2.6.284 AP calculus Exam Lamp and Shadow related rates

In summary, "related rates" in the context of this exam refer to finding the rate of change of one variable with respect to another variable. The problem is typically presented with a diagram of a lamp and its shadow, and key equations and formulas needed include the Pythagorean theorem, chain rule, and formula for related rates. It's important to correctly label variables, use the correct formulas, and pay attention to units when solving related rates problems.
  • #1
karush
Gold Member
MHB
3,269
5
yes I know this is a very common problem but likewise many ways to solve it
View attachment 9488

ok I really have a hard time with these took me 2 hours to do this
looked at some examples but some had 3 variables and 10 steps
confusing to get the ratios set up... ok my take on it is here

see if you can solve it under 5 min
View attachment 9487
 
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  • #2
given $\dfrac{dx}{dt}= 4 \text{ ft/sec}$

$\dfrac{15}{x+s} = \dfrac{6}{s} \implies s = \dfrac{2x}{3} \implies \dfrac{ds}{dt} = \dfrac{2}{3} \cdot \dfrac{dx}{dt} = \dfrac{8}{3} \text{ ft/sec}$
 

1. What is the significance of the "2.6.284" in the title of the AP calculus exam?

The "2.6.284" refers to the specific section and problem number in the AP calculus exam. This indicates that the problem is from section 2.6 of the exam and is problem number 284.

2. How are Lamp and Shadow related rates typically tested on the AP calculus exam?

The Lamp and Shadow related rates problem is a common type of related rates problem that is often included in the AP calculus exam. It involves finding the rate of change of the length of a shadow cast by a moving object, such as a lamp, as the object moves.

3. What are the key concepts needed to solve a Lamp and Shadow related rates problem?

In order to solve a Lamp and Shadow related rates problem, students need to have a solid understanding of related rates, including the chain rule and implicit differentiation. They also need to have a good understanding of geometric concepts, such as similar triangles and the Pythagorean theorem.

4. Are there any common mistakes that students make when solving Lamp and Shadow related rates problems?

One common mistake that students make when solving Lamp and Shadow related rates problems is not setting up the problem correctly. It is important to clearly define the variables and equations before attempting to solve the problem. Another common mistake is not differentiating correctly, particularly when using the chain rule.

5. How can students prepare for Lamp and Shadow related rates problems on the AP calculus exam?

To prepare for Lamp and Shadow related rates problems, students should practice solving similar problems and make sure they have a strong understanding of the key concepts and formulas. They should also review the steps for solving related rates problems and practice setting up and solving problems correctly.

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