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Math problems in grade two.
1。 Xiao Cong designed a program: after inputting data X, the output result is Y, (when X=0, Y =-1; When X= 1, y = 0;; When X=4, y =1; When X=9, y = 2;; When X= 16, Y=3. )

Q: If the input number is a, the output number is _ √ A- 1. _ _ _ _ _ _.

2。 It is known that m power of 16 = 2N-2 power of 2 multiplied by 4; N power of 27 = M+3 power of 3 times 9. Find the values of m and n (detailed process)

Answer: According to the meaning of the question, you must:

16^m=2^(2n-2)*4……( 1)

27^N=3^(M+3)*9 ……(2)

From (1):

2^4M=2^2N

4M=2N

m = 1/2 * N……………………(3)

From (2):

3^3N=3^(M+5)

3N=M+5 …………(4)

Substituting (3) into (4) gives: N=2,

Substitute N=2 into (3): M= 1.

3。 The sales of a commercial building this year 1 month is 6.5438+0 million yuan. In February, due to various reasons of poor management, sales fell by 4%. Later, the management was improved, and the sales in April reached 6.5438+0.5 million yuan. Find the average monthly growth rate for three or four months. Accurate to 0. 1% (detailed process)

Solution: Let the average monthly growth rate of three or four months be x, then:

100*( 1-4%)( 1+x)^2= 150

96( 1+x)^2= 150

( 1+x)^2= 1.5625

1+x= 1.25

X 1=25% x2=-2.25 (omitted)

That is, the average monthly growth rate in March and April is 25%.