Math questions to detail the process answers

Use the discriminant method.

y=(mx^2+4√3x+n)/(x^2+1)m-y)x^2+4√3x+n-y=0

The unknown of the above equation is the discriminant 0 of x

i.e. (4 3) 2-4(m-y)*(n-y) 0y 2-(m+n)y+mn-12 0

m+n-√(m^2+n^2-2mn+48)]/2≤y≤[m+n+√(m^2+n^2-2mn+48)]/2

Because the maximum value of the function is 7 and the minimum value is -1, then.

m+n-√(m^2+n^2-2mn+48)]/2=-1...1)m+n+√(m^2+n^2-2mn+48)]/2=7...2) 1) + (2) get.

m+n=6, so m+n=6

Answer Choose C if you are satisfied.

x+3)^2+16=(x-(-3))^2+(0-(-4))^2；

x-5)^2+4=(x-5)^2+(0-(-2))^2；

Thus y can be seen as the sum of the distances from the point (x,0) to the point (-3,-4) and the point (5,-2), and the point of symmetry (-3,4) with respect to the x-axis (-3,4) should be the shortest distance.

The root number ((-3-5) 2+(4-(-2)) 2) = 10, so the range is y 10

The last digit of a number divisible by 5 can only be a multiple of 0 or 5, and 7 is an unrepeating two-digit number (07, 14, 21, 28...).The smallest row from small to largest is the smallest, so this 6-digit minimum is 140735.

According to the title, let the four-digit number be 33x, then 1000<33x<9999, and the minimum x is 31, so the smallest four-digit number is 33x31=1023

(1) The last digit of the number divisible by 5 can only be 0 or 5, and the last digit is 0 and cannot be divisible by 7, so the last digit is 5;

The smallest 6 digits are 102345 = 14620*7+5, and adding 30 can be divisible by 7, which is 102375.

2) 33*30=990, 31 is a prime number, so the smallest is 990+33=1023

1 different digits: 100,000 digits, 10,000 digits, 0 thousands, 2 hundred digits, 3 places, so 102300 35=2922....30 is divisible by 35 102305 102340 102375 because different numbers are required, and 102375

2 1000/33=30…10 then the minimum four digits are 1023

, multiples of 7 divisible by 35.

35*>100000

102305 102340 102375 can be 1023752 because the numerical requirements are differentSum of odd positions - sum of even positions = divisible by 11.

abcda + b-c-d = divisible by 11.

a+b+c+d=divisible by 3.

a=1,b=0,c=0,d=2,5,8 (divisible by 3) are not divisible by 11, a=1,b=0,c=1,d=1,4,7 (divisible by 3) are not divisible by 11a=1,b=0,c=2,d=0,3,6,9 (divisible by 3)are not divisible by 11, and 1023 is divisible by 11 (minimum).

1.Divisible, first find the least total multiple of 35...The minimum 6-digit number formed by how many 35s is 100000 35 = 2857 and 5

So the smallest 6 digits are 100030

2.The same goes for 33...

1000 33 = 30 more than 10

The smallest 4-digit number is 1023

The smallest of six different numbers is 102345

102375 minimal.

1023 minimum.

Because 4 y=(2 2) y=2 (2y)=5

2^(x-2y)=2^x/[2^(2y)]=3/5

I was recommended by my math teacher.

2^(2y)=5 2y=lg5/lg2

2^x-2y=3-lg5/lg2=3-log5:2

log5: 2 represents the logarithm of 5 with 2 as the base.

After walking for two hours, he walked two laps.

2 Answer: The minute hand has gone by centimeters, and the area is square centimeters.

Solution: (a) At point p, x=rcos=10cos120°=-5, y=rsin=10sin20°=5 3. i.e. the Cartesian coordinates of p are (-5,5 3).

b) The length of pq = 丨pq丨=丨-10 + 5 3i丨 = [10 2 + (5 3) 2] = 5 7. FYI.

1) Obviously, the focus of c is on the x-axis, and it is easy to get the left focus (-1,0), and one vertex is (0,1).

Let the equation (x 2 a 2) + (y 2 b 2) = 1, then b 2 = 1, c 2 = 1, a 2 = 2

Equation: (x 2 2) + y 2 = 1

2) It is easy to obtain two intersection points as (1,1 2), (1,-1 2), and symmetry with respect to the x-axis, and the modulo fb=modulo fa=3 2, modulo ab= 2, cos fab=cos fba=1 3

Vector product = (1 3)· (3 2)· (2)=1

It's also quite hard to do homework at night.