The arm and blade of a windshield wiper have a total length of 30 inches. The blade is 24 inches long and the wiper sweeps out a
n angle of 125 degrees.
1 answer:
Answer:
942.5 in²
Step-by-step explanation:
The formula for the area (A) of a sector of a circle is
A = ½r²θ
where θ is the angle in radians.
1. Convert the angle to radians
θ = 125°
2. Area swept out by wiper arm
A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²
3. Area missed by wiper
A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²
4. Area covered by wiper
A = 450 θ in² - 18 θ in² = 432 θ in²
5. Insert the value of θ
A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²
The area swept out by the wiper blade is 942.5 in².
You might be interested in
Answer:
(0,2.3) if only one choice expected.
(0,2.3) and (0,0) if "all that apply" expected, since (0,0) is also a vertex of the green region.
Step-by-step explanation:
From the attached diagram, the given answer optsions are shown in brown.
The red line shows the optimal combinations of the two variables, hence a maximization problem.
Out of the four answer options, two coincide with a vertice of the valid region (shown in green), namely (0,0) and (0, 2.3).
Out of the two indicated options which correspond to a vertex, the origin (0,0) is usually ignored for a maximization problem, which leaves us with (0,2.3) as the answer.
