Find the equation of a line perpendicular to y = 4x+3 that goes through the point (7, -11).
To solve this problem, we can separate the question into two parts: finding a line perpendicular to the one given, and finding how to alter it as to make it pass through the given point. As it's easier to shift a line once its slope has been found, we're going to start by identifying the line parallel to y = 4x+3. As we're initially only working with slope, we can disregard any unrelated components of the equation, such as an x or y intercept. Now that we've dropped the (+3) at the end of our given equation, we can find a perpendicular line by finding the given slope's opposite. Our slope is 4, therefore the perpendicular line's slope must be -1/4. Now that we've solved the first part of the question, we can find the exact equation by modifying it to pass through point (7, -11). We can do so by plugging this point's values into our new equation. In doing so, we get: -11 = -1/4*(7) + z, with 'z' being our unknown variable. Upon simplification, the equation comes out to: -11 = -1.75 + z. Solving this gives us -9.25 as our unknown 'z' variable, which we will use as our equation's y-intercept. Following the slope-intercept form of y = mx+b, we achieve our final result of y = -1/4x - 9.25
How can the presence of others affect one's performance on a given task?
Individual performance can be affected by the presence of others due to a number of psychological concepts. One such concept is that of social loafing—an individual's tendency to exert less effort towards an objective while working in a group rather than alone. This phenomenon explains why group work is often less productive than the sum of said group's individuals working alone. Additionally, social facilitation can impact individual performance. Also known as the "audience effect", social facilitation refers to a person's change in performance when in the presence of others. In such a case, individuals tend to perform better on simple tasks and worse on novel ones than they would if acting without an "audience". Finally, individual performance can be impacted by the conformity effect, in which behavior of others within a group can pressure a person to adapt their beliefs or actions to align with the majority. In other words, a group majority's shared attitude can cause similar behaviors to arise from other individuals within said group.
What are the three main types of market structures, and how do they differ?
The three main types of market structures are as follows: Perfect Competition, Oligopoly, and Monopoly. These three market structures extend across a spectrum measured by market power—a firm's ability to affect the equilibrium (market) price. Perfect Competition, in which firms cannot affect market price, represents the weakest market power of the three. As no firm has a large share of the market, both buyers and sellers are forced to exhibit "price-taking" behavior by accepting whatever the market price happens to be. After perfect competition comes Oligopoly, a market structure characterized by the presence of a small number of producers. The small amount of firms means that each has a greater share of the overall market. As a result of this increased market power, firms can draw in buyers through differentiation of both price and quality. Additionally, consolidated power within an Oligopoly can create barriers to entry—thus preventing the market structure from becoming Perfect Competition. The most market power of all, however, can be observed within a Monopoly. In this case, only one firm holds all the market power, and therefore has the ability to change the equilibrium price at will. As monopolies can create buyer dependence on a single firm, governments actively try to prevent the their creation through antitrust laws.