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# Tutor profile: Meaghan L.

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Meaghan L.
High School Math Teacher for 8 Years
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## Questions

### Subject:Pre-Calculus

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Question:

A Ferris wheel whose maximum height reaches 100 feet sits 7 feet above the ground. This wheel makes 2 rotations per minute. Model a person’s height (feet) on the Ferris wheel over time (seconds) using a sinusoidal function.

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Meaghan L.

### Subject:Calculus

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Question:

A 6ft tall man is walking away from a 20ft lamppost at a rate of 5 ft/min. How fast is his shadow growing when he is 9 feet from the poll?

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Meaghan L.

Let x be the distance the man is from the light pole. Remember that this is a changing value. Let s be the length of the shadow. This is also changing. The rate at which it is changing is what we are trying to find. The height of the lamppost and the man’s height are fixed values. We are given the rate at which he is walking away (5ft/min). This means that x is changing at a rate of 5ft/min. So we can say that dx/dt is 5. We are looking for ds/dt. We need a formula to relate these rates (hence, related rates problems). To do these we will use some properties of similar triangles. There are two similar triangles in our picture. The big one with legs 20 and (x+s) and the smaller one with legs 6 and s. We can set up a proportion with the side lengths since “corresponding parts of congruent triangles are proportional.” That will look like this: 20/(x+s)=6/s We will use implicit differentiation so we can plug in the information we now. Let’s cross multiply and simplify to make that easier. 20s=6(x+s) 20s=6x+6s 14s=6x Use implicit differentiation to find this derivative. This gives us: 14(ds/dt)=6(dx/dt) Plug in what we are given (dx/dt) and solve for (ds/dt). 14(ds/dt)=6*5 14(ds/dt)=30 ds/dt=30/14=2.14 ft/min

### Subject:Algebra

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Question:

Write a linear equation in slope intercept form to model the following situation, then answer the question that follow: Its Saturday morning and you have decided to ride your bike to your friends house to spend the day. She lives 7 miles away from you. You usually average 15 mph when riding your bike. 1. Write an equation to model your distance from your friends house (y) in terms of the about of time (in hours) you have been riding (x).

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Meaghan L.

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