What is the positional relationship between the line 3x 4y-13 = 0 and the circle (X-2) &# 178; (Y-3) &# 178; = 1?

What is the positional relationship between the line 3x 4y-13 = 0 and the circle (X-2) &# 178; (Y-3) &# 178; = 1?

What is the distance from the center of the circle to the straight line
d=|3*2+4*3-13|/√(3²+4²)=1=r
So the line is tangent to the circle
If you don't understand, I wish you a happy study!
Three mathematical problems, solved by equation (once in one variable or once in two variables is OK)
1. Sister and brother started to do their homework on the same day. Sister did five more pages a day than brother. Brother did not do it for three days. Eight days later, sister did twice as many pages as brother. At this time, how many pages did sister and brother do?
2. There are some students in the classroom. After ten girls, the number of boys is 1.5 times that of girls. After another ten girls, the number of boys is 4 times that of girls. Q: how many students are there in the classroom?
3. Someone said to a friend, "if you give me 100 copper coins, I will be twice as rich as you." the friend replied, "if you only give me 10 copper coins, I will be six times richer than you." how many copper coins do they have?
1. My brother does x every day
（x+5）*8=（8-3）*x*2
2. Set X as female
1.5（x-10）=（x-10-10）*4
3. Let someone be X
（x-10）*6=（x+100）÷2+100+10
How to solve Fractional Inequality
Common method: transform the numerator denominator factorization factor into integral inequality
Of course, we can't just remember how to deal with specific problems~
First find a few typical types of questions to be familiar with the method, and then find some more flexible methods to practice the feeling, I believe that you will find it easy to get this kind of questions
Given 3x-4y + 7 = 0, then the minimum value of X * x-2x + y * y is 0
A.1 B.2 C.3 D.4
3x-4y+7=0
y=3x/4+7/4
x*x-2x+y*y
=x*x-2x+(3x/4+7/4)^2
=25x^2/16+5x/8+49/16
=1/16*(5x+1)^2+3
C yes
The system of linear equations with two or three variables is listed and solved
If a project is completed by team a and team B within 6 days, the manufacturer shall pay team a and team B a total of 8700 yuan; if team B and team C complete within 10 days, the manufacturer shall pay Team B and team C 9500 yuan; if team a and team C complete 2 / 3 (two thirds) of the whole project within 5 days, the manufacturer shall pay team a and team C a total of 5500 yuan
How many days does it take for each team a, B and C to complete the whole project,
The payment in this question is the number of confused problem solvers, so it is not necessary to consider that a, B and C each need x, y, Z days, 1 / (1 / x + 1 / y) = 6 1 / (1 / y + 1 / z) = 10 (2 / 3) / (1 / x + 1 / z) = 5 to solve the equations: x = 10, y = 15, z = 30
How to solve Fractional Inequality?
Let me give you an example
Inequality 3 / (x + 1) > 3
First, remove the denominator, then analyze three cases of denominator ≠ 0, denominator ＞ 0 and denominator ＜ 0, and each case should be combined with the inequality after removing the denominator to form a system of inequality equations, and finally each group should be combined
If the algebraic formula 2 (X-2) and 1-3x are opposite to each other, then x =? (column calculation)
Because they are opposite numbers
SO 2 (x - 2) + 1 - 3x = 0
2x - 4 + 1 - 3x = 0
3x - 2x = -4 + 1
x = -3
Solve the bivariate linear equation and fill in the blanks,
1. Then the solution of the system of equations AX = - 7 is known to be a-y = - 1
2. If the 2A power of 7x, the 5B power of Y and the 1 + 3B power of - 5x, the 11-3a power of Y are of the same kind, then a =, B=
3. To solve the bivariate linear equation 3 (x-1) = 4 (y-4)
5（y-1）=3（x-5）.②
4. To solve the linear equation x-4y-z = 3
2x+y-z=18...②
x-y-z=7.③
If 2A = 1 + 3b, 5b = 11-3a, then A-B = 7-2a (a belongs to any constant). 2. Similar terms are interpreted as the same power of unknown quantity, that is, the same power. 2A = 1 + 3b, 5b = 11-3a. It is possible to solve the system of equations. 3,4? The system of equations is that multiple variables are expressed by one variable, and finally the equation of one variable is solved. That is y = * * *
How to solve the Fractional Inequality with the method of pinprick
First, the inequality = 0
Find the root of X
Then mark the root of X on the number axis
And then start with the biggest one, from top to bottom, through a root, and then from bottom to top, sort of like a SiNx image
Then the inequality > 0 is the set of regions above the number axis
If f (x) = (3x-1) x ^ 4 + 4 (3x-1) x & # 179; + 6 (3x-1) x & # 178; + 4 (3x-1) + 1, find the remainder of F (x) divided by X-10
It's the value of F (10). It's very simple. Junior high school knowledge
41917？
There are 3277 divisions in higher algebra