Analyze the following statement: An aquarium is a good example of a balanced ecosystem.

Analyzing Processes If you clean up your room, its order increases. According to the second law of thermodynamics, what else must happen?

Which of the following processes is not a part of the water cycle? a. evaporation b. condensation c. biomagnification d. precipitation

Let f and g be real-valued functions defined on $R^1$ with continuous second derivatives ${f}^{\prime \prime}$ and ${g}^{\prime \prime}$. Define $F(x, y)=f[x+g(y)]$ or each (x, y) in $R^2$. Find formulas for all partials of F of first and second order in terms of the derivatives of f and g. Verify the relation $\left(D_{1} F\right)\left(D_{1,2} F\right)=\left(D_{2} F\right)\left(D_{1,1} F\right)$.

What changes took place in South Africa after the presidential elect ion of F. W. de Klerk?

What are the three major types of galaxies? a. spiral, elliptical, and irregular b. closed, elliptical, and open c. spiral, quasar, and pulsar d. irregular, giant, and cluster

Find the area below the graph. $y=\dfrac{x}{x^2+1},x\in[0,1]$

If a space vehicle circled Earth at a distance equal to the Earth-Moon distance, how long would it take for it to make a complete orbit? In other words, what would be its period?

Generalize the previous problem. Let c and d be integers and let C={x$\in \mathbb{Z}$:x|c} and D={x$\in \mathbb{Z}$:x|d}. Find and prove a necessary and sufficient condition for C$\subseteq$D.

A bacterial colony is estimated to have a population of $P(t)=\frac{24 t+10}{t^{2}+1}$ million t hours after the introduction of a toxin. a. At what rate is the population changing 1 hour after the toxin is introduced (t = 1)? Is the population increasing or decreasing at this time? b. At what time does the population begin to decline?

Consider $f(x)=\frac{x}{1+x^{2}}$. Find the position and nature of all turning points of y = f(x).

Everett has just received $500 as a birthday gift and has decided to spend it on DVDs and video games. He has determined that the utility (satisfaction) derived from the purchase of x DVDs and y video games is

$$U(x, y)=\ln \left(x^{2} \sqrt{y}\right)$$

If each DVD costs $20 and each video game costs$50, how many DVDs and video games should he purchase to maximize utility?

An electron starts from rest in a vacuum, in a region of strong electric field. The electron moves through a potential difference of 35 V. What would happen if the particle were a proton?

Which security policies and procedures would you use as a business owner?