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In the triangle ABC, if a is known to be an acute angle and B = 3asinb, then Tana=
b=3asinb
Using the sine theorem,
a/sinA=b/sinB=c/sinC
∴ sinB=3sinAsinB
∴ sinA=1/3
∴ cos²A=1-sin²A=1-1/9=8/9
∵ A is an acute angle,
Then cosa = 2 √ 2 / 3
∴ tanA=sinA/cosA=1/(2√2)=√2/4
In △ ABC, the edges of angles a, B and C are a, B and C respectively, satisfying sina2 = 55 and BC = 5. (I) find the value of cosa2 and the area of △ ABC; (II) if B2 + C2 = 26, find the value of A
(13 points in total) (I) because sina2 = 55, and 0 < a < π, so 0 < A2 < π 2, ∩ cosa2 = 255, (3 points) ∫ Sina = 2sina2cosa2 = 45, BC = 5, (6 points) so s △ ABC = 12bcsina = 2; (8 points) (II) because sina2 = 55, so cosa = 1 − 2sin2a2 = 35, (10 points) ∵ BC = 5, B2 + C2 = 26, ∫ according to the cosine theorem: A2 = B2 + c2-2bccosa = 26 − 2 × 5 × 35 = 20, (12 points) a = 25. (13 points)
Given that the area of triangle ABC is 1 / 2 and Sina = 1 / 4, the minimum value of 1 / B 2 / C is
S△ABC=1/2bcsinA=1/2
bc=4
1/b+2/c
=(c+2b)/ab
=(c+2b)/4
≥2√(2bc)/4
=√2
A car drives from the east to the West. After a journey, it is 210 kilometers away from the west, and then 20% of the whole journey. At this time, the ratio of the distance traveled to the distance not traveled is 3:2. How many kilometers are there between the East and the west?
Suppose the distance between the East and the west is x km, we can get: & nbsp; x-210 + 20% x = 35x, x-210 + 0.2x = 0.6x, & nbsp; 1.2x-210 = 0.6x, & nbsp; 1.2x-0.6x = 210, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 0.6x = 210, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 3
It takes 40 hours for a job to be done by one person. Now it is planned that two people will work for four hours first, and the rest work will be finished in eight hours. How many more people do you need?
You need to add x people
2*4*1/40+8/40X=1
X=4
It takes 40 hours for one person to do a job. Now it is planned that two people will do it for 4 hours first, and the rest of the work will be completed in 8 hours. How many more people are needed? (same efficiency)
It seems that this question is very difficult My God, to be honest, I don't know if I'm right
2 × 4 = 8 (hours)
40-8 = 32 (hours)
32 divided by 8 = 4 (people)
4-2 = 2 (person)
A: two more people are needed. Right? I'm afraid. The man upstairs said four people It's not a Brain Twister
It takes 40 hours for one person to do a job. Now it is planned that two people will do it for 4 hours first, and the rest of the work will be completed in 8 hours. How many more people are needed? (assuming everyone's efficiency is the same)
Suppose X more people are needed, then according to the meaning of the question: 140 × 2 × 4 + (x + 2) 40 × 8 = 1, the solution is x = 2
It takes 40 hours for one person to do a job. Now it is planned that two people will do it for 4 hours first, and the rest of the work will be completed in 8 hours. How many more people are needed? (assuming everyone's efficiency is the same)
Suppose X more people are needed, then according to the meaning of the question: 140 × 2 × 4 + (x + 2) 40 × 8 = 1, the solution is x = 2
It takes 40 hours for one person to do a job. Now it is planned that two people will do it for 4 hours first, and the rest of the work will be completed in 8 hours. How many more people are needed? (assuming everyone's efficiency is the same)
Suppose X more people are needed, then according to the meaning of the question: 140 × 2 × 4 + (x + 2) 40 × 8 = 1, the solution is x = 2
Master Wang plans to process a batch of parts in two hours. When there are 160 parts left, the machine breaks down and the efficiency is 1 / 5 lower than the original plan. As a result, the task is delayed by 20 minutes. How many parts are there?
Solve (as long as it's not an equation) arithmetically
20 minutes = 1 / 3 hour
When the efficiency is reduced, the time is as follows:
1÷(1-1/5)x2
=5/4x2
=5 / 2 (hours)
The total number of parts is:
160÷[1/3÷(5/2-2)]
=160÷2/3
=240
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