# Tutor profile: Alex H.

## Questions

### Subject: Trigonometry

How far away is a building from me if I am 5ft tall, it is 100ft tall and I have to look up at a 35 degree angle from horizontal to see the top of it?

To solve this problem, it helps to draw a right triangle. The height of the triangle will be the vertical distance from my eye to the top of the building (100-5) = 95. the horizontal distance is x, and at the corner of the triangle where I am standing, the acute angle is 35 degrees. We can now solve for x using tangent because we have an angle, and the two non-hypotenuse legs of a triangle. Thus (95/x) = tan(35) x = 95/(tan(35)) x = 135.67 ft

### Subject: Calculus

What distance has been covered by a runner from time 0 to 5 minutes who's velocity (in meters per minute) is modeled by the equation: v(t) = 3sin(5t) - 5t^2 + 14 ?

Because integrating velocity with respect to time yields the distance, all we need to do is to integrate our velocity function and evaluate at t = 0 and at t = 5. integrating v(t) yields p(t) = (-3/5cos(5t)) -(5/3 t^3) + (14t) We can now find distance covered by evaluating p(5) - p(0) = -138.33 meters. Wow--that is a slow runner! And it looks like they are also going backwards too... each to their own :)

### Subject: Algebra

Max is on a tremendous shopping spree at Walmart. He has $500 to spend, and he has decided to buy a flat screen TV that costs $100. How many iPads can he buy if they cost (incredibly) only $25 each?

Questions like this might look confusing, but I promise they are not! Here is how I would think about the question: First, we can identify the unknown which is how many iPads Max can buy. Let's call that x. Next, we have to deal with the set cost of the $100 TV. Because we start with $500 and we KNOW we will spend $100 on the TV, we can subtract 500-100 = 400. This means that Max has $400 to spend on iPads. Now we just need to know how many iPads Max can but with $400. We can achieve that by dividing $400 by the cost of each iPad ($25). Thus Max can buy 16 iPads. We can also model this situation with an equation: 500 = 100 + 25x -subtract 100 from both sides 400 = 25x -divide both sides by 25 x = 16

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