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Alex M.
University Student, IB Graduate with Tutoring Experience
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Calculus
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Question:

A 10 foot ladder is leaning against a wall, and its base is sliding away from the wall at a rate of 0.5 feet per second. At what rate will the top of the ladder be sliding down the wall when the base is 6 feet from the wall?

Alex M.

Related rates problems are tricky at first, but easily mastered. This ladder problem is very basic, and I chose it because more complex related rates problems are much easier with the help of a sketch to illustrate the situation. 1. Ladder problems almost always use the Pythagorean Theorem: a^2 + b^2 = c^2 Take the derivative of this with respect to time: 2a(da/dt)+2b(db/dt)=2c(dc/dt) 2. The question gives us 3 things: the length of side A, side C, and the rate that A is sliding away from the wall: A=6 C=10 dA/dT=0.5 3. Because it is a right triangle, we can figure out the length of B: 6^2+B^2=10^2 B^2=100-36 B=8 2(6)(0.5)+2(8)dB/dT=2(10)dC/dT 4. Because the ladder does not change height, dC/dT will equal 0. 6+16(dB/dT)=0 5. Solve for dB/dT dB/dT = -3/8 ft/sec The top of the ladder is falling at a rate of 0.375 ft/min

World History
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Question:

My teacher keeps scoring my essays low, saying that they are too narrative. What does she mean by that?

Alex M.

ACT
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Question:

For the writing portion, what are some tips for scoring high marks?

Alex M.

One thing my English teacher told me was that the graders prefer concise answers. On the test, there will be many questions that give you a passage from a piece of text and ask you to select the best sentence that belongs in a particular place. For example, some options they give you will include sentences like, "The pottery is brightly colored" or "The pottery is brightly colored and iridescent." In this instance, the first option is the correct choice as in the latter, "brightly colored" and "iridescent" mean virtually the same thing. It seems tempting to choose the longest and most wordy answer, but in reality it is better to choose the most concise and straightforward one. I used this advice and scored a perfect 36 on the writing portion.

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