Question

I go to a baseball game with my family. We have $24 to

spend on food. Hot dogs cost $2 each, hamburgers

cost $3 each. An equation for this could be

2x + 3y = 24, or y=-3x+8. What type of domain

would this situation have?

A. Discrete

B. Continuous

C. I need help understanding

Answer 1

B. There’s multiple equations

Answer 2

Answer:

  A. Discrete

Step-by-step explanation:

You want to know the sort of domain (discrete, continuous) of the equation 2x +3y = 24, or y = -2/3x +8, when x and y are numbers of hot dogs and hamburgers, respectively.

Discrete vs. Continuous

A set is described as "discrete" if it consist of particular values, and those only. Here, the numbers describing the numbers of hot dogs and hamburgers will be whole numbers. Fractions and irrational numbers are not allowed. (You cannot purchase √2 hot dogs, for example.)

That means the domain of this equation is "discrete."

If fractions and irrational numbers are allowed in a given expression or formula, the domain is "continuous." Lengths of string, for example, tend to be values that do not fall into a specific set of values. ("Nominal" length may be discrete (50', 100', and so on), but actual length likely will not be, especially when one considers that it stretches.)

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Additional comment

Quantum physics seems to be telling us that many things in the universe are quantized (discrete) at the lowest levels. In the practical world, the effect of numerous quantized values added together has the effect of making any particular measurement appear to be continuous.