Research the price of a product. Using the price you found as the equilibrium price, create an imaginary supply and demand schedule showing how the quantity supplied and the quantity demanded for the product changes at various prices. Then, graph your results.

According to the graph, if the price started at $5 today what would happen to the price tomorrow? Explain

Look at Figure 4.1 on page 99. Write a caption for the figure that explains the law of demand.

How are price and quantity demanded related? Refer to your completed cluster diagram.

A demand schedule is a table showing the relationship between

a. quantity demanded and quantity supplied.

b. income and quantity demanded.

c. price and quantity demanded.

d. price and expected price.

Research supply and demand. Think about how a foodservice manager might consider supply and demand when making decisions. Discuss your thoughts with the class.

By using a price floor or a price ceiling as an example, tell why trying to achieve one economic or social goal might conflict with another.

How large is the shortage or surplus at $25 on the graph?

Write a blog post in which you argue whether or not the price system is the most effective way of allocating goods and services in the community.

Assume that the price of school lunches has become too high, and you need to set a price ceiling to remedy the problem. What would the consequences of such a policy be for both students and the school?

Consider the

$$m \times n$$

homogeneous system of linear equations Ax = 0. (a) If

$$\mathbf { x } = \left[ x _ { 1 } x _ { 2 } \ldots x _ { n } \right] ^ { T } \text { and } \mathbf { y } = \left[ y _ { 1 } y _ { 2 } \ldots y _ { n } \right] ^ { T }$$

are solutions to Ax = 0, show that z = x + y and w = cx are also solutions, where c is an arbitrary scalar. (b) Is the result of (a) true when x and y are solutions to the nonhomogeneous system Ax = b? Explain.

A(n) ___ is a large volume of water flowing in a certain direction.

Verify each identity.

$$\sin \theta \cos \theta + \cos ^ { 2 } \theta = \frac { \cos \theta ( 1 + \cot \theta ) } { \csc \theta }$$

Determine whether there are two, one, or no real solutions. Both a and b are greater than 0 and c is less than 0 in a quadratic equation.