answer:To solve the equation 4cdot 2sqrt{x}=x^2, we can follow these steps: 1. **Simplify the left-hand side of the equation:** 4cdot 2sqrt{x} = 8sqrt{x} 2. **Square both sides of the equation:** (8sqrt{x})^2 = x^4 64x = x^4 3. **Divide both sides of the equation by x (assuming x neq 0):** frac{64x}{x} = frac{x^4}{x} 64 = x^3 4. **Take the cube root of both sides of the equation:** sqrt[3]{64} = sqrt[3]{x^3} 4 = x 5. **Check for extraneous solutions:** Since we squared both sides of the equation in step 2, we need to check if x = 4 is a valid solution. Substituting x = 4 back into the original equation, we get: 4cdot 2sqrt{4} = 4^2 8cdot 2 = 16 16 = 16 This checks out, so x = 4 is a valid solution. Therefore, the solution to the equation 4cdot 2sqrt{x}=x^2 is x = 4.

answer:Predicative logic is a type of logic that does not allow for self-reference. This means that a definition of an object cannot involve quantifying over a set that contains the object itself. Cantor's Theorem states that the set of real numbers is uncountable. The proof of this theorem does not involve any self-reference, so it can be proven using predicative logic. No, Cantor's Theorem can be proven using predicative logic.

answer:Retained earnings is a component of the equity section of the balance sheet, representing the cumulative earnings that a company has chosen to retain rather than distribute as dividends. We can use the following equation to solve for net income: Change in Retained Earnings = Net Income - Dividends Plugging in the known information, we get: -310 = Net Income - 1,300 Solving for net income, we find: Net Income = 1,300 - 310 = 990 Therefore, the net income for the year is 990.

answer:Myths often include references to supernatural beings, such as gods, goddesses, or other mythical creatures. These beings are often depicted as having powers or abilities beyond those of ordinary humans, and they may play a significant role in the story. In this excerpt, the reference to a supernatural being is the mention of "the gods." This reference helps to establish the mythical nature of the story and to create a sense of wonder and awe. It features a reference to a supernatural being.