The length of an equilateral triangle is four. If the length of an equilateral triangle is increased by X, the area will be increased by Y. find the functional relation of Y with respect to X

The length of an equilateral triangle is four. If the length of an equilateral triangle is increased by X, the area will be increased by Y. find the functional relation of Y with respect to X

Help to solve a proof problem with mathematical induction (to prove the formula of the sum of the first n terms in the sequence of equal difference and equal ratio)
Using mathematical induction to prove Sn = Na1 + (1 / 2) n (n-1) D and Sn = [A1 (1-Q to the nth power)] divided by (1-Q)
The formula of arithmetic sequence proves that:
(1) N = 1, S1 = A1
(2) Let SK = KA1 + (1 / 2) K (k-1) d, then SK + 1 = SK + AK + 1 = KA1 + (1 / 2) K (k-1) d + A1 + KD
=(K + 1) a1 + (1 / 2) (K + 1) KD, so n = K + 1 also holds
Equal ratio sequence
(1) N = 1, S1 = A1
(2)Sk+1=Sk+ak+1=a1(1-q^k)/(1-q)+a1q^k
=[a1/(1-q)][1-q^k+q^k-q^(k+1)]
=a1[1-q^(k+1)]/(1-q)
So the formula still holds when n = K + 1
To sum up, both formulas hold
Why is electric work equal to voltage times current times time? Please don't tell me that it is derived from the formula P = UI. I'm not an idiot. What I want to ask is the principle, its essence
When we talk about the electric field in senior high school, we should first know that w = FD, which is well known. The force is multiplied by the distance of action. Definition ah. Look at electricity, it is actually the electron from one section to another, such as resistance. When it is balanced, the electron is forced by the electric field, but the current is constant. That is, the electron does not accelerate
The length of an equilateral triangle is 4. If the length of an equilateral triangle increases by X, then the area is y. find the functional relation of Y with respect to X. who can help,
Y=(√3/4)x²+ =(√3/2)x+4√3
According to Helen's formula s = [P (P-A) * (P-B) * (P-C)] ^ 1 / 2
So y = [P (P-A) (P-B) (P-C)] ^ 1 / 2
Side length a = b = C = 4 + X half of perimeter P = (4 + x) * 3 / 2
So y = √ 3 (4 + x) ^ 2 / 4
You can bring in specific numerical verification, for example, when x = 2, y = 9 √ 3
How to prove the arithmetic sequence and the arithmetic sequence and how to find the method
Usually by definition
Arithmetic sequence: prove that an-an-1 is a fixed value, then it is arithmetic sequence
Equal ratio sequence: prove that an / an-1 is a fixed value, then it is equal ratio sequence
Or use the middle term method
Arithmetic sequence: proving an + 1 + an-1 = 2An
Equal ratio sequence: proving an + 1 * an-1 = an square
Formulas for calculating voltage, current, electric heating and resistance
Anyway, it's a series of electrical calculation formulas. I want to calculate formulas
Electrical formula and basic law
1、 Features of series connection and parallel connection (two circuits)
1. Series connection: ① the current is equal everywhere. I = I 1 = I 2
② The voltage is equal to the sum of the voltages of all electrical appliances. U = U1 + U2
③ The total resistance in a series circuit is equal to the sum of the resistances of the consumers
R total = R1 + R2
④ Voltage distribution law:
⑤ Electric power (electric power) distribution law:
2. Parallel connection: ① the voltage of parallel circuit is equal. U = U1 = U2
② The main current of parallel circuit is equal to the sum of branch currents. I = I 1 + I 2
③ The reciprocal of the total resistance in a parallel circuit is equal to the sum of the reciprocal of the resistances
④ The current distribution law is as follows
⑤ Electric power (electric power) distribution law:
2、 Two laws:
1. Ohm's Law: I = two deformation formulas: (principle of resistance measurement)
*Definition of current intensity: I = (Q: electric quantity)
2. Joule's Law: q = I2 RT (Q: heat)
3、 Electric power, electric power:
1. Electric power: 2. Electric power
Note: where R is included in the formula, it is only applicable to pure resistance circuit. Joule's law q = i2rt can only be used for heat of non pure resistance circuit
Voltage symbol u in volt V U = IR
Current symbol I unit ampere a i = u / R
Resistance symbol r in ohm r = u / I
The above three are Ohm's law
Electrothermal q = I ^ 2rt = IUT = Pt
The formula of electric heating seems to be the same as that of electric work, but only pure resistance circuit is involved here. The above Ohm's law is also used in pure resistance circuit.
If the side length of an equilateral triangle is x, then the functional relationship between its area and X is
It is proved by mathematical induction that the same term formula of equal ratio sequence is n-1 power of an = A1 * Q
First, a (n + 1) = an * q for the equal ratio sequence, which is useful in the fourth line
When n = 1, A1 = A1 * q ^ (1-1) = A1, indicating that the formula holds when n = 1
Suppose the formula holds when n = k, that is AK = A1 * q ^ (k-1)
Then n = K + 1, a (K + 1) = AK * q = A1 * q ^ (k-1) * q = A1 * q ^ K
Then the formula is proved
Because A1 is true to the formula, the conclusion is drawn from the fourth line, A2 is also OK, and then A3 is drawn from A2
Seeking: the formula of current, voltage, resistance and power
In addition to the basic formula, there are several extended formulas. I hope the extended formula can indicate which two original formulas are pushed out
I=U/R；P=UI=I2R=U2/R=W/t；W=UIt=I2Rt=U2t/R=Pt；Q=I2Rt
In the series circuit: I = I1 = I2; u = U1 + U2; r = R1 + R2; P = P1 + P2; w = W1 + W2; q = Q1 + Q2; U1 ∶ U2 = P1 ∶ P2 = W1 ∶ W2 = Q1 ∶ Q2 = R1 ∶ R2; in the series circuit, the more resistance in series, the greater the total resistance; when two lamps are in series in the circuit, the lamp with larger resistance is brighter
In parallel circuit: I = I1 + I2; u = U1 = U2; 1 / r = 1 / R1 + 1 / r2; P = P1 + P2; w = W1 + W2; q = Q1 + Q2; U1 ∶ U2 = P1 ∶ P2 = W1 ∶ W2 = Q1 ∶ Q2 = R2 ∶ R1; in parallel circuit, the more resistance in parallel, the smaller the total resistance; when two lamps are in parallel circuit, the lamp with smaller resistance is brighter
Inference: the two lamps are connected in different ways in the circuit: the brighter lamps in series must be darker when they are connected in parallel
Ohm's Law: I = u / R
Derivation formula: r = u / I
U=I*R
Electric power: P = I * u [applicable to any circuit]
Derivation formula: P = u ^ 2 / R P = I ^ 2 * r [only applicable to pure resistance circuit]
Let the length of an equilateral triangle be x (x > 0) and the area be y, then the functional relation between Y and X is ()
A. y=12x2B. y=14x2C. y=32x2D. y=34x2
Let ad. ∵ △ ABC be an equilateral triangle with side length x, ∵ CD = 12x, ∵ height h = 32x, ∵ y = 12x × H = 34x2