Aaa container company wants to manufacture a rectangular box with a square base that has a volume of 16 cubic meters. for the top and the bottom of the box, the company decides to use material that costs $4 per square meter. for the sides, the company will use cheaper material that costs $2 per square meter. what dimensions should the box have in order to minimize the cost of manufacturing it? (assume that no material is wasted during the manufacture of the box.)

G(x) = 2 sin(2x - π) + 4. using complete sentences, explain how to find the minimum value for the function.

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

What is the solution to the equation below? 3/x-2+6=square root x-2 +8