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Given that the function f (x) = loga (AX ^ 2-x + 1 / 2) (a > 0 and a ≠ 1) is always positive on [1,3], the value range of real number a is obtained Given that the function f (x) = loga (AX ^ 2-x + 1 / 2) (a > 0 and a ≠ 1) is always positive on [1,3], find the value range of the real number A. (a is the base number, the one with brackets is the real number)
(1) If O1 / (2x ^ 2) + 1 / x = (1 / 2) (1 / x + 1) ^ 2-1 / 2. (1 / 2) (1 / x + 1) ^ 2-1 / 2, the maximum value in [1.3] is 3 / 2. Therefore, a > 3 / 2
Let g (x) = ax & # 178; - x + 1 / 2,
When 0
What is the sine of 0.404
sina=0.404
a=arcsin0.404=23.83°
In the known sequence {an}, the N-1 power satisfying A1 = 1, an = 2A (n-1) + 2, let BN = the N-1 power of an / 2,
(1) It is proved that the sequence {BN} is an arithmetic sequence
(2) The general term formula of the sequence {an}
The answer you want is: BN = an / 2 ^ (n-1) get an = BN * 2 ^ (n-1) a (n-1) = B (n-1) * 2 ^ (n-2) by an = 2A (n-1) + 2 ^ (n-1), get BN * 2 ^ (n-1) = 2 * B (n-1) * 2 ^ (n-2) + 2 ^ (n-1) by dividing by 2 ^ (n-1): BN = B (n-1) + 1B1 = A1 / 2 ^ (1-1) = A1 = 1, then {BN} is an arithmetic sequence with the first term of 1 and the tolerance of 1
Given that the average of x1, X2 and X3 is 10 and the variance is 3, what is the variance of 2x1, 2x2 and 2x3?
The average difference of 2x1, 2x2 and 2x3 is 20s1 = 1 / 3 {(x1-10) ~ 2 + (x2-10) ~ 2 + (x3-10) ~ 2} = 3s2 = 1 / 3 {(2x1-20) ~ 2 + (2x2-20) ~ 2 + (2x3-20) ~ 2} = 4 * 1 / 3 {x1-10) ~ 2 + (x2-10) ~ 2 + (x3-10) ~ 2} = 4 * S1 = 12
It's three
Given the function f (x) = ln (AX + 1) + the cube of X - the square of X - ax (1), if x = the extreme point of 2 / 3, find the value of real number a
According to the meaning of the title f '(2 / 3) = 0, the derivation f' (x) = A / (AX + 1) + 3x ^ 2-2x-a is obtained by substituting the above conditions into a = 0
What is the angle with sine value of 0.7692307692307693
28486277 degrees
Scientific calculator
Given that the sequence {an}, {BN} is an arithmetic sequence, and A1 = 5, B1 = 15, A100 + B100 = 100, the sequence {CN} satisfies CN = an + BN (n ∈ n *), then the sum of the first 100 terms of the sequence {CN} is______ .
Because the sequence {an}, {BN} is an arithmetic sequence, and A1 = 5, B1 = 15, A100 + B100 = 100, the sequence {CN} satisfies CN = an + BN (n ∈ n *), then the sum of the first 100 items of the sequence {CN} is: 100 (a1 + A100 + B1 + B100) & nbsp; & nbsp; 2 = 100 × 1202 = 6000
Given that the standard deviation of x1, X2, X3 is 3, then the variance of data 2x1 + 3, 2x2 + 3, 2x3 + 3 is
Secondary school practice:
If the standard deviation (s) of x1, X2 and X3 is 3 and the mathematical language is x '= (x1 + x2 + x3) / 3, then
S1 = root {1 / 3 * [(x1-x ') ^ 2 + (x1-x') ^ 2 + (x1-x ') ^ 2]} = 3
x"=[(2x1+3)+(2x2+3)+(2x3+3)]/3=2x'+3
S2 = root {1 / 3 * [(2x1 + 3-x ") ^ 2 + (2x2 + 3-x") ^ 2 + (2x3 + 3-x ") ^ 2]} = 2 * S1 = 6 (simplify the process and calculate by yourself)
University practice:
Let x1, X2 and X3 be random variables X, and the standard deviation (s) of x1, X2 and X3 is 3. The variance D (x) = s ^ 2 = 3 ^ 2 = 9 of random variable x is obtained;
Let 2x1 + 3,2x2 + 3,2x3 + 3 be random variable y, then y = 2x + 3, then d (y) = D (2x + 3) = 2 ^ 2D (x) + D (3) = 4 * 9 + 0 = 36
So the standard deviation is s' = root sign D (y) = 6
(1) Given that the definition domain of function y = ln (- x2 + x-a) is (- 2,3), the value range of real number a can be obtained; (2) given that function y = ln (- x2 + x-a) is meaningful in (- 2,3), the value range of real number a can be obtained
(1) The solution set of - x2 + x-a ＞ 0 is (- 2,3), i.e. - 2,3 are the two roots of the equation - x2 + x-a = 0, so there is - 2 × 3 = a, i.e. a = - 6; If △ = 1 − 4A ＞ 0f (− 2) ≥ 0f (3) ≥ 0, that is, a ＜ 14a ≤− 6a ≤− 6, the solution is a ≤ - 6, so the value range of real number a is (- ∞, - 6]
Given that the angle a is an acute angle, (sine a + cosine a) divided by (sine a - cosine a) = 2
Divide by cosa at the same time
We get (1 + Tana) / (tana-1) = 2
The solution is Tana = 3
Angle a is not a special angle
a= arctan3
RELATED INFORMATIONS
- 1. In the arithmetic sequence an and BN, a1 + B100 = 100, B1 + A100 = 100, then the sum of the first 100 terms of the sequence [an + BN] is
- 2. Let f (x) = LG1 + 2x + 4xa3, if f (x) is meaningful when x ∈ (- ∞, 1], find the value range of real number a
- 3. In {an}, the first n terms of A1 = 2 and Sn satisfy Sn + 1 + sn-1 = 2Sn + 1 (1) to find the general term formula of sequence an (2) the n power of BN = 4 + the N-1 power of negative 1 multiplied by the an power of 2
- 4. If the function y = ax ex has an extreme point less than zero, then the value range of real number a is () A. （0，+∞）B. （0，1）C. （-∞，1）D. （-1，1）
- 5. If S3 + S6 = 2s9, then the common ratio of the sequence is______ .
- 6. If loga ^ 2 (3-ax) (a is not equal to 0 and a is not equal to plus or minus 1) is a decreasing function on [0,2], then the range of a
- 7. Let the sum of the first n terms of the arithmetic sequence {an} be Sn, and the sum of the first n terms of the arithmetic sequence {BN} with positive common ratio be TN. let A1 = 1, B1 = 3, A2 + B2 = 8, t3-s3 = 15. (1) find the general formula of {an}, {BN}. (2) if the sequence {CN} satisfies a1c1 + a2c2 + +An-1cn-1 + ancn = n (n + 1) (n + 2) + 1 (n ∈ n *), find the first n terms and wn of sequence {CN}
- 8. As shown in the figure, △ ABC, ab = AC, ad ⊥ BC intersection D point, e and F are the midpoint of DB and DC respectively, then the logarithm of congruent triangle in the figure is () A. 1B. 2C. 3D. 4
- 9. In the equal ratio sequence {an}, A1 = 512, common ratio q = negative half, and TN is used to express the product of the first n terms; In the equal ratio sequence {an}, A1 = 512, common ratio q = negative half, and TN is used to represent the product of his first n terms; TN = A1A2... An, then the largest of T1, T2,... TN is:
- 10. If the area of △ ABC is known as s, and the vector ab ● vector BC = 1, if s = 3 / 4 | vector ab |, find the minimum value of | vector AC |
- 11. It is known that the sum of the first n terms of the sequence {an} is Sn = N2 (n ∈ n *), the sequence {BN} is an equal ratio sequence, and satisfies B1 = A1, 2b3 = B4 (1) the general term formula of the sequence {an}, {BN}; (2) the sum of the first n terms of the sequence {anbn}
- 12. Given the locus of a point whose distance ratio between a curve and two points (0,0), (3,0) is 1 / 2, find the curve equation o
- 13. Sequence an, A1 = 4, Sn + s (n + 1) = 5 / 3an + 1, an Sequence an, A1 = 4, Sn + s (n + 1) = 5 (a (n + 1)) / 3, find an
- 14. Given the ellipse X / 4 + y = 1, a straight line at point a (- 3,0 under the root sign) crosses the ellipse at the origin and BC, the maximum area of triangle ABC is obtained
- 15. The known sequence {an} and {BN} satisfy: A1 = λ, an + 1 = 2 / 3an + n-4, BN = (- 1) ^ n (an-3n + 21), where λ is a real number and N is a positive integer 1. Prove that the sequence {an} is not equal ratio sequence for any real number λ 2. Prove that when λ≠ - 18, the sequence {BN} is an equal ratio sequence The first question has already been made, mainly the second one, which requires a specific process
- 16. If the ellipse MX ^ 2 + my ^ 2 and the line x + Y-1 = 0 are compared with two points a and B, and the slope k of the line passing through the origin and the midpoint of the line AB is two-thirds root sign, then n / M =? Detailed process The answer is root 2 / 2
- 17. Let {an} satisfy a1 + 3a2 + 3 ^ 2A3 +. 3 ^ n-1 × an = n / 3, a ∈ n + (1) Find the general term of the sequence {an}; (2) Let BN = n / an, find the first n terms and Sn of the sequence {BN} At home on weekends
- 18. If the complex Z satisfies that the modulus of Z is equal to 1, then Z
- 19. If A1 = 1 and q = 2, then A1 ^ 2 + A2 ^ 2 + a3 ^ 2 +. + an ^ 2
- 20. If the square of 3x - 2x + b-x-bx + 1 contains NO x term, B =?