Answer:
n geometry, the notion of a connection makes precise the idea of transporting data[further explanation needed] along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields, measuring the deviation of a vector field from being parallel in a given direction.
Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry embraces several variations on the connection theme, which fall into two major groups: the infinitesimal and the local theory. The local theory concerns itself primarily with notions of parallel transport and holonomy. The infinitesimal theory concerns itself with the differentiation of geometric data. Thus a covariant derivative is a way of specifying a derivative of a vector field along another vector field on a manifold. A Cartan connection is a way of formulating some aspects of connection theory using differential forms and Lie groups. An Ehresmann connection is a connection in a fibre bundle or a principal bundle by specifying the allowed directions of motion of the field. A Koszul connection is a connection which defines directional derivative for sections of a vector bundle more general than the tangent bundle.
Connections also lead to convenient formulations of geometric invariants, such as the curvature (see also curvature tensor and curvature form), and torsion tensor.
Step-by-step explanation:
Answer:
15 feet.
Step-by-step explanation:
We have been given that Nicole measured the shadow of the snow sculptures highest point to be 10 feet long. At the same time of day Nicole's shadow was 40 inches long. Nicole is five feet long.
We will use proportions to solve our given problem as proportions states that two fractions are equal.
Let us convert given measurements from feet to inches.
1 feet = 12 inches.
10 feet = 10*12 inches = 120 inches.
5 feet =5*12 = 60 inches
Let us multiply both sides of our equation by 120.
So the height of the snow sculpture is 180 inches. Let us convert our final answer to feet by dividing 180 by 12.
Therefore, the height of the snow sculpture is 15 feet.
Answer:
the second option is the right one pretty sure
Option C:
x = 6 units
Solution:
QR = 7 units, RS = 5 units, UT = 4 units and ST = x
<em>If two secants intersect outside a circle, the product of the secant segment and its external segment s equal to the product of the other secant segment and its external segment.</em>
⇒ SR × SQ = ST × SU
⇒ 5 × (5 + 7) = x × (x + 4)
⇒ 5 × 12 = x² + 4x
⇒ 60 = x² + 4x
Subtract 60 from both sides.
⇒ 0 = x² + 4x - 60
Switch the sides.
⇒ x² + 4x - 60 = 0
Factor this expression, we get
(x - 6)(x + 10) = 0
x - 6 = 0, x + 10 = 0
x = 6, x = -10
Length cannot be in negative measures.
x = 6 units
Option C is the correct answer.
Answer:
<h3>after 2 secs</h3>
Step-by-step explanation:
The paths crossed at when the height are equal i.e when f(x) = g(x)
Given
f(x)=−x^2+2x+4
g(x) = 2x
IF f(x) = g(x), then;
−x^2+2x+4 = 2x
−x^2+2x+4 - 2x = 0
−x^2+4 = 0
-x^2 = -4
x^2 = 4
x = ±√4
x = 2 and -2
Time cannot be negative
Hence x = 2
The path crossed after 2 seconds