f(x)=log2(x/8)*log2(2/x)

f(x)=log2(x/8)*log2(2/x)

f(x)=log2(x/8)*log2(2/x)
=(log2(x)-3)(1-log2(x))

A rectangle whose length is 1cm more than width is equal to the perimeter of a square whose side length is ACM, then the length of the rectangle is () we are a mathematical problem

The second answer: a + 0.5 reason: the circumference is 4a, so the sum of length and width is 2A. If the length is x, then X-1 can be obtained
+X = 2A, the solution is available, I wish you happiness and progress!

Several calculation problems of physical series circuit
A 8-ohm resistor and a 10 ohm small lamp are connected in series in the circuit. After the key is closed, the current through the resistor is 0.3 A. calculate: (1) current through the small lamp (2) power supply voltage (3) voltage at both ends of the resistor (4) voltage at both ends of the small lamp
Two resistors R1 and R2 are connected in series in the circuit. It is known that the resistance of R1 is 6 ohm, the voltage at both ends of R1 is 2 V, and the voltage at both ends of R2 is 3 V. calculate: (1) power supply voltage (2) current through R1 (3) resistance of R2 (4) total resistance of the circuit
The resistance values of R1 and R2 are 5 ohm and 10 ohm respectively. If the voltage at both ends of R1 is 2 V, calculate: (1) the voltage at both ends of R2 and (2) the total voltage in the circuit
If a consumer with a resistance value of 10 Ω is connected to the power supply, the current passing through it is 0.4 A. to reduce the current passing through the consumer to 0.1 A, how large a resistor needs to be connected in series?
Two resistors R1 and R2 are connected in series in the circuit. The power supply voltage is 6V. R1: R2 = 1:2. Find the voltage at both ends of R1 and R2,
The above five questions are not clear after class. Every question will be stuck if you write a little. I hope you can give me a simple explanation when solving the questions. In addition, please pay attention to the format of calculation. Please answer the questions completely. Thank you!

Series circuit: R1 = 8 Ω, R2 = 10 Ω, I = 0.3A;
(1) The current in the series circuit is equal & nbsp; so the bulb current = 0.3A
(2) U = I * r & nbsp; r = R1 + R2 = 18 Ω & nbsp; & nbsp; u = 18 Ω * 0.3A = 5.4v
(3) U1 = R1 * I = 8 Ω * 0.3A = 2.4V
(4) U2 = R2 * I = 10 Ω * 0.3A = 3V
(1)U=U1+U2=5V
(2)I=U1/R1=0.33A
(3) R2 = r-r1 & nbsp; r = u / I = 15 euro & nbsp; R2 = 9 Euro
(4) R = 15 Ω
Voltage division of series circuit & nbsp;
(1) U1: U2 = R1: R2 = 1:2 & nbsp; because U1 = 2V & nbsp; & nbsp; so U2 = 4V
(2)U=U1+U2=6V
U = I1 * R1 = 4V & nbsp; & nbsp; & nbsp; r = (R1 + R2) = u / I2 = 4V / 0.1A = 40 Euro & nbsp; & nbsp; R2 = 40 Euro - 10 euro = 30 euro
U1=2V  U2=4V

For example, a is a set, how to represent the number of elements in a

Use Carda or | a | to indicate the number of elements in a

In trapezoidal ABCD, ab ∥ DC, ab = BC, ab = 20cm, DC = 4cm, AE ⊥ BC is equal to e, CE = 4cm?

Obviously, AEB is a right triangle, ab = 20, be = bc-ce = 20-4 = 16,
SINB = AE / AB = 12 / 20 = 3 / 5, make CF perpendicular to AB and F. in the right triangle BFC, SINB = CF / BC, that is, 3 / 5 = CF / 20, we can get CF = 12, trapezoidal area = (4 + 20) * 12 / 2 = 144

It is proved that any matrix A of order n can be expressed as the sum of symmetric matrix and antisymmetric matrix

(1) after a and B begin to move, they meet in a few minutes. (2) if a and B turn back immediately after they reach each other's starting point, a will continue to walk 1m more than the previous one minute, and B will continue to walk 5m more than the previous one minute, How about the second meeting in a few minutes?
2. In the triangle ABC, the opposite sides of the angle A.B.C are a.b.c. the known vector M = (cos3a / 2, sin3a / 2) n = (COSA / 2, Sina / 2), and satisfy the following conditions
_
｜M+N｜= √3
(1) Find the size of angle A~
(2) If B + C = 3 times a under the root sign (a is outside the root sign), the shape of triangle ABC can be judged
3. It is known that each term of the sequence {an} is a positive number, and the sum of the first n terms is Sn = [(an + 1) / 2] & sup2;, let BN = 10-an (n ∈ n)
(1) Proving: the sequence {an} is an arithmetic sequence, and finding the general term formula of the sequence {an}
(2) Let the sum of the first n terms of the sequence {BN} be TN, and find the maximum of TN
(3) Finding the sum of the first n terms of the sequence {BN} (n ∈ n)~

1. (1) suppose that a and B meet each other in X minutes, and the distance a takes in every minute is arranged in an arithmetic sequence, then the total distance a takes in the X minute is (2 + X + 1) x / 2 = x (x + 3) / 2 m  5x + X (x + 3) / 2 = 7010 x + X & sup2; + 3 x = 140 X & sup2; + 13 x-140 = 0 (x + 20) (X-7) = 0 x =... (2 + X + 1) x / 2 = x (x + 3) / 2 = 0

How to find the definite integral from SiNx / X zero to positive infinity
make a concrete analysis

For SiNx Taylor expansion and then divided by X, we have:
sinx/x=1-x^2/3!+x^4/5!+… +(-1)^(m-1)x^(2m-2)/(2m-1)!+o(1)
Two sides of the integral are:
∫sinx/x·dx
=[x/1-x^3/3·3!+x^5/5·5!+… +(-1)^(m-1)x^(2m-1)/(2m-1)(2m-1)!+o(1)]
From zero to infinite definite integral
Then substitute 0, X (x → 00) (where x is a large constant, which can be arbitrarily taken) into the right side of the above formula and subtract it, and the result can be obtained by computer
The above is just personal opinion, and the following is the practice of experts:
(the master is extraordinary!)
Consider the generalized double integral
I=∫∫ e^(-xy) ·sinxdxdy
D
Where d = [0, + ∞) × [0, + ∞],
Now we integrate in two different orders
I=∫sinxdx ∫e^(-xy)dy
0 +∞ 0 +∞
= ∫sinx·(1/x)dx
0 +∞
On the other hand, the order of exchange integral is as follows:
I=∫∫ e^(-xy) ·sinxdxdy
D
=∫dy ∫e^(-xy)·sinxdx
0 +∞ 0 +∞
=∫dy/(1+y^2）=arc tan+∞-arc tan0
0 +∞
= π/2
So:
∫sinx·(1/x)dx=π/2
0 +∞

English translation
An exchange visit is educational and interesting!
A group of British students from Woodpark School in London are visiting Xinhua Junior High School in Beijing on an educational exchange.

Exchange visits are educational and interesting;
A group of British students from London wood garden are visiting Beijing Xinhua high school through an academic exchange

Given that M is a root of the equation x2-x-1 = 0, find the value of the algebraic formula 5m2-5m + 2004

5m2－5m＋2004
=5（m^2-m）+2004
=5+2004
=2009
Here m is a root of the equation x2-x-1 = 0
m^2-m-1=0
M ^ 2-m = 1