Question 3: GYMNASTICS A gymnast throws a baton up into the air during her floor routine. The height of the baton can be modeled by
y= -16^2 +24x + 4, where x is the time in seconds and y is the height of the baton in feet since it was released. The celling of
the gym can be represented by the function y = 42.
a. Solve the system of equations algebraically.
b. Will the baton reach the ceiling of the gym? Explain your reasoning.

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

Abus travels 36 miles in 45 minutes. enter the number of miles the bus travels in 60 minutes at this rate.

What are the solutions of the system? y = x^2 + 2x +3y = 4x - 2a. (-1, -6) and (-3, -14)b. (-1, 10) and (3, -6)c. no solutiond. (-1, -6) and (3, 10)