What is the volume of a cylinder with radius 3 and height 7?
Answering this question requires using one of the volume formulas provided to you on the test. The volume of a cylinder is represented by V = pi*r^2*h. "r" represents the radius, which is 3 in the question, "h" represents the height, which is 7 in the question, and pi is a constant (we can get into that in another lesson). To solve for the volume, the numbers provided should be inserted into the formula. V = pi*3^2*7. 3^2 equals 3*3, which equals 9. This can be multiplied by 7, which equals 63, and this can be multiplied by pi, which equals 197.92. On a no calculator section, this answer can also be represented as 63pi.
Does a supply curve slope up or slope down?
A supply curve slopes up. Let's start with what a supply graph represents. For the supply curve, it shows the total amount of a good that will be available in the market at any level of price. Imagine car manufacturers are selling cars. There are a bunch of manufacturers. They all have to decide how much to produce and sell. Some of them can produce their cars very cheaply (maybe they are located close to a steel factory, or are in a country with low labor costs). Others can only produce them at higher costs. When the price is low, the total supply to the market (total number of cars produced among all the manufacturers) will be low, because only the suppliers that can produce their cars for very low costs, and who can make a profit on low prices, will produce and sell cars. As the price increases, more and more manufacturers will realize that they can make a profit, because the price is higher than their costs, and they will make more and more cars. In this way, as the price increases, the quantity of goods produces increases. On a supply graph, the two axes are price and quantity. In the situation described above, price and quantity start out low, then both increase as the other increases, which ends up looking like a line sloping up.
Mary has taken her kitten to the veterinarian. When she goes to the veterinarian, she has to weigh her kitten, but since it's young, she uses a box to hold it. She know that the box weighs 2 oz. and when she weighs her kitten and the box, the scale shows that the box and kitten together weigh 15 oz. How can we set up an equation that we can solve to represent how much her kitten weighs?
First, it's important to know that whenever we're doing an algebra problem, we're going to be setting up an equation or solving an equation to get a piece of information that we don't already know ("an unknown", often indicated by an "x"). In this problem, the piece of information that we don't know is the weight of the kitten. We can represent the weight of the kitten by "x". Another helpful piece of information is that there are certain key words in word problems that communicate how the things they are describing should be represented mathematically. Here, when it says "the kitten and the box" that can be represented as "the kitten" + "the weight of the box," because "and" usually indicates that two things should be combined or added together. We already said that the weight of the kitten is represented by an "x," and the problem says that the box weighs 2 oz, so the kitten and the box can be represented as "2 + x" Next, it's important to know that an equation (which the problem requests) has an equals sign in it, because an equation represents how two things are equivalent. This brings us to "the weight of the kitten and the weight of the box are equal to" which can be represented as "x + 2 =." We can finish the equation by identifying from the word problem that they are equal to (from the problem, "the scale shows that the box and kitten together weigh 15 oz"), bringing us to "x + 2 = 15"