answer:Using De Moivre's theorem, we can simplify the expression as follows: left(4 sqrt{3} left(cos left(frac{1}{30}piright)+i sin left(frac{1}{30}piright)right)right)^9 = (4 sqrt{3})^9 left(cos left(frac{1}{30}piright)+i sin left(frac{1}{30}piright)right)^9 = 262144 sqrt{3}^9 left(cos left(frac{1}{30}piright)+i sin left(frac{1}{30}piright)right)^9 = 262144 sqrt{3}^9 left(cos left(frac{1}{30}piright)+i sin left(frac{1}{30}piright)right)^{9} = 262144 sqrt{3}^9 left(cos left(frac{9}{30}piright)+i sin left(frac{9}{30}piright)right) = 262144 sqrt{3}^9 left(cos left(frac{3}{10}piright)+i sin left(frac{3}{10}piright)right) = 21233664 sqrt{3} left(cos left(frac{3}{10}piright)+i sin left(frac{3}{10}piright)right) Therefore, the simplified expression is 21233664 sqrt{3} left(cos left(frac{3}{10}piright)+i sin left(frac{3}{10}piright)right). The answer is 21233664 sqrt{3} left(cos left(frac{3}{10}piright)+i sin left(frac{3}{10}piright)right)

answer:To determine this, we need to update the incremental analysis schedule with the increased variable manufacturing overhead costs: Make Direct materials: 42,000 Direct labor: 63,000 Variable manufacturing overhead: 58,000 * 1.10 = 63,800 Fixed manufacturing overhead: 43,000 Total Cost to Make: 211,800 Buy Cost of units from Rayco: 14 x 15,000 = 210,000 Additional Rental Income: 25,500 Fixed Overhead Eliminated: 43,000 Incremental Profit: 211,800 - 210,000 + 25,500 + 43,000 = 70,300 Even with the 10% increase in variable manufacturing overhead costs, the incremental profit is still positive at 70,300. Therefore, RSW Company should still accept Rayco's offer.

answer:To determine the convergence of the sum sum_{n=1, k=1}^infty (n+k)^{-2}, we can use the integral test. The integral test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, infty), then the series sum_{n=1}^infty f(n) converges if and only if the improper integral int_1^infty f(x) , dx converges. In this case, we can define f(x) = (x+x)^{-2} = x^{-2}. This function is continuous, positive, and decreasing on the interval [1, infty). Therefore, we can use the integral test to determine the convergence of the sum. Evaluating the improper integral, we get: int_1^infty x^{-2} , dx = lim_{ttoinfty} int_1^t x^{-2} , dx = lim_{ttoinfty} left[ -frac{1}{x} right]_1^t = lim_{ttoinfty} left( -frac{1}{t} + 1 right) = 1 Since the improper integral converges, the sum sum_{n=1, k=1}^infty (n+k)^{-2} also converges by the integral test.

answer:By applying the properties of logarithms, we can rewrite the expression as follows: begin{align} log_9 left(frac{x}{y^4}right)^5 & = 5 cdot log_9 left(frac{x}{y^4}right) & = 5 cdot left(log_9 x - log_9 y^4right) & = 5 cdot log_9 x - 5 cdot log_9 y^4 & = 5 cdot log_9 x - 5 cdot left(4 cdot log_9 yright) & = 5cdot log_9 {x} - 20cdot log_9 {y} end{align}