Given pair of lines are x² + 4xy + y² = 0
⇒ (y/x) ² + 4 y/x + 1 = 0
⇒ y/x = -4±2√3/2 = -2±√3,
∴ The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle
Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,
The perpendicular distance form origin to x - y = 4 is the height of the
h = 2 √ 2
∵ Area of triangle = h²/√3 = 8/√3
Answer:
6
Step-by-step explanation:
-4x -3 = -6x +9
-4x = -6x +12
2X = 12
x = 6
A great circle is a section of a sphere that passes through its center. If the earth were a sphere, a great circle would be the equator and its axis would be the line connecting the geographic north and south pole. The length of the axis is then equal to the diameter of the sphere. For this problem, the radius of the sphere is 12 inches. A section is formed by slicing through the sphere and all sections of a sphere are circles. Considering the plane to be cut above and parallel with the equator (which is a great circle), the distance of the plane from the center of the sphere would then be the distance between the centers of the sphere and section. It is also given that the radius of the section is 9 inches. A right triangle is formed by connecting the center of the sphere, an edge of the section, and back to the center of the sphere whose hypotenuse is 12 inches (radius of the sphere), one leg is the 9 inches (radius of the section), and another leg is the distance of the plane from the sphere's center. Thus, the distance can be calculated using the Pythagorean theorem, d = sqrt(12^2 - 9^2) = sqrt(144 - 81) = sqrt(63) = 3*sqrt(7).
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Answer:
The measure of the third angle is 35°.
Step-by-step explanation:
The sum of the three angles of a triangle is always 180°.
Let the measure of the third angle be x.
∴ 61° + 84° + x = 180°
145 + x =180°
x = 180 - 145
x = 35°
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