Analyze the provided image and extract the mathematical expressions and equations.

Mathematical Expressions and Equations:

• The main equation appears to be a physics formula: \( v_{0y}t - \frac{gt^2}{2} = 0 \)
• A series of numerical puzzles with missing operators:
  • \( 3 \_ 2 = 7 \)
  • \( 5 \_ 4 = 23 \)
  • \( 7 \_ 6 = 47 \)
  • \( 9 \_ 8 = 79 \)
  • \( 10 \_ 9 = \_ \times 9 = \text{start} \)
• An equation for time: \( t = \frac{x}{v_0} \)
• An equation for vertical displacement: \( y = y_0 - \frac{g(\frac{x}{v_0})}{2} = y_0 \cdot \frac{gx^2}{2v_0^2} \)

Note: The specific operation for the blanks in the numerical puzzles is not explicitly defined in the image, but the pattern suggests a potential relationship. The phrase '= start' in the last puzzle implies a starting point or initial condition.