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The name of the article I chose is ____ and the author is ______.
Please write one paragraph in response to the article. In your paragraph summarize the article and specifically explain the connection it has to math.
Contain at least 4 complete sentences.
Have sentences that start with capital letters and end with punctuation.
Be written in your own words.
Include a specific quote or evidence from the article to show the math connection.
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:
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:
1. what is the exact demical value of 225/16?
2. what is the exact decimal value of 77/12?
Answer:
14.0625 = [tex]\frac{225}{16}[/tex]
6.41666666666... = [tex]\frac{77}{12}[/tex]
Hope that this helps!
6g = 48
g=?
What does g=?
Answer:
8
Step-by-step explanation:
6g = 48
/6 /6
divide 6 by both sides
g = 8
hope this helped!
Helppp math help !!!!!!
Step-by-step explanation:
it should be x= -3 and x= 1
HELPPPP!!!!! Please
Answer:
180 D
Step-by-step explanation:
Evaluate: 4x(5+3)=8-2
A 2
B 8
C 12
D 15
Answer:
The answer to the problem is 15.
I need answer Immediately pls!!!!!!!
Answer:
x = 4.4
Step-by-step explanation:
Flat cost = $57.5/month
Cost of 1GB = $4
But Aubrey wants to keep her bill at $75.1/month.
Let 'x' be the number of GBs she can use while staying within her budget.
So, the equation will be → 4x + 57.5 = 75.1
Now, solve the equation :-
Substract both the sides from 57.5[tex]=> 4x + 57.5 - 57.5 = 75.1 - 57.5[/tex]
[tex]=> 4x = 17.6[/tex]
Divide both the sides by 4[tex]=> \frac{4x}{4} = \frac{17.6}{4}[/tex]
[tex]=> x = 4.4[/tex]
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
360 cubic inches (remember your units!)
Step-by-step explanation:
the formula for volume of a rectangular prism is length times width times height times depth so you have to do 8 times 5 times 9 witch is 360 cubic inches
In an arithmetic series, the 6th term is 39 In the same arithmetic series, the 19th term is 7.8 Work out the sum of the first 25 terms of the arithmetic series.
Answer:
1,500
Step-by-step explanation:
a + 5d = 39 (1)
a + 18d = 78 (2)
Subtract (1) from (2) to eliminate a
18d - 5d = 78 - 39
13d = 39
d = 39/13
d = 3
Substitute d = 3 into (1)
a + 5d = 39 (1)
a + 5(3) = 39
a + 15 = 39
a = 39 - 15
a = 24
Sum of the first 25 terms
Sn = n/2[2a + (n – 1)d]
S25 = 25/2{2*24 + (25-1)3}
= 12.5{48 + (24)3}
= 12.5{48 + 72)
= 600 + 900
= 1,500
S25 = 1,500
Kevin will take 4 math tests this term. All of the tests are worth the same number of
points. After taking the first 3 tests, his mean test score is 88 points. How many points
does he need on his last test to raise his mean test score to 90 points?
Answer:
96
Step-by-step explanation:
Total of 4 test at 90
90 * 4 = 360
Current total
88 * 3 = 264
Score needed
360 - 264 = 96
Answer:
96
Step-by-step explanation:
this is how i solved it:
88 x 3 = 264 ( the sum of the three test score )
now i just gotta look for a number to add to 264 that will give me 90 (the wanted mean score) if i divide the sum by 4 (the four test scores).
so the equation would be:
(264 + x) / 4 = 90
264 + x = 360
x= 96
What is the value of x?
Enter your answer in the box.
Step-by-step explanation:
which class are you
just to confirm
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
i really need help!! please! 10 points
Answer:
48°
Step-by-step explanation:
The angle CRS looks like a "L" shape, meaning that both lines are perpindicular to each other, resulting in a right angle (which is 90°)
90° + 42° = 132°
180° - 132° = 48°
Answer:
<RCS = 48 degrees
Step-by-step explanation:
I'm pretty sure that is a right triangle
180-90-42=48
Which expression is equivalent to 4f2/3 ÷ 1/4f ?
Answer:
[tex] \frac{16 {f}^{3} }{3} [/tex]Step-by-step explanation:
[tex] \frac{4f^{2} }{3} \div \frac{1}{4f} [/tex]
[tex] \frac{4 {f}^{2}}{3} (4f)[/tex]
[tex]4 \frac{4 {f}^{2} }{3} f[/tex]
[tex] \frac{16 {f}^{2} }{3} f[/tex]
[tex] \frac{16 {f}^{3} }{3} [/tex]
Hope it is helpful....Which of the following is a graph of x2 < 25?
А
2
3
4
5
5
1
-5
.
3
B.
3
6
2
4
s
5
.2
-4
-3
С
5
E
.5
3
- 1
2
0
D
0
1
.
1
3
5
4
6
5
.
E
1
2
4
6
-6
-4
5
F No Solution
A. Graph A
B. Graph B
Ở Granh
Answer:
why are you running
Step-by-step explanation:
why are you running
What is the range of {(0, 2), (1, 3), (2, 4), (1,4)}
Answer:
Mean: 2.125
median: 2
range: 4
If the unit's and ten's digits of a two digits of a two digit number are y and x, then the number is
Answer:
10x+ y
Step-by-step explanation:
The unit's digit is y and the ten's digit is x.
The ten's digit has a zero placed beside it .
So multiply x by 10 giving 10 x and then add the unit's digit .
This wil give 10x+ y
The number is 10 x + y
This can be elaborated through the use of numbers . Suppose we have unit's digit as 6 and the ten's digit as 5.
Multiply 10 by 5 and add 6
5*10 +6= 50+6= 56
Can someone help me with this question?
Answer:
number 3 sir
Step-by-step explanation:
What is the slope of the line that passes through the points (3,5) and (-1,5)?
Answer:
slope=y2-y1/x2-x1
=5-5/-1-3
=0/-4
=0
Step-by-step explanation:
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (- 1, 5)
m = [tex]\frac{5-5}{-1-3}[/tex] = [tex]\frac{0}{-4}[/tex] = 0
find the value of sin30/cos^(2)45 , tan^(2)60+3cos90+sin0
Answer:
according to me the ans is 3.
Using the graph above, find out how much money miguel saves per month (his unit rate of dollars saved per month).
write your answer. here:____ dollars saved per month
Answer:
15
Step-by-step explanation:
To find the unit rate you divide.
• the points that is in bold is ( 2, 30) from that information you would see what times 2 gives me 30.
• 30/2 =15
• unit rate= 15
HELP DUE IN 10 MINS!
Will GIVE BRAINLEST
Answer:
AB= 5.582
Step-by-step explanation:
Centeral angle /360° = AB length/2 pi r
[tex] \frac{80}{360} = \frac{ab}{4} \\ ab = 5.582[/tex]
Answer:
5.6
Step-by-step explanation:
the length of arc AB =
80/360 × 2× 3.14×4
= 2/9 × 3.14 × 8
= 5.58 => 5.6
can someone please help me
Answer:
yeah what you need help with
Find a formula for dy/dx if sin x + cos y + sec(xy) = 251
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Algebra I
FactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Trig Differentiation
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
sin(x) + cos(y) + sec(xy) = 251
Step 2: Differentiate
[Implicit Differentiation] Trig Differentiation [Chain Rule]: [tex]\displaystyle cos(x) - sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = 0[/tex] [Subtraction Property of Equality] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex] terms: [tex]\displaystyle -sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = -cos(x)[/tex][Distributive Property] Distribute sec(xy)tan(xy): [tex]\displaystyle -sin(y)\frac{dy}{dx} + ysec(xy)tan(xy) + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x)[/tex][Subtraction Property of Equality] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex] terms: [tex]\displaystyle -sin(y)\frac{dy}{dx} + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x) - ysec(xy)tan(xy)[/tex]Factor out [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx}[-sin(y) + xsec(xy)tan(xy)] = -cos(x) - ysec(xy)tan(xy)[/tex][Division Property of Equality] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Implicit Differentiation
Book: College Calculus 10e
3 A circle centered at the origin has a radius
of 7 units. The terminal side of
a 210 degree angle intercepts the circle in
Quadrant III at point C. What are
the coordinates of point C?
Step-by-step explanation:
x = 7 cos 210 = 7×(-½√3) = -3.5√3
y = 7 sin 210 = 7×(-½) = -3.5
point C (-3.5√3 , -3.5)
Why are the coordinates of the fountain? Show your work
Answer:did u ever get it
Step-by-step explanation:
I need help on this please
Answer:
12√3
Step-by-step explanation:
sin 60° = 18/h
h = 18/sin 60°
h = 12√3
1) Determine the value written as a fraction , decimal & a percent. fraction decimal percent
Answer:
what value??????
An angle has a reference angle of 40° in the third quadrant what is a positive measure of the angle and a negative measure of this angle
Answer:
2, probably
Step-by-step explanation:
I need help wit this