Area, Volume, and Sequences Problems

The video tutorial covers various mathematical problems, including calculating the area of a fenced schoolyard, determining the volume of an open-top box, and modeling algae growth in a pond. It also explores defining sequences recursively and graphing sloth populations over time. Each section provides a detailed explanation of the problem, the mathematical concepts involved, and the solution process.

What is the expression for the area of the schoolyard if the length of each side is x meters?

• x * (150 - x)

• x * (150 - 2x)

• x * (150 + 2x)

• x * (150 + x)

If x is 40 meters, what is the area of the schoolyard?

• 2,800 square meters

• 3,000 square meters

• 2,400 square meters

• 2,600 square meters

What is the appropriate domain for the length x in the schoolyard problem?

• 0 < x < 75

• 0 < x < 150

• 0 < x < 100

• 0 < x < 50

What is the maximum volume of the open-top box according to the graph?

• 10 cubic inches

• 15 cubic inches

• 20 cubic inches

• 25 cubic inches

What is the more appropriate domain for the volume function of the open-top box?

• 0 ≤ x ≤ 4

• 0 ≤ x ≤ 5

• 0 ≤ x ≤ 3

• 0 ≤ x ≤ 2.5

What is the expression for the volume of the box when x is the length of the cutout?

• (10 - 2x)^2 * x

• (10 - 4x)^2 * x

• (10 - x)^2 * x

• (10 - 3x)^2 * x

What is the volume of the box when x equals 3 cm?

• 60 cm³

• 36 cm³

• 54 cm³

• 48 cm³

On day 3, what is the area of the pond covered by algae?

• 0.75 square meters

• 0.5 square meters

• 2 square meters

• 1 square meter

What is the recursive formula for the sequence P?

• P(n) = P(n-1) + 10

• P(n) = P(n-1) - 10

• P(n) = P(n-1) / 10

• P(n) = P(n-1) * 10

What is the first term of the sequence P?

• 10000

• 5000

• 1000

• 2000