The illustration is omitted. Please see the attachment below.
Answer:
The area of the shaded sector is 144π square units.
Step-by-step breakdown:
Given:
The central angle for the sector is, 
The circle's radius is, 
The area of a sector with radius 'R' and angle 
can be determined with:
Substituting 
gives
Thus, the area of the shaded sector calculates to 144π square units.
∠1 and ∠8 are alternate exterior angles while ∠3 and ∠6 are alternate interior angles.
step-by-step explanation:
When transversal l intersects lines m and n, the angles formed outside each line on the opposite side of the transversal constitute alternate angles (like ∠1 and ∠8). In contrast, alternate interior angles appear on opposite sides but are located between the two lines (like ∠3 and ∠6).
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Keywords: Transversal, angles
Based on the provided information about the metals' melting point, boiling point, and density, the response is A. The gold sample transitions from liquid to gas at the highest temperature, while the copper sample occupies the most volume. Gold's boiling point is the highest at 2660, and copper has the lowest density, which correlates with a larger volume since density is defined as mass divided by volume.
Let's sketch the triangle.
The sides are a= 37.674 miles
b= 11.164 miles
c= 36.318 miles
We'll apply the cosine rule for angle calculations
(since the sine law cannot be employed without knowing any angle measurements).
The cosine law is given by
Substituting the values results in
C = 74.48°
We can find angle A using the sine law
A= 
A = 87.38°
The third angle B can be determined by calculating 180° minus the sum of angles A and C
B = 180 - 161.86
B = 18.14°
Thus, we have calculated all three angles (as shown in the attached figure).
The formula for distance in this scenario is:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting gives us:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = √(468)
d = 21.63 Km
Answer:
1) She failed to calculate the total distance each had covered in 1.5 hours.
2) She should have applied 12 km for Joseph's distance and 18 km for Isabelle's distance.
