Questions:The Great Lakes—Huron, Ontario, Michigan, Erie, and Superior—form the largest freshwater system in the world. Each of the lakes tends to stratify, or form layers of warmer and colder water, depending on the season. This is called seasonal turnover. In winter, for example, the coldest water in the lake lies just below the surface ice. The water gets progressively warmer at deeper levels. In spring, the sun melts the ice, and the surface water warms. Because the surface water is still cooler than the layers below, the water at the surface sinks to the bottom of the lake, forcing the cooler water at the bottom of the lake to the surface. This mixing, known as spring turnover, eliminates the temperature stratification that was established during the winter. In the absence of this thermal layering, wind continues to mix the water to a greater depth, bringing oxygen (O2) to the bottom of the lake and nutrients to the surface. This results in a relatively even distribution of O2 throughout the lake. When summer arrives, the lake again becomes stratified, with warm water at the surface, and cold water at the bottom. A narrow zone of water undergoing rapid temperature changes separates these layers. This zone is called the thermocline. Cool, fall temperatures cause the lake water to mix again, until the surface begins to freeze and the winter stratification is reestablished. The stability of the lake’s stratification depends on several factors: the lake’s depth, shape, and size, as well as the wind and both the inflow and outflow of lake water. Lakes with a lot of water flowing into and out of them do not develop consistent and lasting thermal stratification. Figure 1 shows an example of lake stratification during the summer.
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The following problem appeared on the SAT.
A cubic box with edge of length x inches is tied with a string 106 inches long. The string crosses itself at right angles on the top and bottom of the box. If the bow required 10 inches of string, what is the maximum number of inches x could be? 1. Write an equation based on this information. 2. Solve the equation for x. Are we born with the ability to tell which things are close and which are far away? Or, do we learn it? Two psychologists at Cornell University, Eleanor Gibson and Richard Walk, did an interesting experiment to answer this question.
The kitten in the photograph above is sitting on a strip in the middle of a sheet of glass. Behind the kitten is a floor directly underneath the glass; in front of it is another floor several feet below the glass. Even when the kitten is just old enough to move about, it is afraid to move off the "cliff" to the "deep" side. Chicks and baby goats just 1 day old and human infants just old enough to crawl behave exactly the same way. What explains this phenomenon? Surprisingly, it all about inequalities! Question:A certain perfect square has exactly 4 digits (it is an integer between 1,000 and 9,999). The positive square root must have how many digits? A) 4 B) 3 C) 2 D) 1 E) Cannot be determined from the given information. Solution:The correct answer is H.
A good approach to answering this question is to look first at the high end of the interval. You know that 100^2 = 10,000, which is not in the interval. Therefore, the largest perfect square in the interval must be 99, which has 2 digits. Eliminate answer choices A and B. Use common sense and trial and error to find the smallest perfect square in the interval: Start with 30 (an easy number to work with): 30^2 = 900, which is not in the interval. Try 31: 31^2 = 961, which is not in the interval. Try 32: 32^2 = 1,024, which is in the interval. So, the perfect squares range from 32 to 99, which means that the positive square root of any number in the given interval must have 2 digits. Randall is scheduling his classes for next term. He has a choice of 3 different science classes, 4 different math classes, and 5 different humanities classes. How many different class schedules can Randall create if he must take 1 science class, 1 math class, and 1 humanities class?
F. 14 G. 23 H. 30 J. 45 K. 60 Moroccan MosaicThe mosaic above was created in the fourteenth century for a wall in Morocco. Write an expression for each of the following parts of it shown in the detail below in terms of a or b or both a and b. Find:1. The perimeter of the square. 2. Its area. 3. The perimeter of the other rectangle. 4. Its area. 5. The perimeter of one of the trapezoids. 6. Its area. Answers:1. 4a.
The perimeter is just the sum of all the sides. 2. a^2. The area is length times height. 3. 4a + 4b. Add all the sides of the shaded rectangle = a + b + a + b + a + b+ a + b = 4a + 4b. 4. a^2 + 2ab. The length of the shaded rectangle = b + a + b = a + 2b. The height of the shaded rectangle = a. So, the area = a x (a + 2b) = a^2 + 2ab. 5. 4a + 2b Traversing the trapezoid we get, a + a + a + b + a + b = 4a + 2b 6. ab+ b^2 Area of a trapezoid = (width 1 + width 2)/2 x height. width 1 = a width 2 = b + a + b = a + 2b height = b. So, area = (a + a + 2b)/2 x b = (2a + 2b)/2 x b = (a + b)b = ab+ b^2 
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