Answer:
Perimeter is 17.07
Step-by-step explanation:
We know that DF = EF = 5 cm, since D and E are the midpoints of AC and AB, both of which are 10 cm in length.
We need to use the Pythagorean theorem to get the length of DE.
So the perimeter of DEF is 5 + 5 + 7.07 = 17.07
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