Write this second order differential equation as a first order matrix-vector system of differential equations. Show your work in detail. Now, suppose the front left portion of your vehicle drifts off a curb of height 0.15 meters without an initial velocity. Write an appropriate initial condition using proper notation describing this event and pair it with your first order system.

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Arecipe uses 2 cups of sugar to make 32 brownies. how many cups of sugar are needed to make 72 brownies?

Kathy spent 5/8 of her money on books and another 1/6 of her money on stationeries. what fraction of kathy’s money was left?