Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars). +51x²+1250x-500), 0 ≤x≤25 R(x)= 9 (-x³ 16 The point of diminishing returns is ☐

Is det(AB) = det(B A)? Justify your answer.

A single question with sub-parts. Please answer them all step by step. Thank you so much.

Atlantic hurricanes form off the western coast of Africa. As warm moist air rises, it begins to rotate around a low- pressure system. This rotation is sustained by warm ocean temperatures and a central low pressure. Once a sustained wind speed of 74 miles per hour is reached, the storm is considered a hurricane. As man-made climate change continues to increase the temperature of the Earth's oceans, it is expected that the strength of hurricanes will Typically, a lower central pressure within a hurricane's eye is associated with a higher wind speed. Here, statistical software (R/RStudio) will be used to explore this relationship by applying linear regression methods. Using a database of landfalling hurricanes in the United States, a linear regression will be used to correlate the central pressure of each hurricane to its maximum sustained wind speed. increase. Regression Plot y=942.196-0.884*x R^2=0.768 ----- ----------- -. •... •. 980 1000 940 960 900 920 Independent Variable (x)…