Suppose the supply and demand for a certain textbook are given by supply: p equals one half q squared comma demand: p equals negative one half q squared plus 30 comma where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of $10.

Demand quantity: 6.3246

Supply quantity: 4.4721

Step-by-step explanation:

Supply equation:

p = (1/2) * q^2

Demand equation:

p = - (1/2) * q^2 + 30

(p is the price, q is the quantity)

If the price p is equal to 10, then we can calculate:

Supply quantity:

10 = 0.5 * q^2

q^2 = 20

q = 4.4721

Demand quantity:

10 = - 0.5 * q^2 + 30

0.5 * q^2 = 20

q^2 = 40

q = 6.3246