# Tutor profile: Stacy J.

## Questions

### Subject: Biology

What are the similarities and differences between sexual and asexual reproduction?

Both sexual and asexual reproduction involve the process of cell division and both result in production of a new organism. Sexual reproduction involves the genetic material of two parents. Each parent provides this by means of haploid cells which, by definition, contain half of the usual amount of chromosomes for that organism. These cells are created during the process of meiosis. In humans, we often refer to these haploid cells as the sperm and the egg. When these combine, bringing together two distinct sets of genetic material, they create a zygote (offspring) that differs genetically from both its parents. Asexual reproduction is accomplished through the process of mitosis. Unlike in sexual reproduction, the offspring that is produced is genetically identical to that of its parent - like a clone. To clarify, asexual reproduction only requires a single parent and is often faster and requires less energy. (*this solution is written under the assumption that the student knows the difference between meiosis and mitosis*)

### Subject: Calculus

Please differentiate the following using the Chain Rule: f(x) = (5x + 3) ^ 2

To implement the Chain Rule, you must multiply the derivative of the outer function by the derivative of the inner function. To begin, once must first determine the outer and inner functions. (*this solution is based on the assumption that the student knows how to take simple derivatives*) Outer Function: (x) ^ 2 To determine the outer function, you need to first imagine that what is present inside of the parentheses is simply the variable, x. Since we aren't dealing with the inner function yet, we abstract it away by referring to it as x only. Inner Function: 5x + 3 The inner function is just the function that is being passed into the outer function - located inside of the parentheses. The derivative of the outer function: x^2 = (2x)^ 1 or simply 2x The derivative of the inner function: 5x+3 = 5 In the final step, you replace the "x" in the derivative of the outer function with the original value of the inner function because you abstracted it away earlier. This results in: 5 *2(5x+3) The final answer: 10(5x+3) or simplified, 50x + 30.

### Subject: Algebra

Given the following two lines: y = 7x + 16 & y = 7x - 5 determine whether the lines are: A. perpendicular - B. horizontal - C. vertical - D. parallel

The answer is: D. parallel In order for two lines to be perpendicular, they must have slopes that are the negative reciprocals* of one another [for example. if the lines had slopes of 7 and - (1/7)]. We see that this is not the case for this problem. For horizontal lines, y is set equal to a constant value [for example, y = 7]. This is similar to the case for vertical lines where x is set equal to a constant. Upon closer examination, we note the equations for the lines above do not involve x being set equal to a single number. Since the two lines have the same exact value for the slope, 7x, the two lines are parallel and thus will never intersect. * A reciprocal is a mathematical expression related to another that their product is one

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