Solve Related Rates Problems: Problem 1 & 2

In summary: What is the rate of change of the tightrope walker's shadow along the ground?2.b. What is the distance from point A to the tightrope walker when her shadow reaches the base of the Tee Building?2.c. What is the rate of change of the tightrope walker's shadow up the wall of the Tee Building when she is 10 feet from point B?In summary, the conversation discussed two related rates problems involving a circle inscribed in a square and a tightrope walker on a tightrope between two buildings. The first problem involved finding the rate of increase of the square's perimeter as the circle expands, and the rate of increase of the area between the circle and the square
  • #1
biggie23228
1
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Hello. I really need help on my math homework. Please anybody help me. I would really appreciate it. These 2 problems have to do with related rates and they are too advanced for me... I just need to be shown the way and I could get it I just need to know how to start... thank you.

Problem 1
A circle is inscribed in a square. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency. (Note: A circle with radius r has circumference C = 2(pi)r and Area A = (pi) r^2.)
a) Find the rate at which the perimeter of the square is increasing. Indicate units of measure.
b) At the instant when the area of the circle is 25(pi) square inches, find the rate of increasing in the area enclosed between the circle and the square. Indicate units of measurement.

Problem 2
A tightrope is stretched 30 feet above the ground between the Jay (J) and the Tee (T) buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A, as shown in the diagram.

a) How fast is the shadow of the tightrope walkers feet moving along the ground when she is midway between the buildings?
b) How far from point A is the tightrope walker when the shadow of her feet reaches the base of the Tee Building?
c) How fast is the shadow of the tightrope walker's feet moving up the wall of the Tee building when she is 10 feet from point B?
 
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  • #2
1.a. What is the relation of the square's circumference to the circle's?
1.b. What is the relation of the square's area to the circle's?
 

FAQ: Solve Related Rates Problems: Problem 1 & 2

What are related rates problems?

Related rates problems are mathematical problems that involve finding the rate of change of one variable with respect to another variable. These types of problems often involve multiple variables that are related through an equation or formula.

How do you solve related rates problems?

To solve related rates problems, you must first identify the variables involved and their relationships. Then, use the given information and relevant equations to set up a differential equation. Finally, solve the differential equation to find the rate of change of the desired variable.

What is the difference between problem 1 and problem 2 in related rates?

Problem 1 and problem 2 in related rates are two different types of problems that require different approaches to solve. Problem 1 typically involves a single variable changing with respect to time, while problem 2 involves multiple variables changing with respect to time.

What are some common mistakes made in solving related rates problems?

Some common mistakes made in solving related rates problems include not correctly identifying the variables and their relationships, not setting up the differential equation correctly, and not properly differentiating the equation. It is important to carefully read and understand the given information and double-check your work to avoid these mistakes.

What are some real-life applications of related rates problems?

Related rates problems have many real-life applications, such as in physics, engineering, and economics. For example, related rates can be used to calculate the rate at which a population is growing, the rate at which a balloon is inflating, or the rate at which a tank is filling with water.

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