In a subduction zone setting such as the one off the coast of Chile known as the Andean Volcanic Belt, the geological feature of a volcanic arc is formed. Why did this form with this tectonic setting and what type of volcano and rock is formed?
There are three main types of tectonic plate movement: Divergent, Convergent, and Transform boundaries. A subduction zone is the same as a convergent boundary where one plate subducts beneath another particularly when the ocean plate subducts beneath a continental plate. However, when this happens a volcanic arc is formed due to the ocean water hitting the hot rock underneath the continental crust, therefore, transforming it to magma. So how does this dictate what type of volcano and rocks are formed? Since the magma generation starts way down below the Earth's crust, it takes a long time for the magma to reach the surface. As the magma makes its way to the Earth's surface, it begins to cool. As the magma cools it also begins to lose certain minerals that crystallize at high temperatures which then falls out of the magma and sinks back down. After the magma takes a long time to surface, eventually all that is left in the magma in this type of setting are feldspar and quartz minerals making the rock types after the magma has cooled are typically Andesitic or Rhyolitic. These are very thick flows that build up at the mouth of the volcano which is why we find mainly Stratovolcanos in the Andean Volcanic Arc found in Chile.
Take the derivative of the following equation: f(x)= 4x^6-3x^(-6)+9x-2
When taking a derivative, look at each component containing an "x" separately. Then with each component, take the high power number and multiply it by the number in front of the "x" and there is your new number that stays in front of the "x". Then simply subtract "1" from the high power number and there is your new number in the high power position. For example, 4x^6 will now become 24x^5 after taking the derivative. However, you are not done solving the entire equation for the derivative. After repeating the same steps on each component, your entire final answer should be f'(x)= 24x^5+18x^(-7)+9 Basically what happened was that the negative sign on the power 6 made the 3 positive, then the 9 got multiplied by 1 which therefore took the last "x" away since there was only 1 power left to subtract and same goes for the 2 on the end. Here is a fully written out equation using the original equation I provided above: f(x)= 4x^6-3x^(-6)+9x-2 (4*6)x^(6-1) -(3*-6)x^(-6-1) +(9*1)x^(1-1) -(2*0) = 24x^5-(-18)x^(-7)+9 .... f'(x)= 24x^5+18x^(-7)+9
What does the equation x^2-8x-20 factor down to using the "grouping" method?
By using the "grouping" method and realizing that the two numbers (2 and 10) will both equal -8 when subtracted from one another and -20 when multiplied by each other, will help factor the original equation (x^2-8x-20) into the new factored equation of (x+2)(x-10). Now, if you want to check to see if your answer is right just simply use the FOIL method to multiply your new factored equation back out to see if it matches the original equation. If it is the same equation, then you have solved the problem properly. If it does not match, the problem hasn't been solved and you would just simply need to try again and catch either a small error from before or try another set of numbers.