The cost of a computer system increases with increased processor speeds. The cost C of a system as a function of processor speed is estimated as \( \mathrm{C}=8 \mathrm{~S}^{2}-2 \mathrm{~S}+1,600 \), where S is the processor speed in MHz . Find the processor speed for which cost is at a minimum. Round to two decimal places. A. 0.10 MHz B. 1.00 MHz C. 2.50 MHz D. 0.13 MHz

Calculate the area under the curve defined by the function \( f(x) = x^3 + 2x - 1 \) from \( x = 1 \) to \( x = 3 \).

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. \( e^{1-5 x}=851 \) The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is \{ (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Solve the equation: \( e^{2x} = 7 \)

Dada la funcion implicita: \( \frac{1}{x}=\frac{4^{x}}{8^{y}} \)

\( \int _ { 0 } ^ { 1 } \frac { 1 } { 1 + \sqrt[ 3 ] { x } } d x \)