answer:To find when the rate of change of the concentration is greatest, we need to find the maximum of the derivative of the concentration function. The derivative of the concentration function is given by: {eq}C'(t) = frac{128 - 4t^3}{(64+t^3)^2} {/eq} To find the maximum of this function, we need to find its second derivative and set it equal to zero: {eq}C''(t) = frac{24t^2(t^3-64)}{(64+t^3)^3} {/eq} Setting this equal to zero, we get: {eq}24t^2(t^3-64) = 0 {/eq} This equation has two solutions: {eq}t = 0{/eq} and {eq}t = 4{/eq}. Since {eq}t{/eq} represents time, we can discard the solution {eq}t = 0{/eq}. Therefore, the rate of change of the concentration of the chemical in the bloodstream is greatest at {eq}color{blue}{t = 4 text{ hours}} {/eq}.

answer:- Cevian: A cevian is a line segment that connects a vertex of a triangle to a point on the opposite side. The coordinates of the points that define the line for the cevian are (18.4, 0) and (7.1, 1.09). - Median: A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. The coordinates of the points that define the line for the median are (18.4, 0) and (9.2, 1.38). - Symmedian: A symmedian is a line segment that connects a vertex of a triangle to the centroid of the triangle. The centroid is the point of intersection of the medians. The coordinates of the points that define the line for the symmedian are (18.4, 0) and (13.31, 2.05). - Altitude: An altitude is a line segment that is perpendicular to a side of a triangle and passes through the opposite vertex. The coordinates of the points that define the line for the altitude are (18.4, 0) and (17.97, 2.77). Cevian: left( begin{array}{cc} 18.4 & 0. 7.1 & 1.09 end{array} right) Median: left( begin{array}{cc} 18.4 & 0. 9.2 & 1.38 end{array} right) Symmedian: left( begin{array}{cc} 18.4 & 0. 13.31 & 2.05 end{array} right) Altitude: left( begin{array}{cc} 18.4 & 0. 17.97 & 2.77 end{array} right)

answer:To differentiate the given function, we can use the chain rule. The chain rule states that if we have a function f(x) = g(h(x)), then the derivative of f(x) with respect to x is given by: f'(x) = g'(h(x)) cdot h'(x) In this case, we have g(x) = -sinh^{-1}(4) and h(x) = cot(1-6x). So, we can find the derivatives of g(x) and h(x) as follows: g'(x) = -frac{1}{sqrt{16+x^2}} h'(x) = 6 csc^2(1-6x) Now, we can substitute these derivatives into the chain rule formula to get: f'(x) = -frac{1}{sqrt{16+x^2}} cdot 6 csc^2(1-6x) f'(x) = 6 sinh^{-1}(4) csc^2(1-6x) Therefore, the derivative of the given function is 6 sinh^{-1}(4) csc^2(1-6x). The answer is f'(x) = 6 sinh^{-1}(4) csc^2(1-6x)

answer:** **a. Cost of Equity using the DCF Approach:** {eq}Cost of Equity (DCF) = dfrac{Current Dividend (1 + Growth Rate)}{Common Stock Price} + Growth Rate Cost of Equity (DCF) = dfrac{2.14 (1 + 0.07)}{23} + 0.07 Cost of Equity (DCF) = dfrac{2.2898}{23} + 0.07 Cost of Equity (DCF) = 0.0995 + 0.07 Cost of Equity (DCF) = 0.1695 or 16.95% {/eq} **b. Cost of Equity using the CAPM Approach:** {eq}Cost of Equity (CAPM) = Risk-Free Rate + Beta times (Expected Market Return - Risk-Free Rate) Cost of Equity (CAPM) = 0.09 + 1.6 times (0.13 - 0.09) Cost of Equity (CAPM) = 0.09 + 1.6 times 0.04 Cost of Equity (CAPM) = 0.09 + 0.064 Cost of Equity (CAPM) = 0.154 or 15.40% {/eq} **c. Cost of Equity using the Own-Bond-Yield-Plus-Judgmental-Risk-Premium Approach:** {eq}Cost of Equity (Own-Bond-Yield) = Return on Bonds + Risk Premium Cost of Equity (Own-Bond-Yield) = 0.12 + 0.02 Cost of Equity (Own-Bond-Yield) = 0.14 or 14.00% {/eq} **d. Estimate of Shelby Inc.'s Cost of Equity:** Based on the results obtained using the DCF, CAPM, and own-bond-yield-plus-judgmental-risk-premium approaches, a reasonable estimate of Shelby Inc.'s cost of equity would be: {eq}Average Cost of Equity = dfrac{16.95% + 15.40% + 14.00%}{3} Average Cost of Equity = dfrac{46.35%}{3} Average Cost of Equity = 15.45% {/eq} Therefore, Shelby Inc.'s cost of equity is estimated to be approximately 15.45%.