When finding the velocity of an object that is moving vertically and horizontally, why are the x- and y-components found independently?
Even though we interact in a 3-dimensional world, the actions in each dimension are independent from the actions of the others, but when an object is affected by those actions it reflects those actions at the same time - thus the reason why a ball will fly forward and down when thrown.
Why do triangle angles always add up to 180 degrees?
In short, as one of the simplest polygons a triangle's angles cannot be any less than the degree of a straight line, also known as 180 degrees. (Note: this only applies to flat, 2 dimensional triangles)
How many times do you derive an equation in order to locate local maximums and minimums? How do you determine if a point is a max or min?
1)Take the first derivative and set the equation to 0, them solve for the independent variable to determine max and min points, Method 1: Plug one point into the origianl to determine its y-value, To label the points, take a value greater than one of the points found and plug it into the original equation. Do the same with a value less than that same point. If both results are less than the y-value of the point, it is a max. If both points are greater than the y-value of the point, it is a min, it is neither if the results don't match Method 2: Take the second derivative and plug in those points to label each point as a max, min, or neither, A positive number will be a min, a negative a max, anything else would be neither.