# Tutor profile: Pamela L.

## Questions

### Subject: Pre-Algebra

Simplify $$ \frac{y-3}{y^{2}-9}$$

The denominator $$ y^{2} - 9$$ is a difference of two squares which can be expressed as ($$ a^{2} - b^{2}$$) and can thus be factored by taking the square root of $$ y^{2}$$ and 9 (or $$a$$ and $$b$$), which are $$y$$ and 3, respectively, to get $$(a+b)(a-b)$$ or $$(y+3)(y-3)$$. Thus the equation $$ \frac{y-3}{y^{2}-9}$$ can be simplified to $$ \frac{y-3}{(y+3)(y-3)}$$. We can cancel out the $$y-3$$ in both numerator and denominator, giving us: $$ \frac{1}{y+3}$$

### Subject: Psychology

Differentiate positive/negative reinforcement from positive/negative punishment.

In psychology, the term reinforcement refers to an action performed in order to increase the frequency of the desired behavior, while punishment refers to an action performed in order to decrease the frequency of the undesired behavior. On the other hand, the term positive refers to presenting a stimulus, while the term negative refers to removing/taking away a stimulus. Therefore, positive reinforcement refers to presenting a positive stimulus after the performance of the desired behavior, with the goal of increasing such behavior. An example would be a preschool student getting a stamp after correctly answering her teacher's question. Negative reinforcement refers to taking away an aversive stimulus after the performance of the desired behavior in order to increase the desired behavior. An example would be getting exempted from doing the dishes if the child finishes her food. Positive punishment refers to presenting a negative stimulus after performing an undesired behavior in order to decrease such behavior. An example would be a student getting reprimanded in front of the class after starting a fight with his classmate. Negative punishment refers to taking away a positive stimulus after performing an undesired behavior in order to decrease such behavior. An example would be being grounded or not being allowed to go out after class after failing an exam.

### Subject: Algebra

Give the equation of the line that has a y-intercept of -2 and is perpendicular to the line 4x + 2y = 5.

The equation of a line is typically written as y = mx + b, with m as the slope and b as the y-intercept. In the question above, we are already given the value of b, which is -2. Substituting it into the linear equation will give us y = mx - 2. In order to compute for the slope using the given equation of the perpendicular line, we have to solve for the negative reciprocal of the slope of the perpendicular line. We can get the slope of the perpendicular line by converting it from the general form of ax + by = c to the slope-intercept form of y = mx + b. To do this, we have to isolate y: 4x + 2y = 5 (We transpose 4x to the right side of the equation to isolate y, which will make 4x negative) 2y = -4x + 5 (Then we divide both sides of the equation by 2) y = -2x + 5/2 Therefore, the slope of the perpendicular line is -2. To get the slope of the line in question, we get the negative reciprocal of -2, which is 1/2. Thus, the equation of the line with a y-intercept of -2 and perpendicular to the line 4x + 2y = 5 is y = 1/2x - 2

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