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nikklg [1K]
3 years ago
5

There are a total of 122 countries in Africa, Europe, and North America (as of 2003). Europe has twice as many countries as Nort

h America, and Africa has seven more than Europe. How many countries are in each of these three countries?
Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0
A + E + N = 122
E = 2N
A = 7 + E....A = 7 + 2N

(7 + 2N) + 2N + N = 122
5N + 7 = 122
5N = 122 - 7
5N = 115
N = 115/5
N = 23 <== North America

E = 2N
E = 2(23)
E = 46 <== Europe

A = 7 + E
A = 7 + 46
A = 53 <=== Africa
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Answer:

22.5

Step-by-step explanation:

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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

r_1, r_2 = \frac{3 ^+_- \sqrt { 9 +72}}{2} = \frac{3^+_-9}{2} , 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:

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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

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