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Cutegirlrocks1071
20.05.2021 •
Mathematics
The equation x2 + y2 - 4x + 2y = b describes a circle. The radius of the circle is 7 units. What is the valine of b in the equation?
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Ответ:
44 = b
Step-by-step explanation:
The equation for a circle centered in the point (a, b) and of radius R is:
(x - a)^2 + (y - b)^2 = R^2
Now we start with the equation:
x^2 + y^2 - 4x + 2y = b
First, we can reorder the terms as:
(x^2 + 2*(-2)*x) + (y^2 + 2*y) = b
Now let's complete the squares:
In the first parentheses we can add and subtract 4
(x^2 + 2*(-2)*x + 4 - 4) + (y^2 + 2*y) = b
(x^2 - 2)^2 - 4 + (y^2 + 2*y) = b
Now let's complete the other square, here we need to add and subtract 1.
(x^2 - 2)^2 - 4 + (y^2 + 2*y + 1 - 1) = b
(x^2 - 2)^2 - 4 + (y + 1)^2 - 1 = b
(x^2 - 2)^2 + (y + 1)^2 = b + 1 + 4
Then the radius of this circle is:
R = √(b + 1 + 4)
And we know that R = 7, then:
7 = √(b + 1 + 4)
7^2 = b + 1 + 4
49 = b +5
49 - 5 = b
44 = b
Ответ:
h(x) = -1200x^2 + 1950x + 4950
Work Shown:
f(x) = revenue from the north
f(x) = -750x^2 + 1500x + 2250
g(x) = revenue from the south
g(x) = -450x^2 + 450x + 2700
h(x) = total revenue, ie add the two revenues
h(x) = f(x) + g(x)
h(x) = (-750x^2+1500x+2250)+(-450x^2+450x+2700)
h(x) = -1200x^2 + 1950x + 4950