Direct Square Variation

What is the definition of direct square variation?

• Direct square variation is a relationship between two variables where one variable is inversely proportional to the square of the other variable.

• Direct square variation is a relationship between two variables where one variable is directly proportional to the square of the other variable.

• Direct square variation is a relationship between two variables where one variable is not related to the other variable.

• Direct square variation is a relationship between two variables where one variable is directly proportional to the cube of the other variable.

If y varies directly as the square of x, what is the equation that represents this variation?

• y = kx^-2

• y = kx^3

• y = kx

• y = kx^2

Solve the direct square variation problem: If y = 25 when x = 5, find the value of y when x = 10.

• 75

• 100

• 50

• 30

If y varies directly as the square of x, and y = 16 when x = 4, find the value of x when y = 64.

• 16

• 12

• 32

• 8

What are some real-life applications of direct square variation?

• Temperature of a liquid

• Some real-life applications of direct square variation include gravitational force between two objects, intensity of light or sound waves, and electrical force between two charged particles.

• Speed of a moving object

• Volume of a gas

If y varies directly as the square of x, and y = 9 when x = 3, find the value of x when y = 36.

• x = 9

• x = 6

• x = 4

• x = 12

Explain the relationship between direct square variation and the area of a square.

• The area of a square is unrelated to its side length

• The area of a square is inversely proportional to the square of its side length

• The area of a square is directly proportional to its side length

• The area of a square is directly proportional to the square of its side length, which means that as the side length increases, the area also increases by the square of the side length.

If y varies directly as the square of x, and y = 100 when x = 10, find the value of y when x = 20.

• The value of y when x = 20 is 50.

• The value of y when x = 20 is 150.

• The value of y when x = 20 is 200.

• The value of y when x = 20 is 400.

How is direct square variation different from direct variation and inverse variation?

• Direct square variation involves the square of the variable, while direct variation involves a constant ratio and inverse variation involves the product of the variables being constant.

• Inverse variation involves the square of the variable

• Direct variation involves the sum of the variables being constant

• Direct square variation involves the cube of the variable

If y varies directly as the square of x, and y = 36 when x = 6, find the value of x when y = 144.

• When y = 144, x = 12

• When y = 144, x = 24

• When y = 144, x = 8

• When y = 144, x = 18