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In the rectangular coordinate system, given the points a 5 to 2 and B 2 to 5, we can make a circle with point a as the center and ab as the radius, and judge the position relationship between the circle a and the X, Y axes
Intersect the x-axis and separate from the y-axis
In rectangular coordinate system, the point whose abscissa and ordinate are integers is an integral point. For any natural number n, the origin o is connected with the point an (n, N + 3). TN is used to represent the number of integral points on the line segment o an except the two end points. Then T1 + T2 + T3 +... " +t1997=
It seems that we can use the method of analysis
In a rectangular coordinate system, a point whose abscissa and ordinate are integers is called a grid point, then the grid point of the line represented by equation 3x + y = 10 in the first quadrant is
When x = 1, y can take 1, 2, 3, 4, 5, 6, 7 seven points; when x = 2, y can take 1, 2, 3, 4; when x = 3, y can take 1 point; when x = 3, y can take 1 point, and there are 12 grid points. For this type of problem, there is a general solution (provided that the two intersection points are integral points) with 2x +
1. The equation passing through the intersection of two circles x ^ 2 + y ^ 2 + 2x + 3y-7 = 0, x ^ 2 + y ^ 2 + 3x-2y-1 = 0 and the point (1,2) circle is 2. If the equation y ^ 2 - (LGA) x ^ 2 = 1 / 3-A denotes an ellipse with two focal points on the x-axis, then the value range of a is 3. When there are two intersections between the curve y = 1 + 4-x ^ 2 and the straight line y = K (X-2) + 4, the range of real number k is
Solution: 1
Let the circle equation be x ^ 2 + y ^ 2 + DX + ey + F = 0
x^2+y^2+2x+3y-7=0,x^2+y^2+3x-2y-1=0
By subtracting the two equations, x-5y + 6 = 0
X ^ 2 + y ^ 2 + DX + ey + F = 0 minus x ^ 2 + y ^ 2 + 2x + 3y-7 = 0
(D-2) x + (E-3) y + (F + 7) = 0
Then D-2 = k, E-3 = - 5K, F + 7 = 6K
So d = K + 2, e = 3-5k, f = 6k-7
So the equation of circle: x ^ 2 + y ^ 2 + (K + 2) x + (3-5k) y + 6k-7 = 0
Because the circle passes through the point (1,2), then 1 + 4 + (K + 2) + (3-5k) 2 + 6k-7 = 0
K = 2, so d = 4, e = - 7, f = 5
So the equation of the circle: x ^ 2 + y ^ 2 + 4x-7y + 5 = 0
Two
Y ^ 2 - (LGA) x ^ 2 = 1 / 3-A is transformed into
x^2/[(-1/lga)*(1-3a)/3]+y^2/[(1-3a)/3]=1
According to the meaning of the title:
(- 1 / LGA) * (1-3a) / 3 > (1-3a) / 3 > 0, and a > 0
The solution is: 1 / 10
O is a point in the triangle ABC. It is proved that ab + AC + BC is greater than OA + ob + OC
It is proved that there is ob in △ OBD and △ ACD
Prove lim2 ^ n / N! = 0 with pinch theorem
The following is a general case, and it can be proved by another a = 2 that there exists n ＞ 2 | a | a | n / N! = m * [| a | / (n + 1)] * [| a | / (n + 2)] * *[|a|/(n)]＜M*(1/2)*(1/2)*…… *(1 / 2) = m / 2 ^ (N-N), when n ＞ n, 0 ＜ a | n / N
Given that the complex Z satisfies Z * z-3i * z = 1 + 3I, find Z
z*z-3i*z=1+3i
Simplification
(z+1)(z-1-3i) = 0
So z = - 1 or Z = 1 + 3I
The complex Z satisfies Z + Z If 4 is a real number and | Z-2 | = 2, then Z=______ .
Let z = a + bi (a, B ∈ R),
By Z + Z
4 is a real number and | Z-2 | = 2
Five
4b＝0
(a − 2) 2 + B2 = 2
a＝4
B = 0 or
a＝0
b＝0 ．
ν z = 4 or 0
So the answer is: 4 or 0
Calculation formula for converting liter into ton Five liters of gas oil is about 9.2 Jin So, how many liters of gas oil is one ton of gas oil? The price of a ton of oil is 6350 yuan. How much is a liter of gas oil? It's better to write down the working style, too
Let the density be r g / L
Then:
5 L * r g / L = 9.2 Jin = 4600 G
=>R = 920 g / L = 0.92kg/l
Then 1000 kg / (0.92 kg / L) = 1086.96 L
=>6350 yuan / 1086.96 liter = 5.84 yuan / liter
Hard work,
How to convert the kilogram of knitted fabric into yards? What is the most convenient formula? For example: 848.1kg should be how much, used to 848.1 divided by 205.226 = the actual number of yards, it seems that it is not accurate
848 total kg / 1.7
Width / 0.17 g weight / 0.9144 = actual code number
You have to unify the units into meters and kg
Weight = gram weight x length x amplitude
Calculate the length, then meter and inter code conversion
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- 16. As shown in the figure, given that D is a point on the extension line of edge BC of △ ABC, DF ⊥ AB is at point F, intersects AC at point E, ∠ a = 40 ° and ∠ d = 30 °, then the degree of ∠ ACB is obtained______ Degree
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- 20. It is known that AB and CD are the two diameters of ⊙ o, and the chord CE ∥ ab. it is proved that ad = AE