Umbilical
point.
An
umbilic point, likewise called just an umbilic, is a point on a surface at
which the arch is the same toward any path.
In
the differential geometry of surfaces in three measurements, umbilics or
umbilical focuses are focuses on a surface that are locally round. At such
focuses the ordinary ebbs and flows every which way are equivalent,
consequently, both primary ebbs and flows are equivalent, and each digression
vector is a chief heading. The name "umbilic" originates from the
Latin umbilicus - navel.
<span>Umbilic
focuses for the most part happen as confined focuses in the circular area of
the surface; that is, the place the Gaussian ebb and flow is sure. For surfaces
with family 0, e.g. an ellipsoid, there must be no less than four umbilics, an
outcome of the Poincaré–Hopf hypothesis. An ellipsoid of unrest has just two
umbilics.</span>
Answer:
Q1) (x+7)² = 9
x = -10, -4
Q2) (x-8)² = 144
x = -4, 20
Q3) (x-1)² = 81
x = -8, 10
Step-by-step explanation:
Q1) x² + 14x + 49 = 9
x² + 2(x)(7) + 7² = 9
(x + 7)² = 9
x + 7 = +/- sqrt(9)
x + 7 = 3
x = -4
x + 7 = -3
x = -10
Q2) x² - 16x + 64 = 144
x² - 2(x)(8) + 8² = 144
(x - 8)² = 144
x - 8 = +/- sqrt(144)
x - 8 = 12
x = 20
x - 8 = -12
x = -4
Q3) x² - 2x + 1 = 81
x² - 2(x)(1) + 1² = 81
(x - 1)² = 81
x - 1 =+/- sqrt(81)
x - 1 = 9
x = 10
x - 1 = -9
x = -8
