In the triangle ABC, we know that 2sinbxcosc = Sina, a = 120 degrees, a = 1, and find the area of B and triangle ABC

In the triangle ABC, we know that 2sinbxcosc = Sina, a = 120 degrees, a = 1, and find the area of B and triangle ABC

B = 30 degrees, area (root 3) / 12

In △ ABC, if a & # 178; + B & # 178; - AB = C & # 178; = 2 √ 3 s △ ABC (2 √ 3 times the area of △ ABC), then △ ABC must be △ ABC

A ^ 2 + B ^ 2-C ^ 2 = divide both sides of AB equation by 2Ab
cosC=1/2 ∠C=60°
S=1/2 ab*sinC=√3ab/4
a²+b²-ab=c²=2√3 S=3ab/2
We get (a-2b) (2a-b) = 0, a = 2B or a = B / 2
A = 2B = = > C & # 178; = 3AB / 2 = 3B & # 178; in this case, B & # 178; + C & # 178; = A & # 178; is a right triangle
A = B / 2 = = > C & # 178; = 3B & # 178; / 4 at this time, a & # 178; + C & # 178; = B & # 178; is a right triangle
Delta ABC must be a right triangle

The three sides ABC of mathematical problem △ ABC satisfy a & sup2; + B & sup2; + C & sup2; + 338 = 10A + 24B + 26c, find the area of △ ABC
The more detailed the better, write out the process. Thank you

Transfer formula
（a-5）^2+（b-12）^2+（c-13）^2=0
So a = 5, B = 12, C = 13
According to the inverse law of Pythagorean theorem, △ ABC is a right triangle,
So the area of △ ABC = 5 * 12 / 2 = 30

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?

When 20 points = 13, 1-15 = 45160 ^ [13 ^ (1 ^ 45-1)] × 2, = 160 ^ [13 ^ (54 − 1)] × 2, = 160 ^ [13 ^ [14] × 2, = 160 ^ 43 × 2, = 120 × 2, = 240 (pieces); answer: there are 240 pieces of this batch of parts

30 people rush to repair a section of highway, which is planned to be completed in 8 hours. After 2 hours of work, it is required to be completed ahead of schedule, and another 15 people are added. How many hours did it actually take?

2 + (8-2) * 30 / 45 = 6 hours

18 people took part in moving bricks. They planned to move bricks in 8 hours. Six people were transferred when they worked in 2 hours. How many hours will it take to move the remaining bricks?

18×(8-2)=108
be left over
18-6 = 12 (person)
Still need
108 △ 12 = 9 (hours)

In the original plan, 600 bricks were moved by the existing boys. Later, two more girls came. The workload was evenly distributed. Each boy moved 25 bricks less than the original plan, but now

There are x boys in the solution
600/x-600/（x+2）=25
24（x+2）-24x=x²+2x
x²+2x-48=0
（x+8）（x-6）=0
X1 = 6, X2 = - 8 (rounding off)
600 ÷ (6 + 2) = 75 pieces
A: now each boy has 75 bricks

It is planned that 15 people can move a pile of bricks in 4 hours. After 2 hours of actual labor, 5 people will be transferred. How many hours will it take to move the remaining bricks

(1-14 × 2) / [115 × 14 × (15-5)] = (1-12) / [160 × 10], = 12 ／ 16, = 3 (hours); answer: it will take 3 hours to move the remaining bricks

1. The project team of 30 people rush to repair a highway, which is planned to be completed in eight hours. After two hours of work, due to the urgent task, it is required to be completed ahead of time, and another 15 people are required to be added. The actual situation is very good
How many hours did it take?
2. If two numbers are divided, the quotient is 12, the remainder is 26, and the sum of divisor, divisor, quotient and remainder is 454, what are the divisor and divisor?

1、1÷（30×8）=1/240
1-1/8×2=3/4
3 / 4 △ 1 / 240 × (30 + 15)] = 4 hours
Actually used: 2 + 4 = 6 hours
5、454-12-26-26=390
Divisor: 390 (12 + 1) = 30
Divisor: 30 × 12 + 26 = 386

Master Wang plans to make a batch of parts in 5 hours, and actually finish it in 4 hours. The work efficiency will be improved by 100 points!

（5-4）/4=25%
Increase by 25%