John leaves for a trip at 2PM (time t=0) and drives with a velocity that is modeled by the equation v(t) = 60 - (1/2)t, where t is measured in hours. Find the indefinite integral of this equation from 0 to 2, and explain what that means in the context of the problem.
The answer is 119. In the context of the problem, we must first analyze what each variable is. "t" represents time, and "v", the dependent variable, is velocity. Taking the integral of the equation simply takes you up one step in the power of time to give you position. Plugging in the 0 and the 2 for time simply evaluated the position equation at those times to gives you back the distance John traveled in 2 hours.
Explain the importance of the outermost layer of electrons in an atoms electron shell.
The outermost layer of electrons are known as the valence electrons. They are important in the process of bonding. Every layer before the valence layer is completely filled, and is therefore not able to take place in bonding. However, the valence electrons are looking to fill their shell up to the maximum 8 and are therefore crucial to an atoms ability to bond.
Factor 18x^3 + 3x^2 - 6x
3x (2x - 1) (3x + 2)