The sum of 5 times of a certain number and 2 / 3 of a certain number is equal to 17

Let a number be X
According to the meaning of the title: 5x + 2x / 3 = 17,
Both sides * 3,15x + 2x = 17 * 3
17X=51
X=3

Given sin α = 2Sin β, Tan α = 3tan β, find the value of COS 2 α

∵ given sin α = 2Sin β, ∵ sin β = 12sin α & nbsp; ①. ∵ Tan α = 3tan β, ∵ sin α cos α = 3sin β cos β, we can get cos β = 32cos α & nbsp; ②, or sin α = 0 ③. If ② is true, then by adding the squares of ① and ②, we can get & nbsp; 1 = 14sin α 2 + 94cos 2 α = 14 + 2cos 2 α, and the solution is cos 2 α = 38. If ③ is true, there is cos 2 α = 1. In conclusion, cos 2 α = 38, or cos 2 α = 1

The points P (a, - 2), q (2, b), PQ are parallel to the x-axis. Find the values of a and B

PQ is parallel to the X axis, so y is constant, so B = - 2, a is any real number

Given that the minimum positive period of the function f (x) = sin (Wx + π / 6) is π / 2, where w > 0, find f (0). W

W = 2 π / T = 4 (t is the minimum positive period)
So f (0) = 1 / 2

If the intercept of the line passing through point P (1,4) on two coordinate axes is positive and the sum of the intercepts is the smallest, then the equation of the line is____

Let intercept be a and B, then x / A + Y / b = 1 through P1 / A + 4 / b = 1A + B = (a + b) (1 / A + 4 / b) = 1 + 4A / B + B / A + 4A > 0, b > 0, so 4A / B + B / a > = 2 √ (4a / b * B / a) = 4, when 4A / b = B / A, take the equal sign B & sup2; = 4A & sup2; so B = 2A substitute 1 / A + 4 / b = 11 / A + 2 / a = 1A = 3, B = 6, so it is 2x + y-6 = 0

The simple method of 112 + 58 + 58 + 112

112+58+58+112
=112×2+58×2
=(112+58)×2
=170×2
=340

Let the moving line l be tangent to the circle C: x ^ 2 + y ^ 2-2x-2y = 1 = 0, and intersect with the positive half axis of X and Y axes at two points a and B, and the tangent is above the circle C. find the trajectory equation of the midpoint m of the line AB and the minimum area of the triangle AOB

(1) X ^ 2 + y ^ 2-2x-2y = 1 = 0 (x-1) ^ 2 + (Y-1) ^ 2 = 0, center of circle C (1,1) r = 1, let the equation of line l be x / A + Y / b = 1, that is, BX + ay AB = 0, the distance between center of circle C and line l d = | B + a-Ab | / √ (a ^ 2 + B ^ 2) = r = 1, then (2x-2) (2y-2) = 2 (x-1) (b-2) = 2

The sum of the first n terms of the arithmetic sequence {an} is SN. It is known that for any n ∈ n *, the point (n, Sn) is on the graph of quadratic function f (x) = x2 + C, then C= ，an= ．

∵ point (n, Sn) on the image of quadratic function f (x) = x2 + C ∵ Sn = N2 + C ∵ when n = 1, A1 = 1 + C; when n ≥ 2, an = sn-sn-1 = 2N-1 ∵ arithmetic sequence {an} 1 + C = 1 ∵ C = 0, so the answer is 0; 2N-1

At point P in an electric field, put a test charge with charge quantity Q1 = - 3.0x10 to the negative 10th power C, and calculate the
At point P in an electric field, put a test charge with charge quantity Q1 = - 3.0 x 10 to the negative 10th power c. the electric field force on the negative charge is measured as F1 = 6.0 x 10 to the negative 7th power n. the direction is horizontal to the right and the direction is calculated
(1) The magnitude and direction of the electric field at P point
(2) Put a test charge at point P with the charge quantity of Q2 = 1.0x10 minus 10 power C, and calculate the magnitude and direction of the electric field force F2 on Q2

1. Because the negative charge is forced in the same direction as the field strength, the direction is left
(take positive) e = f / Q = 2.0x10 to the third power
The field strength is constant
The direction of F = EQ = 2.0x10 to the negative 7th power is horizontally right

Given the proposition p: "for any x ∈ [1,2], x2-a ≥ 0", proposition q: "there exists x ∈ R, X2 + 2aX + 2-A = 0". If the proposition "P and Q" is true, the value range of real number a is obtained

For any x ∈ [1,2], x2-a ≥ 0. Then a ≤ X2, ∵ 1 ≤ x2 ≤ 4, ∵ a ≤ 1, i.e. when the problem P is true: a ≤ 1. If there is x ∈ R, X2 + 2aX + 2-A = 0, then △ = 4a2-4 (2-A) ≥ 0, i.e. A2 + A-2 ≥ 0, the solution is a ≥ 1 or a ≤ - 2, i.e. when the proposition q is true: a ≥ 1 or a ≤ - 2

The sum of 5 times of a certain number and 2 / 3 of a certain number is equal to 17