equation is irrational and comes to the square root at the end it must have a + and – sign with it. This represents that there are 2 possible answers, one with either a positive root sign and the other with a negative root sign. This is an example of what an equation would look like:
If the equations at the end were put into a calculator solved they would give the points at which the parabola will cross the x-axis.
This past week in Pre-Calculus we started unit 3 – Solving Quadratic Equations. I learned how to factor an ugly trinomial. A ugly trinomial is when there is a number in front of the variable in the first term. Ex:
This is how you factor a ugly trinomial:
The week in pre calculus we learned how to add, subtract, multiply and divide radical expressions. Something I learned this week was how to rationalize a denominator. When a denominator is not a whole number and it is in radical form you need to get it to a rational number so you are able to divide. To do so you multiply the radical by itself, example:
Here I have made the denominator rational.
This past week in Pre Calculus we finished unit 1-Sequences and Series and then we started unit 2-Absolute Value and Radicals. We learned what absolute value was and what the symbol to represent it looks like.
Absolute value is the distance of any number to 0. Example is 4 is 4 numbers away from 0 so it would be written as 
If the number is negative like 
Last week in Pre Calculus 11 we learned about Arithmetic Series and Sequences where the common difference is always added, this week we learned about Geometric Series and Sequences where instead of adding, you multiplied. Something I struggled with this week was putting the correct numbers into the correct spots where the variables were. I chose to make my blog post about how to use the geometric sequence formula which is:
Using this formula you will be able to find how much any term is equal to.
Sequence: 1, 5, 9, 13, 17
Difference: 4
Finding 
Finding the sum of the first 50 terms:
In the first week of Pre-Calculus 11 we started unit 1 – Sequences and Series. Something I learned this week was what an arithmetic sequence is and what it does or the purpose of it. In my own definition, an arithmetic sequence is a series of numbers that have the same difference between each number. An example of this would be -3, 0, 3 ,6… is an arithmetic sequence because the difference between each number is 3 and its always 3. The numbers 1, 4, 6, 10… is not an arithmetic sequence because the difference between 1 and 4 is 3 but the difference between 4 and 6 is 2 so it changed and didn’t always have the same difference.
We learned this week what an arithmetic sequence is but also what the purpose of it is. If I wanted to know what the 45th term in the series that might be challenging to find out but using the formula
After filling in the formula and solving you will get the 45th term in the series which is 129.
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My essential question I had about space was: What technological advancements do we need to explore past mars?
There are a lot of technological advancements needed to go past Mars because we haven’t yet been able to send humans there but everything is a learning experience and helps further our technology and ability to go different places.
InSight is a lander that is going to Mars already but when it was being made it had a lot of different factors that were taken into consideration including EDL – entry, decent, landing. These factors are crushal to getting the space craft to safely land on Mars. They are landing this space craft at a higher elevation than they did with Phoenix Mars Lander so there will be less time for deceleration and there is more dust storms up there. To adjust to these conditions they used a thicker heat shield and its parachute will open at higher speed with stronger suspension lines. This might not be a huge technological advancement but when exploring other places to land space crafts they have to look at these types of factors and this helps with exploration of other places where they have to assess the conditions of what they need. InSight isn’t the first space craft to go to mars and they have learned from past experiences of what they need to excel further. This was a small change in just landing at a higher elevation but landing on a different planet will be a whole other challenge with its own factors.
As they say in the end of the video “We learn everything from the past that we can and we apply all those things to the future projects and future missions” and this is a very important part in my opinion because they are learning from their experiences and mistakes and will apply it to the future projects and missions to make them better and more successful.
NASA build a engine that broke records for being able to run without issue of over 12 years. This is important because having an engine that can run for this long will help them be able to go further. This engine would be eligable to go past mars on a round trip but they need to test the consistency of this and what other factors can play into not making it run smoothly.
At this point NASA is very focused on going to Mars because there is possible life there and it is the closest planet to earth in our solar system to us. Other expeditions they are working on are going closer to the sun than they ever have before and are also planning on landing on an asteroid.
In conclusion this question is very open ended because there is endless amounts of places we could explore and so many things are needed. NASA’s main focus is going to mars at the moment and there is not a lot of information about the other places. There is a lot of factors into going to anyplace because everyplace is different and those have to be researched and found out before the technological advancements are made, but many of the inventions listed above are a every good start to getting there and based on conditions of where the space craft would be landing, these inventions can be modified and improved.
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