Determine whether each argument is valid or invalid. No A are B, some A are C, and all Care D. Thus, some D are B.
True or False:
[148+2−250]=[1210−251−1]\left[\begin{array}{ccc} 1 &\sqrt4 &8+2\\ -2& 5 & 0 \end{array}\right] = \left[\begin{array}{ccc} 1 &2 &10\\ -2& 5 & 1-1 \end{array}\right] [1−2458+20]=[1−225101−1]
Consider the logistic differential equation dPdt=kP(1−PL)\frac{dP}{dt}=kP\left(1-\frac{P}{L}\right)dtdP=kP(1−LP).
a. What does kkk represent? What does LLL represent?
b. Write two constant solutions of the equation, and explain their meaning.
c. What can you say about the rate of change of the population if the initial population is greater than LLL? If it is greater than zero but less than LLL? Interpret your answers.
Identify the rule of algebra illustrated by the statement. (x2−1)(1x2−1)=1\left(x^{2}-1\right)\left(\frac{1}{x^{2}-1}\right)=1(x2−1)(x2−11)=1