answer:A. "How does exercise improve heart health?" is a well-structured research question that focuses on the relationship between exercise and heart health. It is specific enough to allow for a thorough investigation while also being broad enough to encompass a variety of potential factors and mechanisms. This question would allow researchers to explore the physiological, psychological, and social aspects of how exercise can contribute to improved heart health. B. "How much cardiovascular exercise can an 80-year-old man do every day?" is too specific and limits the scope of the research. It focuses on a particular demographic and a specific type of exercise, which may not provide generalizable insights. C. "What kind of person is healthier: an obese person or a fit person?" is a comparative question that does not provide a clear direction for research. It is also subjective and may lead to biased or inconclusive results. D. "Are people who exercise healthy?" is a yes or no question that does not provide much opportunity for in-depth exploration or analysis. It is too broad and does not allow for a nuanced understanding of the relationship between exercise and health. A. How does exercise improve heart health?

answer:Advantages: * Provides better insights into the entire population * Yields more accurate results Challenges: * Can be difficult to obtain a truly representative sample * May be expensive and time-consuming * Requires careful planning and execution to avoid bias

answer:First, we can simplify the left-hand side of the equation using the rule for multiplying exponential expressions with the same base: 3^{15 x+2}3^{20 x-24} = 3^{15 x+2 + 20 x-24} = 3^{35 x-22} Next, we can rewrite the equation as: 3^{35 x-22} = 3^{-13 x-5} Since the bases are the same, we can equate the exponents: 35 x-22 = -13 x-5 Combining like terms, we get: 48 x = 17 Dividing both sides by 48, we find: x = frac{17}{48} Therefore, the only real solution to the equation is x = frac{17}{48}. The answer is left{xto frac{17}{48}right}

answer:The eigenvalues of the given matrix can be found by solving the characteristic equation, which is given by: [ det(A - lambda I) = 0 ] where ( A ) is the matrix, ( lambda ) is the eigenvalue, and ( I ) is the identity matrix. For the 2x2 matrix: [ begin{bmatrix} 9-lambda & -4 9 & -lambda end{bmatrix} ] Solving for ( lambda ), we get: [ (9 - lambda)(-lambda) - (-4 cdot 9) = 0 ] [ lambda^2 - 9lambda + 36 = 0 ] Factoring the quadratic equation: [ (lambda - 3)(lambda - 6) = 0 ] Thus, the eigenvalues are: [ lambda_1 = 3, quad lambda_2 = 6 ] However, it seems there was a typo in the original answer, and the given complex eigenvalues are incorrect. The correct eigenvalues are ( 3 ) and ( 6 ).