# Tutor profile: Luke S.

## Questions

### Subject: SAT

Correct the sentence: wow, that test sure was hard" said frank as he sit on the tree

There several errors in this sentence. 1. "wow" should be capitalized as it is the start of a sentence 2. There is missing quotation mark before "wow" leading to an incomplete quote 3. Frank is not capitalized as it is a proper noun 4. There is no punctuation at the end of this sentence 5. "sit" should be "sat"

### Subject: Geometry

A man has 200 ft of fencing. He wants to make the largest garden possible with the fence he has to keep the rabbits out. What shape should he use and what area will it have.

This is a concept question. It is important for the student to realize that the circle is the shape with the least perimeter with the largest area (same with the sphere). If a student tried to solve using a rectangle, one example of an area would be a rectangle of dimensions 99x1, leading to an area of 99 ft^2. Another example is if the rectangle is 50x50 ft. Then, the area is 2500 ft^2. However, if we look at the circle circumference formula ( C = 2*pi*r). Solving for r we see that it is 31.8 ft. Using the are formula of a circle (A = pi*r^2), we see that the area is 3176.9 ft^2. Here we see that indeed the circle is has the most area

### Subject: ACT

The growth rate of the Cheese and Wine Company is estimated to be y = 7x + 27, whereas the growth rate of Pickles 'r' Us company has a growth rate estimated to be y = 2x^2 + 6x + 16. When will Pickles 'r' Us overtake the Cheese and Wine Company (assume x is in years)?

To see when Pickles 'r' Us will overtake the Cheese and Wince company, we have to set their growth rates equal to each other. Thus we must set y = 7x + 27 = 2x^2 + 6x + 16 = y. To solve, we must isolate the x's, which will lead to the expression 0 = 2x^2 - x - 11. Now we must solve for x, which we will do with the method of factoring or the quadratic equation. This equation is too complicated to do factoring by eye, so we will use the quadratic formula ( y= (-b +- sqrt(b^2 - 4ac))/2a)). This will tell us that x = 2.6, -2.1. As we can see, negative time is impossible, so we know that 2.6 years is the answer.

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