Convert using exponential notation ex: 3 meters to centimeters 3m=300cm 3×10squared equals 300 a)125 cm to meters =? b)3.24 meters to centimeters=?

In a box lenght 1m breadth 60 cm and height 40 cm small rectangular packets of dimension 5 cm into 8 cm into 10 cm are packed. how many such small packets can be packed in the big box?

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.

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.