Problem 4: throwing an apple straight up with drag for reference see events finding and odes pdf document on assignment drag force is a vector in the opposite direction of an objects velocity vector. which means the governing differential equations of an apple thrown straight up can be modeled with a piecewise differential. = − − cc ∗ � � 2 while the ball is apple is rising = − + cc ∗ � � 2 while the ball is apple is falling where g is the acceleration due to gravity (9.8 m/s2 ) and c is the drag coefficient. use odeset, "events" with ode45 to find how long an apple will be in the air if: • it is thrown straight up from an initial height of 2.5 m • it has an initial velocity of 10 m/s • c = 0.1

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.

Δabc is dilated by a scale factor of 3 with the origin as the center of dilation to form δa′b′c′. the slope of is -1.2. the length of is p units, the length of is q units, and the length of is r units. the slope of is . the length of is units.

Bernice paid $162 in interest on a loan of $1800 borrowed at 6%. how long did it take her to pay the loan off?