Let the perimeter of a rectangle be 80, and the length of one side is X. find the analytic function of its area y with respect to x, and write out the domain of definition

Let the perimeter of a rectangle be 80, and the length of one side is X. find the analytic function of its area y with respect to x, and write out the domain of definition

y=x*(80-2x)/2=x*(40-x)(0
If one side is x, the other side is 40-x
Y
=x（40-x）
=-x²+40x
Domain (0)
(college entrance examination) high school mathematics: how to prove that it is an arithmetic sequence by the sum formula of arithmetic sequence! It is Sn = n (a1 + an) / 2, the question of today's exam
(college entrance examination) high school mathematics: how to prove that it is an arithmetic sequence by the sum formula of arithmetic sequence! It's Sn = n (a1 + an) / 2, the question of today's exam! I can't do it for a long time!
an=Sn-Sn-1=n(a1+an)/2-(n-1)(a1+an-1)/2
2an=a1+an+(n-1)(an-an-1)
an=a1+(n-1)(an-an-1)
an+1=a1+(n)(an+1-an)
Subtraction of two formulas
an+1-an=n(an+1-an)-(n-1)(an-an-1)
an=(an+1+an-1)/2
So it's an arithmetic sequence
A motor is a machine that converts electrical energy into mechanical energy. However, due to the resistance inside the coil, part of the electrical energy is also converted into internal energy
The motor is connected to both ends of the 6-volt power supply. When the motor is running normally, the current passing through the motor is 0.3 A. if the main motor shaft is stuck temporarily, the current passing through the motor is 3 A. then the resistance of the motor coil is? The efficiency of normal rotation? Detailed process is required
When it does not rotate, Ohm's law can be used. The resistance of motor coil r = u / I = 6 / 3 = 2 Ω
Under normal rotation, the input power P = UI = 6 * 0.3 = 1.8W. The electric heating power p '= I ^ 2 * r = 0.3 ^ 2 * 2 = 0.18w
Efficiency is equal to (1.8-0.18) / 1.8 = 90%
It is known that the perimeter of a rectangle is 20cm. Let one side of the rectangle be x and the area be y, then the functional relationship between Y and X is______ (and write the value range of x)
∵ the perimeter of the rectangle is 20cm, one side of the rectangle is x, the other side is (10-x) cm, y = x (10-x), (0 < x < 10), so the answer is: y = x (10-x)
How to get the formula Sn = Na1 + n (n-1) d / 2 of the sum of the first n terms of the arithmetic sequence?
First of all, the arithmetic sequence has the following properties:
a1 + an = a2 + a(n-1).
Because: an = AK + (n-k) d, K is less than n
an - ak = (n-k)d
That is to say, in the arithmetic sequence, when (n-k) is fixed, the difference of any two terms is equal
So we can prove that a1 + an = A2 + a (n-1)
his
Small motor coil resistance 5 ohm, 12 V power supply, current 1.6 A, 3 minutes can produce how much heat, into mechanical energy, part of the total electrical energy is a few percent
Thermal power P = I ^ 2 * r = 1.6 * 1.6 * 5 = 12.8w,
The heat generated in 3 minutes is q = P * t = 12.8w * 180s = 2304j;
And the total electric power = u * I = 12V * 1.6A = 19.2w,
Total electric energy in 3 minutes = 19.2 * 180s = 3456j,
It is the difference between the above two that transforms mechanical energy
3456J-2304J=1152J,
Its proportion in total electric energy is 1152j / 3456j = 1 / 3
Let the perimeter of a rectangle be 80, and the length of one side be X. find the function explanation of the area s with respect to x, and write out the definition field to find the maximum value of S
s=X*(80/2-X)
=X^2-40X
(0
Sum formula of arithmetic sequence Sn = n (a1 + an) / 2 or Sn = A1 * n + n (n-1) d / 2 note: an = a1 + (n-1) d an = am + (n-m) * D (m less than n) turn
General term formula:
An=A1+(n-1)d
An=Am+(n-m)d
The sum of the first n terms of the arithmetic sequence:
Sn=[n(A1+An)]/2
Sn=nA1+[n(n-1)d]/2
Sum formula of arithmetic sequence: sum of arithmetic sequence = (first number + last number) * number of items / 2;
The formula of the number of items: the number of items of arithmetic sequence = [(mantissa - first number) / tolerance] + 1
The electromotive force E of the power supply is 110V, the resistance R1 is 20 Ω, the resistance R0 of the motor winding is 0.5 Ω, the key S1 is always closed, when the key S2 is disconnected, the resistance R1 is closed
The electric power is 500W; when S2 is closed, the electric power of R1 is 320W
(1) Internal resistance of power supply;
(2) When the key S2 is closed, the current flowing through the power supply and the output power of the engine
From the point of view, R1 is parallel with motor, S2 only controls motor
(1) The internal resistance of the power supply is set to R
When S2 is disconnected, the electric power of resistor R1 is 500W
I & # 178; = P1 / R1 = 500 / 20 = 25, so I = 5A
U=IR1=5*20=100V
Uine = E-U = 110-100 = 10V
R = u / I = 10 / 5 = 2 Ω
(2) When S2 is closed, the motor is in parallel with R1
U & # 178; = p1r1 = 320 * 20 = 6400, so u = 80V
Uine = E-U = 110-80 = 30V
I total = I internal = u internal / r = 30 / 2 = 15A. The current flowing through the power supply
I1=U/R1=80/20=4A
I machine = I total - I1 = 15-4 = 11A
P machine = UI machine = 80 * 11 = 880W
P machine heat = I machine & 178; R0 = 121 * 0.5 = 60.5w
P machine output = P machine - P heat = 880-60.5 = 819.5w
Do you have a circuit diagram? Question: Yes
Prove the triangle area formula: S = √ (P (P-A) (P-B) (P-C)) where p = (a + B + C) / 2, which is proved by sine theorem, cosine theorem and geometric method respectively