Answer:
Step-by-step explanation:
Statements Reasons
1). Points A, B and C form the triangle 1). Given
2). Let DE be a line passing through 2). Definition of parallel lines
B and parallel to AC
3). ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3). Theorem of Alternate
interior angles
4). m∠1 = m∠4 and m∠3 = m∠5 4). Definition of alternate angles
5). m∠4 + m∠2+ m∠5 = 180° 5). Angle addition and definition
of straight lines
6). m∠1 + m∠2+ m∠3 = 180° 6). Substitution
Answer:
See descriptions below.
Step-by-step explanation:
To construct a perpendicular bisector, draw a line segment. From each end of the line segment, draw arcs above and below which intersect from each side. Be sure to maintain the same radius on each. Where the arcs intersect above and below, mark points. Connect these two points. This is a perpendicular bisector.
To prove theorems about parallel lines, use angle relationships. For instance, when two parallel lines are cut by a transversal, specific angle are congruent. When these relationships are congruent, you must have parallel lines:
- Alternate Interior
- Alternate Exterior
- Corresponding Angles
- Same side interior add to 180
The answer is $7846.15 since $9.99 times 785.4 cubic inches would be 7846.146 but since we cant get a thousandth of a cent we round it to $7846.15
The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.
<h3>What is green's theorem?</h3>
The theorem states that,
Where C is the curve.
<h3>Calculation:</h3>
The given line integral is
Where curve C is a circle x² + y² = 4;
Applying green's theorem,
P = 9y³; Q = -9x³
Then,
⇒ 
Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as
0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π
Then the integral becomes
⇒ 
⇒ 
⇒ 
⇒ 
⇒ ![-108[2\pi - 0]](https://tex.z-dn.net/?f=-108%5B2%5Cpi%20-%200%5D)
⇒ -216π
Therefore, the required value is -216π.
Learn more about green's theorem here:
brainly.com/question/23265902
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