Friday, May 27, 2016

Remember when solving a system of equations, you can either work using substitution or elimination. When dealing with a 3 variable, 3 equation system, generally you want to eliminate a variable from two equations, then eliminate the same variable from another set of two equations. From there solve for one of the two variables in the newly formed system of 2 equations with two variables. From here you can do back substitution to find the values of the other variables. Be sure to check all answers with each equation to make sure they satisfy each.

Wednesday, May 11, 2016

Suppose one travels from point (2,3) to point (11,8)  at a constant speed for one hour. How far did they travel in 35 minutes and where is their location in terms of x and y?

The key is to use the distance formula and slope. For the distance formula, recall it is the square root[(x2-x1)^2 + (y2-y1)^ You can apply that to get the total distance traveled at approximately 10.3, Now I use the slope to determine how much rise and run there is in 35 minutes. Take the slope of see that there is 5 rise and 9 run over the course of 60 minutes. Now take 5(35/60) and 9(35/60) to see how far the x and y coordinates move in the 35 minutes.
we have to know that to find concavity we need the second derivative and since we are looking for concave up, it's where y'' > 0. Given that y is an integral, y' is the integral evaluated at x, so it's y' = 6/(1+2x+ x^2), then for the second derivative I used the quotient rule. I set the second derivative > 0 and see that x > -1 gives us concave up