Mathematical Formulas and Problem Solving

The video tutorial covers solving literal equations, focusing on making a variable the subject of a formula. It includes examples such as solving for r in centripetal acceleration, h in the volume of a cone, and x in various linear equations. Practical applications like calculating the time to fill a bucket with water drops are also discussed. The tutorial concludes with solving for a in a given formula and r in an interest-related equation.

What is the formula for centripetal acceleration?

• a = v / r^2

• a = r / v^2

• a = r^2 / v

• a = v^2 / r

How do you solve for r in the formula a = v^2 / r?

• r = v^2 / a

• r = a / v^2

• r = v / a^2

• r = a^2 / v

What is the formula for the volume of a cone?

• V = 1/3 πr^2h

• V = πr^2h

• V = 2/3 πr^2h

• V = 1/2 πr^2h

How do you solve for h in the formula V = 1/3 πr^2h?

• h = 3V / (πr^2)

• h = V / (3πr^2)

• h = 3πr^2 / V

• h = πr^2 / (3V)

In the equation 4px + 1 = 64, what is the first step to solve for x?

• Divide both sides by 4

• Subtract 1 from both sides

• Multiply both sides by 4

• Add 1 to both sides

What is the value of x when p = -5 in the equation 4px + 1 = 64?

• x = 15

• x = 3

• x = -3

• x = -15

In the equation -2bx - 5 = 16, what is the first step to solve for x?

• Multiply both sides by -2

• Divide both sides by -2

• Add 5 to both sides

• Subtract 5 from both sides

What is the value of x when b = 3 in the equation -2bx - 5 = 16?

• x = 3

• x = 1

• x = -1

• x = -3

In the equation 7 + 2ax = 13, what is the value of x?

• x = 6 / (2a)

• x = 13 / a

• x = 13 / (2a)

• x = 7 / (2a)

In the equation -ax - 20 = -14, what is the value of x?

• x = -6 / a

• x = 6 / -a

• x = 14 / a

• x = -14 / a