It's better to use arithmetic The speed ratio of a, B and C is 8:6:5. Now the three start from the same place in the same direction. A is 900 meters ahead of C, and how many meters ahead of C in 15 minutes?

It's better to use arithmetic The speed ratio of a, B and C is 8:6:5. Now the three start from the same place in the same direction. A is 900 meters ahead of C, and how many meters ahead of C in 15 minutes?

Arithmetic:
900 ÷ (8 × 10-5 × 10) × 15 = 450 (m)
Equation method
If the velocity of a is 8 x, then the velocity of B and C is 6 x and 5 x respectively
(8x-5x) × 10 = 900, the solution is x = 30
(6 × 30-5 × 30) × 15 = 450 (m)
A: B is 450 meters ahead of C

Parallelogram area formula, on the diagonal, to derive the process

The two sides of the quadrilateral are the angle α between a and B
S=(1/2absinα)*2=absinα
Diagonal C1, C2
a^2+b^2-2abcosα=c1^2
a^2+b^2-2abcos(180-α)=c2^2
a^2+b^2+2abcosα=c2^2
c2^2-c1^2=4abcosα
(c2^2-c1^2)/4=abcosα
(abcosα)^2+(absinα)^2=(ab)^2
((c2^2-c1^2)/4)^2+s^2=(ab)^2
s^2=(ab)^2-((c2^2-c1^2)/4)^2

1. In a granary, 33 tons of grain less than 2 / 5 of the total grain was transported away on the first day, and 143 tons were transported in the next day. At this time, the granary increased by 15% compared with the original. How many tons of grain were stored in the granary?
2. Xiao Li read a novel. She read 4 / 7 of the whole book on the first day and 3 / 5 of the rest on the second day. There are still 6 pages left to read. How many pages are there in this book?

1. In a granary, 33 tons less than 2 / 5 of the total amount of grain were transported away on the first day, and 143 tons were transported in the next day. At this time, the granary increased by 15%. How many tons of grain were stored in the granary? X tons of grain were stored in the granary X - (2 / 5x-33) + 143 = (1 + 15%) x1.15x-x + 0.4x = 143 + 330.55x = 176x = 3202

Prove that a ^ m × a ^ n = a ^ (M + n)

In junior high school, we can use the meaning of power to prove, which is only limited to the case that m and N are rational numbers. When m and N are irrational numbers, we should use the knowledge of higher numbers. Please refer to the relevant chapters of "mathematical analysis" of China Normal University

Finding the n-th derivative of y = x & # cos x

Y '= 2xcosx-x & # 178; sinxy' '= 2cosx-4xsinx-x & # 178; cosxy ^ (n) n ≥ 3 = x & # 178; [cosx] ^ (n) + 2XC (n, 1) [cosx] ^ (n-1) + 2C (n, 2) [cosx] ^ (n-2) = x & # 178; cos (x + n π / 2) + 2nxcos [x + (n-1) π / 2] + n (n-1) cos [x + (n-2) π / 2] (Leibniz formula)

The set a = {x | x = 2 ^ n, n ∈ n} is closed to () operations. A, addition; B, subtraction; C, multiplication; D, | X-Y |

2^m*2^n
=2^(m+n)∈A
Choose C

What is the derivative of SiNx? What is the derivative of cosx? What is the derivative of TaNx? What is the derivative of TaNx?

Because SiNx '= cosx, cosx' = - SiNx
tanx'=(sinx/cosx)'=(sinx'cosx-cosx'sinx)/(cosx)^2
=[(cosx)^2+(sinx)^2]/(cosx)^2
=1/（cosx）^2
therefore
-sinx'=-cosx
-cosx'=sinx
tanx'=1/（cosx）^2
-tanx'=-1/（cosx）^2

The fifth grade of Primary School of Jiangsu Education Press

2.5×2= 0.5×10= 0.6×8= 2.1×2=2.8×10= 0.7×0.8= 0.04×20= 5.6+0.4=4.7+2.3= 4.5×2= 6.9－2.5= 7.2×0.8= 6×3.4= 0.62－0.32= 1.4×0.5= 0.75×100=0.02×0.5= 3.6×0.3= 6.3÷7= 5.6×100=0.75÷0.25= 0.12...

In the system of equations 2x + y = 1 − MX + 2Y = 2 about X and y, if x and y satisfy x + Y > 0, then the value range of M is ()
A. m＜3B. m＞3C. m≥3D. m≤3

2X + y = 1 − m, ① x + 2Y = 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ②, ① + ② get: 3 (x + y) = 3-m, that is, x + y = 3 − m3, substituting x + Y > 0 to get: 3 − m3 > 0, the solution is: m < 3

Fill the nine numbers 1 ~ 9 in brackets to make the equation hold. Each number can only be used once in an equation
1.（ ）÷（ ）=（ ）÷（ ）=（ ）÷（ ）
2.（ ）×（ ）=（ ）×（ ）=（ ）

The second one is impossible. I filled in two numbers
1.（8）÷（4）=（6）÷（3）=（2）÷（1）
2.（2）×（9 ）=（3 ）×（ 6）=（18 ）