Given the function f (x) = SiNx + 5x, X ∈ (- 1,1), why is it odd

Given the function f (x) = SiNx + 5x, X ∈ (- 1,1), why is it odd

Let X be (- 1,1)
f(-X)=sin(-X)-5X
=-sinX-5X
f(X)=-f(-X)
So the original function is odd
Let x ∈ R, vector a = (1, x-1), B = (x + 1,3), if a / / B, then the real number x equals (), if a ⊥ B, then the real number x equals ()
When a / / B, x = ± 2,
When a ⊥ B, x = 1 / 2
The solution of (x-1) / 1 = 3 / (x + 1) is x = 2 or x = - 2
Perpendicularity means that vector multiplication = 0 leads to 3 (x-1) + (x + 1) = 0 and the solution x = 0.5
A mathematical problem about the root equation
The square of X + the square of 2 = (2x) is the result the same as this? (1 / 2x) the square of 2 + the square of x = the square of X
That is, X & # 178; + 4 = 4x & # 178;
x²=4/3
x=±2√3/3
The second one is different
Divide both sides by four
Divide by two and divide by four
Is (x / 2) &# 178; + 1 = x & # 178;
Open the parenthesis and move the term to get x = positive and negative root sign 2, which is not equal to the one on the right
It's not the same. The square of X + the square of 2 = (2x) the square of x = 4 * the square of x 3 times the square of x = 4. X is equal to four-thirds of the positive and negative root sign
The equivalent equation should be the square of (1 / 2x) + the square of 1 = the square of X
The first is: X & # 178; + 2 & # 178; = (2x) &# 178; the solution is: 3x & # 178; = 4x & # 178; = 4 / 3
The second: (1 / 2x) &# 178; + 2 & # 178; = x & # 178; the solution is: multiply both sides by 4x & # 178;, and become 1 + 16x & # 178; = 4x ^ 4
Obviously, the solution is different
The application of solving the equation of first degree with one variable
Some of the same rooms need painting. Master Sanming went to paint eight rooms a day. As a result, 40 square meters of walls had to be painted in the future. In the same time, five apprentices painted the walls of nine rooms. Each apprentice painted 30 square meters more than his apprentice in a day
Q: (1) the area of the wall to be painted in each room
(2) There are thirty-six rooms that need a master and two apprentices. How many days can they finish?
(3) The master's salary is 85, and the apprentice's salary is 65. How can it be cost-effective to hire eight people in three days?
(1) Set the painting area of each room as x square meters. (8x-40) / 3-30 = 9x / 55 (8x-40) - 450 = 27x40x-200-450 = 27x13x = 650x = 50, so the painting area of each room is 50 square meters. Master: (8x-40) / 3 = 120 square meters, apprentice: 120-30 = 90 square meters. (2) set y days to finish. (120 + 2x9
Suppose the area of each room is x and one apprentice brushes one day as y.
y+30=8x-40
5y=9x
The solution is x, y
The area of each room is a, the master completes X in one day, and the apprentice completes y in one day.
First question:
Formula 1: 8A = 3x + 40
Formula 2: 9A = 5Y = 5 (X-30): a = 50; X = 120; y = 90
Second question (it takes Z days)
1 * Z * 120 + 2 * Z * 90 = 36 * 50: z = 6.
The third question (employing m masters and N apprentices, with a salary of B)
Equation 1: m * 3 * 120 + n... expansion
The area of each room is a, the master completes X in one day, and the apprentice completes y in one day.
First question:
Formula 1: 8A = 3x + 40
Formula 2: 9A = 5Y = 5 (X-30): a = 50; X = 120; y = 90
Second question (it takes Z days)
1 * Z * 120 + 2 * Z * 90 = 36 * 50: z = 6.
The third question (employing m masters and N apprentices, with a salary of B)
Formula 1: m * 3 * 120 + n * 3 * 90 = 36 * 50 = 1800, namely: 4m + 3N = 20
N = (20-4m) / 3
We get the formula: n * 3 * 5 m + B = 1 300 * 3-5 M
From "B = 1300-5m", it can be seen that only when m is the largest, B is the smallest, so all the three masters are required. When n = (20-4m) / 3 is brought in, n = 8 / 3 is obtained, and N = 3 is rounded
Hire all three masters and three more apprentices. Put it away
2X & # 178; + 7x-3 = 0 (solved by formula method)
2x²+7x-3=0
x²+7/2x+(7/4)^2=3/2+(7/4)^2=73/16
(x+7/4)^2=73/16
x+7/4=±√73/4
x=-7/4±√73/4
Given the function f (x) = SiNx + 5x, X ∈ (- 1,1), if f (1-A) + F (1-a2) < 0, then the value range of a is______ .
Function f (x) = SiNx + 5x, X ∈ (- 1, 1), so the function is an increasing function, odd function, so f (1-A) + F (1-a2) < 0, we can get - 1 < 1-a2 < A-1 < 1, the solution is 1 < a < 2, so the answer is: 1 < a < 2
Given that vector a = (a = 3,1), vector b = (x, - 3), and vector a ⊥ vector B, then the value of real number x is
If a is perpendicular to B, then a * b = 0, that is, 3x-3 = 0, then x = 1
Note: let a = (x1, Y1), B = (X2, Y2), then a * b = x1x2 + y1y2
If X1 = 2-radical 3 is a root of the quadratic equation x & sup2; + ax + 1 = 0, try to find the value of the other root x2 and a of the equation
Are you sure you copied the title correctly? The amount of calculation is huge!
① Take x = 2 √ 3 into quadratic equation, and solve the value of a: (2 √ 3) ^ 2 + 2 √ 3A + 1 = 0 → a = - (13 √ 3) / 6
② Take a into the original equation, that is, x ^ 2 - (13 √ 3) / 6x + 1 = 0 → get X1 =, X2 = (too much calculation, you should be able to do it next, you can find x = (- B ± √ (b ^ 2-4ac)) / 2A according to the formula)
We can find the root sup + 2; + x 1; + A + 2, and then substitute sup + A + 2; = x 1
Solving linear equation with one variable
（30x-1）：24=（2x-1）：3
2x-1 out of 3 minus 2x-3 out of 4 = 1
（30x-1）：24=（2x-1）：3
3（30x-1）=24（2x-1）
90x-3=48x-24
42x=-21
x=-1/2
2x-1 out of 3 minus 2x-3 out of 4 = 1
4(2x-1)-3(2x-3)=12
8x-4-6x+9=12
2x=7
x=7/2
Factorization. X & # 178; - 9. M & # 179; - 4m. 5 (m-n) & # 178; - M (n-m) = (m-n)_____ . xy²－2xy＋x.
a³－ab². a﹙x－y﹚－b﹙y－x﹚＋c﹙x－y﹚. 2x²－18.
x²－9=(x+3)(X-3).
m³－4m=m(M+2)(M-2)
5﹙m－n﹚²－m﹙n－m﹚＝﹙m－n﹚(6M-N)
xy²－2xy＋x.=X(Y-1)²
a³－ab².= a(a+b)(a-b)
a﹙x－y﹚－b﹙y－x﹚＋c﹙x－y﹚.=(x-y)(a+b+c)
2x²－18.=2(x+3)(x-3)
Factorization.
x²－9.=(x+3)(x-3)
m³－4m. =m(m+2)(m-2)
5﹙m－n﹚²－m﹙n－m﹚＝﹙m－n﹚(6m-n)
XY & # 178; - 2XY + X. = x (Y & # 178; - 2Y + 1) = x (y + 1) (Y-1) a & # 179; - AB & # 178;. = a (A & # 178; - B & # 178;) = a (a + B) (a-b)... Expansion
Factorization.
x²－9.=(x+3)(x-3)
m³－4m. =m(m+2)(m-2)
5﹙m－n﹚²－m﹙n－m﹚＝﹙m－n﹚(6m-n)
XY & # 178; - 2XY + X. = x (Y & # 178; - 2Y + 1) = x (y + 1) (Y-1) a & # 179; - AB & # 178;. = a (A & # 178; - B & # 178;) = a (a + B) (a-b) a (X-Y) - B (Y-X) + C (X-Y) = (X-Y) (a + B + C). 2x & # 178; - 18. = 2 (X & # 178; - 9) = 2 (x + 3) (x-3) fold up