The video tutorial explains how to find a formula for R in terms of t when R is proportional to t squared. It demonstrates the process of determining the proportional constant k using graph coordinates and deriving the formula R = 2.5t^2. Additionally, it shows how to prove that t is inversely proportional to the square root of x, using given equations and making t the subject.

What is the initial step in finding a formula for R in terms of t?

• Determine the range of t

• Draw the graph of R against t

• Identify the proportionality constant k

• Calculate the value of R

Which coordinates are used to calculate the proportionality constant k?

• (1, 5) and (3, 15)

• (3, 9) and (6, 36)

• (2, 10) and (4, 40)

• (0, 0) and (5, 25)

What is the value of k when R is proportional to t squared?

• 2.5

• 2.0

• 3.0

• 1.5

What is the final formula for R in terms of t?

• R = 4.0 * t^2

• R = 1.5 * t^2

• R = 2.5 * t^2

• R = 3.0 * t^2

What is the relationship between t and x in part b?

• t is inversely proportional to x

• t is directly proportional to x

• t is inversely proportional to the square root of x

• t is directly proportional to the square root of x

How do you make t the subject in the equation involving R and x?

• Subtract 2.5 from both sides

• Divide both sides by 2.5

• Add 2.5 to both sides

• Multiply both sides by 2.5

What is the simplified expression for t in terms of x?

• t = 0.8 * sqrt(x)

• t = 0.8 / x

• t = 0.8 / sqrt(x)

• t = 0.8 * x