What is the greatest common factor of 15 and 25______ The least common multiple is______ .

What is the greatest common factor of 15 and 25______ The least common multiple is______ .

15 = 3 × 5, 25 = 5 × 5, so the greatest common factor of 15 and 25 is 5, and the least common multiple is 5 × 3 × 5 = 75
The greatest common factor of 3 / 14 and 9 / 35 is () and the least common multiple is ()
The greatest common factor and the least common multiple are discussed in the range of integers, 3 / 14 and 9 / 35 are fractions, and there is no integer division. Therefore, 3 / 14 and 9 / 35 do not have the greatest common factor and the least common multiple
Of course, when learning the score, it is often inseparable from the basic knowledge of integers. When doing the score addition and subtraction method, you often need to pass the score, which requires the knowledge of integer division
According to my experience, you want to divide 3 / 14 into 9 / 35 and ask for the greatest common factor and the least common multiple of 14 and 35
The greatest common factor of 14 and 35 is 7, and the least common multiple is 70
7 70
The greatest common factor of 3 / 14 and 9 / 35 is (7), and the least common multiple is (70)
A plural question
Let a, B, C and d be real numbers. Under what condition does the equation x2 + (a + bi) x + C + Di = 0 have real roots
If there is a real solution m, then
(m^2+am+c)+(bm+d)i=0
So m ^ 2 + am + C = 0 and BM + D = 0
It is concluded that (- A + √ (a ^ 2-4c)) / 2 = - D / B or (- A - √ (a ^ 2-4c)) / 2 = - D / b
What are the characteristics of circuit resonance in RLC series resonant circuit experiment
In series, there is only one circuit for the current, which is equal to the circuit voltage divided by the impedance. The current cannot be greater than the output current of the power supply (equal to the current). However, the voltage on the capacitor and inductor is opposite to each other, and the circuit voltage is equal to the difference between the two voltages plus the resistance voltage drop. Therefore, series resonance is voltage resonance rather than current resonance
In parallel, there is only one load voltage and two current loops. The voltage is the same as the power supply, and the difference between the capacitive current and the inductive current is equal to the power supply current. Therefore, this is current resonance
Of course, series resonant circuit can be used as step-up transformer: when the impedance values of capacitance and inductance are close to each other, the two impedance voltage drops can reach very high values. In the electrical test, the AC test of large transformer uses this principle to improve the test voltage of the tested transformer (the transformer to ground is equivalent to a large capacitance, and the series inductance is calculated, When 0-200-380 V is given, thousands to 10000 V can be obtained
However, the calculation of capacitance and inductance must be accurate, otherwise too high voltage is very dangerous
What is the imaginary part of the complex 5I / (1-I)
five-seconds
5i/(1-i)=5i(1+i)/(1-i)(1+i)=(5i-5)/2
5i/（1-i）=5i*（1+i）/（1-i）*（1+i）
=（5i-5）/2
So the imaginary part is 5 / 2I
In RLC series resonant circuit
Given that r = 50 Ω, l = 4 h, C = 0.25 & # 181; F, the total voltage of the circuit is u = 100 v. then the resonant frequency is f 0 = Hz, the current in the circuit is I = a at resonance, and the voltage on each component is u r = V, u l = V, u c = v
ω 0 = √ 1 / LC = 1000 rad / sf0 = ω 0 / 2 π = 159.236 Hzi = 100 / 50 = 2 AUR = I * r = 100 vul = I * ω 0 * l = 2 * 1000 * 4 = 8000vuc = I * 1 / (ω 0 * c) = 2 / (1000 * 0.25 * 10 ^ - 6) = 8000vul and UC
If the complex number 3 = 5I, 1-I, - 2 + AI and the corresponding points on the complex plane are on the same line, then the value of real number a is
3-5i
3 + 5I or 3-5i?
3-5i, a = 5
3 + 5I, a = - 10
A should be - 7!
Research on RLC series resonant circuit
1. The resonant frequency of the circuit is estimated according to the parameters of the circuit board
2. Which parameters of the circuit can make the circuit resonant? Does the value of R in the circuit affect the resonant frequency?
3. How to judge whether the circuit resonates? What are the plans to test the resonance point?
4. When the circuit is in series resonance, why can't the input voltage be too large? If the signal source gives 3 V voltage, when the circuit is in resonance, what range should be used to measure UL and UC with AC millivoltmeter?
5. How to change the circuit parameters to improve the quality factor of RLC series circuit?
6. Is UL equal to UC at resonance? If so, why?
1. The resonant frequency of the circuit is estimated according to the component parameters given by the experimental circuit board. By F = 1 / 2 π √ LC, the resonant frequency is estimated. 2. Which parameters of the circuit can make the circuit resonant? Does the value of R in the circuit affect the value of resonant frequency? Changing F, l, C can make the circuit resonant, and the value of R in the circuit will not affect
Is the complex number I positive or negative?
I is an imaginary number unit. Since it is called an imaginary number, it means a number that doesn't exist. It's just a hypothetical number for the convenience of solving problems
Both positive and negative numbers are real numbers, and there is no imaginary number ～
The number with I has no positive or negative
1. The complex number cannot be compared in size;
2. 3 + 4I is the simplest complex number, and can't be simplified any more..
What are the conditions and phenomena of resonance in RLC series circuit?
In an AC circuit with resistor R, inductor L and capacitor C, the voltage at both ends of the circuit is different from the phase of the current. If we adjust the parameters of the circuit element (L or C) or the power frequency, the phase of the circuit element (L or C) can be the same, and the whole circuit presents pure resistance