To calculate the total variable cost given the equilibrium output, we need to understand the short period run total cost function and its components.

Short Period Run Total Cost Function:
The short period run total cost function represents the total cost incurred by a firm in the short run. It is given by the equation SC = 0.04q^3 - 0.9k^2 + 10q + 5, where:
- SC represents the short period total cost
- q represents the level of output
- k represents the level of capital

Components of the Short Period Run Total Cost Function:
1. Variable Cost: Variable costs are the costs that vary with the level of output. In the given cost function, the variable cost component is represented by 10q.
2. Fixed Cost: Fixed costs are the costs that do not vary with the level of output. In the given cost function, the fixed cost component is represented by 5. This cost remains constant regardless of the level of output.
3. Other Costs: The terms 0.04q^3 and -0.9k^2 represent additional costs that are not directly related to the level of output. These costs may include overhead costs, depreciation costs, or any other non-variable costs.

Calculating the Total Variable Cost:
Total variable cost (TVC) is the sum of all costs that vary with the level of output. In the given cost function, the variable cost component is 10q. Therefore, to calculate the total variable cost at the equilibrium output of 10, we substitute q = 10 into the variable cost component:

TVC = 10q
TVC = 10(10)
TVC = 100

Hence, the total variable cost at the equilibrium output of 10 is 100.

Summary:
- The short period run total cost function represents the total cost incurred by a firm in the short run.
- The given cost function SC = 0.04q^3 - 0.9k^2 + 10q + 5 consists of variable costs, fixed costs, and other costs.
- The variable cost component is represented by 10q.
- To calculate the total variable cost at the equilibrium output of 10, we substitute q = 10 into the variable cost component and get TVC = 100.