Final answer:
To find (g+h)(10), we evaluate g(10) and h(10) and add them together, resulting in 137. The evenness of a function refers to its symmetry around the y-axis. The quadratic formula is used to solve for t in a quadratic equation, and displacement equals distance covered in the case of a raindrop falling in still air.
Step-by-step explanation:
To find (g+h)(10), we need to evaluate both functions g(t) and h(t) at t = 10 and then sum their values. The function g(t) is given as 3t + 5 and h(t) as t² + 2. So, g(10) is (3*10) + 5 = 35 and h(10) is (10)² + 2 = 102. Adding these together gives us (g+h)(10) = 35 + 102 = 137.
Now, concerning the evenness of a function, if both functions you are multiplying are even, then their product will also be an even function. An even function is symmetric with respect to the y-axis, meaning that f(x) = f(-x) for every x in the function's domain.
To apply the quadratic formula to solve the equation t² + 10t - 2000 = 0, first confirm that the equation is in standard form (which it is), and then identify the coefficients a = 1, b = 10, and c = -2000. Substituting these into the quadratic formula ( -b ± √(b²-4ac) ) / (2a), we can find the values of t.
Lastly, regarding the question of when distance covered is equal to the magnitude of displacement: this occurs when the path taken does not involve any changes in direction. Hence, the correct answer is option (c) A raindrop falls in still air, as it follows a straight path downward.