If there is no common point between two circles Q1 and Q2 with different radii, and the moving circle O and Q1 and Q2 are both inscribed, then the trajectory of the center of circle O is: (according to the definition) the answer is a hyperbola

If there is no common point between two circles Q1 and Q2 with different radii, and the moving circle O and Q1 and Q2 are both inscribed, then the trajectory of the center of circle O is: (according to the definition) the answer is a hyperbola

You can draw several pictures to help you understand. It is easy to find that the absolute value of the distance difference between the center of circle O and Q1. Q2 is the difference between the radii of two circles, which is a hyperbola by definition

Make one, four and nine discs on three same square steel plates respectively. Are the remaining areas of the three plates the same? Calculate and explain the reason

Let the side length of the square steel plate be 12, then the area is 144
Remaining area of one wafer: 144-36 π
The remaining area of the punch is π - 144-4
Remaining area of 9 wafers: 144-9 * 4 π = 144-36 π
So the remaining area of the three plates is the same
If you have any mistakes, please correct them,
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-3, + 9, - 27,81, what is the nth number

The nth number = (- 3) to the nth power

There are five numbers in each row below, one of which is different from the other four. Circle it, 1.3 7 9 14 15 2.20 10 15 27 35

1. 14 is even, the others are odd
2. 27 is not a multiple of 5, the others are multiples of 5

1 1 2 3 5 7 10 15 20 27 37 52 () () [fill in the blank]

53.55.57.72.75.77.

Calculation: 27 ^ 2 * 9 ÷ (- 3) ^ 18

27^2*9÷(-3)^18
=(3³)²×3²÷3^18
=3^6×3²÷3^18
=3^8÷3^18
=3^(-10)

Simple calculation of the 100th power of 3 * 27 * 729

Original formula = 3 ^ 100 * 3 ^ 3 * 3 ^ 6 = 3 ^ (100 + 3 + 6) = 3 ^ 109

-1 / 3 power of (1 / 27)
Using the fractional exponential power of grade one,

-1 / 3 power of (1 / 27)
=- [(1 / 3) & [179;]
=-1/3

Simple calculation (- 1) + 2 + (- 3) + 4 +. + (- 99) + 100 3 + (- 6) + 6 + (- 9) + 9 +. + 27 + (- 30)
Simple calculation
（－1）+2+（－3）+4+。 +（－99）+100；
3+（－6）+6+（－9）+9+。 +27+（－30）

（－1）+2+（－3）+4+.+（－99）+100
=【（－1）+2】+【（－3）+4】+.+【（－99）+100】
=1+1+…… +1
=50
3+（－6）+6+（－9）+9+.+27+（－30）
=3-30
=-27

Prove that 1 + sin1 / 1 + sin2 / 2 × 2 +Sinn / N × n is a convergent function

Because 1 + | sin1 / 1 + | sin2 / 2 × 2 | +|Sinn / N × n | must be less than 1 + 1 / 1 × 1 + 1 / 2 × 2 +1 / N × n, and 1 / 1 × 1 + 1 / 2 × 2 +1 / N × n is a convergent series, so 1 + 1 / 1 × 1 + 1 / 2 × 2 +According to the theorem of comparative convergence and the relationship between absolute convergence and conditional convergence, 1 + sin1 / 1 + sin2 / 2 × 2 +Sinn / N × n is also convergent