# Tutor profile: Michael G.

## Questions

### Subject: Spanish

Use el subjuntivo, el indicativo o el infinitivo según el sentido de la frase. (Use the subjunctive, indicative or infinitive according to the sense of the sentence.): Ella aprendió a cocinar antes de que _____ (poder) andar. (She learned to cook before she _____ (can) walk.) El padre prohibe que su hija y su novio ______ (casarse) a una edad tan joven. (The father prohibits his daughter and her boyfriend from _____ (marry) at such a young age.) Yo esperaba la tempestad antes de _____ (ir) afuera. (I was expecting the storm before _____ (go) outside.)

Ella aprendió a cocinar antes de que pudiera andar. (She learned to cook before she could walk.) El padre prohibe que su hija y su novio se casen a una edad tan joven. (The father prohibits his daughter and her boyfriend from marrying at such a young age.) Yo esperaba la tempestad antes de ir afuera. (I was expecting the storm before going outside.)

### Subject: Biology

Describe the three major differences between DNA and RNA with respect to their structure, function, and location.

Structure: DNA is a typically stable, double-stranded nucleic acid consisting of a deoxyribose and phosphate backbone that is attached to one of four nitrogenous bases: adenine, guanine, cytosine, and thymine. RNA is a typically unstable, single-stranded nucleic acid consisting of an oxyribose and phosphate backbone that is attached to one of four nitrogenous bases: adenine, guanine, cytosine, and uracil. Function: DNA stores all hereditary information that dictates the composition and processes of a cell. RNA carries protein-coding instructions from a cell's DNA to its protein-synthesizing ribosomes. Location: DNA is limited to being within the nucleus of a cell. RNA can be found within the nucleus, cytoplasm, and other regions of the cell.

### Subject: Calculus

A rancher has 500 meters of fencing that he wants to use in order to fence off the largest possible rectangular area along a straight river. What will the dimensions of the fenced off area assuming no fencing is required along the river?

We can solve this by conceptualizing it as a system of equations corresponding to the Area (A = Length (L) x Width (W)) and Perimeter of fencing used (500 = L + 2W). We can then solve for either L or W in the second equation and substitute for the corresponding variable in the first equation in order create a numeric expression for Area of which we can take the derivative: 500 = L + 2W --> 500 - 2W = L A = L x W --> A = (500 - 2W) x W (multiply and distribute)--> A = 500W - 2W^2 Using the power rule, we can now take the derivative of this equation in order to find its critical number (i.e., where the maximum area occurs): A' = 500 - 4W The critical number will occur when A' = 0: 0 = 500 - 4W --> 500 = 4W --> 125 = W We now know the Width at which the maximum Area occurs and can substitute this value into our original Perimeter equation in order to solve for Length: 500 = L + 2(125) --> 500 = L + 250 --> 250 = L We now know both dimensions and can double check this by substituting both into our original Perimeter equation: 500 = 250 + 2(125) --> 500 = 250 + 250 --> 500 = 500 Moreover, these dimensions provide a maximum Area of 31,250 (250 x 125).

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