Units Digits and Mathematical Operations

The video tutorial covers a series of math problems, each focusing on different mathematical concepts. It begins with a problem involving a custom-defined operation, followed by maximizing the volume of a cylinder within a box. The tutorial then moves on to simplifying algebraic expressions, solving a ratio and proportion problem, and concludes with calculating the units digit of a product of powers. Each problem is solved step-by-step, demonstrating various mathematical techniques and principles.

If the operation defined as a star with a circle around it is given by a² * b / 3, what is the result of 2 star with a circle around it 3 star with a circle around it -1?

• 0

• -4

• 4

• -3

What is the maximum radius of a cylindrical canister that can fit inside a box with dimensions 6 by 8 by 10?

• 4

• 5

• 3

• 2

Which formula is used to simplify the expression (a + b)(a - b)?

• a² + b²

• a² + 2ab + b²

• a² - b²

• a² - 2ab + b²

What is the simplified result of (√2 + 1)(√2 - 1)(√3 + 1)(√3 - 1)?

• 4

• 3

• 2

• 1

In a class, the ratio of math majors to non-math majors is 2:5. If 2 more math majors join, the ratio becomes 1:2. How many students are in the class?

• 32

• 28

• 24

• 20

What is the units digit of 13⁴?

• 7

• 1

• 9

• 3

What is the units digit of 17²?

• 1

• 4

• 7

• 9

What is the units digit of 29³?

• 1

• 7

• 9

• 3

How do you determine the units digit of a product of numbers?

• Subtract the units digits

• Multiply the units digits

• Divide the units digits

• Add the units digits

What is the units digit of the product 13⁴ * 17² * 29³?

• 3

• 7

• 9

• 1