Answer:
a)
b)
c)
Step-by-step explanation:
From the question we are told that:
Angle
a)
Generally the equation for Slope is mathematically given by
b)
Given the right Angle triangle with horizontal distance
Generally the equation for Height traveled is mathematically given by
c)
Generally the equation for Horizontal Distance traveled at 313 height traveled is mathematically given by
Answer:
22.5
Step-by-step explanation:
The region R contains every point of the plane with coordinate x between 3 and 9, and with coordinate y positive such that y < f(x) and y < g(x).
We can note that both f and g are positive on [3,9] because g is a decreasing linear function and g(9) = 0, thus g is positive in every other point of the interval, and f(x) = (x-3)^2 is always positive excpept when x = 3, where it reaches the value 0.
The interception of the graphs takes place for a value x such that f(x) = g(x).
We compute x^2-6x+9 = -3x + 27, thus x^2-6x+9-(-3x + 27) = x^2-3x -18 = 0.
The roots of that quadratic function are
, thus r1 = 6, r2 = -3. We dont care about -3 because it is outside the interval, but we know that f and g graphs intersects on x = 6. Thus, we obtain, due to Bolzano Theorem:
Hence, the upper bound is f on the interval [3,6) and g on the interval (6,9]. While the lower bound is the 0 function.
We need to calculate the following integral, using Barrow's rule
As a result, the area of the region R is 22.5