<h3>Answer: 14</h3>
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Work Shown:
Side note: The triangles are similar, which allows us to set up the proportion in step 1.
Answer:
1 task = 6.25 minutes
The robot can complete 9.6 task in 1 hour
Step-by-step explanation:
Number of task = 8
Time taken = 5/6 of 1 hour
5/8 of 1 hour = 5/6 × 60 minutes
= 300/6
= 50 minutes
8 task takes 50 minutes
1 task = 50 minutes / 8 task
= 6.25 minutes
1 task = 6.25 minutes
x task = 60 minutes
1 : 6.25 = x : 60
1/6.25 = x / 60
1*60 = 6.25*x
60 = 6.25x
x = 60/6.25
= 9.6
x= 9.6
The robot can complete 9.6 task in 1 hour
A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
The answer is C
explanation
