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1)f1(x)=[7/4]=1;f2(x)=f1(7/4-1)=f1(3/4)=[3]=3
2)[4x]=1;1<=4x<2;1/4<=x<1/2;
4g(x)]=3;3<=4g(x)<4;3/4<=g(x)<1;When g(x) = 3 4, in 1 4 < = x< 1 2, 7 16< = x<1 2
Hope it helps, hope, thank you!
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1) x=7 16, substitute f1(x)=[4x]=[7 4]=1;
g(x)=7/4 - 4x]=7/4 -1 =3/4, f2(x)=f1( g(x) )=f1(3/4)=[3]=3;
2) -1 < t - t] <1
When f1(x)=1, x satisfies [4x]=1, i.e., 1<=4x<2, 1 4<=x<1 2;
When f2(x)=3, g(x) satisfies [4 g(x)]=3, i.e., there are 3<=4g(x)<4, 3 4<=g(x)<1
Since g(x)=4x-[4x], there are 3 4 <= 4x-[4x] <1, 3 16 <= x-[x] <1 4;
If x-[x]=1 4, then x=1 4 + t;
If x-[x]=3 16, then x=3 16 + t;
So when f2(x)=3, x should satisfy (3 16 + t) <= x< (1 4 + t); t is an integer).
To sum up, the value range of x is obtained: when t > = 0, x is an empty set;
When t <0, x is an empty set;
So constant is an empty set.
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[Solution] set: Break x cups, according to the theme.
1000-x-4x=895
Solution x=21
Answer: Twenty-one cups were broken.
Analysis]: If none of them are broken, then the freight is 1000 yuan, and now, if you break a freight, you will be fined 4 yuan, so you will lose a cup and 5 yuan less, so you can list the above equations, and the solution is not difficult.
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Solution: Set to break x glasses.
According to the question, (1000-x)-4x=895 solves this equation to obtain: x=21
Namely: break 21 glasses.
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Set shattered x glasses.
then, 1000-x-4x=895
Solution x=21
So 21 glasses were broken.
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Broken x 895=1000*1-x-4x
Solution x=21
Smashed 21 of them.
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ACB 90°, Ca CB, straight Mn passes through point C, Ad Mn is in D, Be Mn is in E
sin∠acd=cos∠bce
ad/ac=ce/cb
ac=cbad=ce
The same goes for be=dc
de=dc+ce=be+ad
de=be+ad
ACB 90°, Ca CB, straight Mn passes through point C, Ad Mn is in D, Be Mn is in E
sin∠bce=cos∠acd
be/bc=cd/ac
bc=acbe=cd
cad+∠acd=∠acd+∠ecb=90°∴ cad=∠ecb
sin∠cad=sin∠ecb
ad/ac=ce/bc
ac=bcad=ce
ad=ce=cd+de=be+de
ad=be+de
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Long Answer:1It turned out that the first pile had 22 matches, the second had 14 matches, and the third had 12 matches.
2.A takes out three cents, and B takes out one cent and one five, so the sum of the money is: (1+1+1)+(1+5)=9
3.I don't understand this question, "If all 8 outlet pipes are opened, it will take 3 hours to drain all the water in the pool, and if 5 outlet pipes are opened, it will take 6 hours to drain all the water in the pool",? Is this in the case of water ingress or no water in the inlet pipe?
4.The erased number is 30, and the key breakthrough in this problem is that the remaining average is 13 as the denominator.
Piece. 6.We can analyze it like this: x is an odd number, then a*b must be an even number, we know that odd multiplies odd = odd, even multiplied by even = even, odd multiplied even = even, so, if two prime numbers are multiplied and the result is even, then one of these two prime numbers must be 2, in other words, a=2 or b=2, so how to determine the other one?
If you want x to be the maximum, then only the maximum prime number less than 1000 and multiply 2 to fit the topic. If nothing else, it should be 997, this number is not necessarily accurate, and I can't grind well, but this idea is definitely right, as long as you find the maximum prime number less than 1000, multiply it by 2 and add 3 is the final result.
7.The breakthrough of this problem is that the money of three movie tickets is the equivalent relationship, "if you use the money brought by A, B and C to buy three movie tickets, it will be 26 yuan more, and it is known that C brought 25 yuan", this sentence actually exposes a problem: if the money brought by A and B is combined to buy three movie tickets, then there is one more dollar, then it is one more dollar, then okay, you can use the money of three movie tickets as the equivalent of the series of equations, you will understand.
Suppose: A brings x yuan, B brings y yuan, then x+39 is the money of three movie tickets, and y+50 is also the money of three movie tickets, therefore: x+39=y+50, and then there is a point, the money of three movie tickets can also be expressed as x+y-1, so to sum up, list the following equation:
x+39=y+50=x+y-1, solution: x=51, y=40, then the three movie ticket money can be expressed like this: 51+39, it can also be expressed like this:
40+50, anyway, it's all 90, so the price of a movie ticket is 90 3 = 30 yuan.
8.What is this question? Can you tell me the original question? I didn't understand it when I first saw it.
I have a little doubt, you have so many questions, and they are all so difficult, can the bounty score be improved?? Otherwise, there are few people who are as patient as I am ... It's the truth.
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Question 1: The first 3 piles of matches are x y z
Move x-y 2y z for the first time
The second move x-y 2y-z 2z
The last move 2(x-y) 2y-z 2z-(x-y) gives us the system of equations: 2(x-y)=2y-z=2z-(x-y)x+y+z=48
Too lazy to forget it.
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The title of the first sub-question is wrong, it should be the first pile and put it in the second pile, and you are three.
1. I can't read the question.
2. A takes out three 1-point ones, and B takes out one 1-point and one 5-point one.
Root. I don't want to think about the others.
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I dizzy when I looked at the title.
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If you sell 40 white melons a day; Watermelons and white melons are sold at a ratio of 7:5, and watermelons should be sold every day: 40 5x7=56 (pieces).
The difference between selling 50 pieces per day: 56-50 = 6 (pieces).
Sold: 36 6 = 6 (days).
Watermelons shipped from fruit stores: 50x6+36=336 (pcs).
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7x watermelons and 5x white melons were shipped. Sell out of white squash on day Y.
5x/40=y
y*50+36=7x
Solving the binary system of linear equations gives x=48,y=6, so there are 7*48=336 watermelons.
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There are x watermelons and y white melons, and they have been sold for n days.
x/y=7/5
40*n=y
50*n+36=x
40*n=5/7*x
50*n+36=x
56*n=50*n+36
n=6x=50*6+36=336
The fruit store shipped 336 watermelons.
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336, set x days, 40x is better than 50x+36 is equal to 5 than 7, solve this equation to get x is equal to 6, and then substitute 50x+36 to get 336 watermelons from the fruit store.
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Solution: The fruit in the fruit store was sold for x days.
Then, (50x+36): 40x=7:5
The solution is x=6
So the fruit store brought watermelon, 50x6 + 36 = 336
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336 watermelons.
7x watermelons and 5x white melons were shipped. Sell out of white squash in n days.
5x/40=n
n*50+36=7x
Solving the binary system of equations gives x=48, so there are 7*48=336 watermelons.
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