Two math problems functions, one math function problem

1: It should be that when m is valued, there are two intersection points greater than 0, that is, (4m) squared - 4*2 (m+1)(2m-1)>0, and m can be solved.

2: Substituting x=0 and y=0 to get 2m-1=0, so m=

1. The first question should be when m is what is the value, the function image and the x-axis have two intersection points.

There are two intersections with the x-axis, which means that the equation has two real roots (can be solved with b 2-4ac 0 4m) 2-4*2(m+1)*(2m-1) 0 can solve this inequality to get m 1

It is also required that 2(m+1)≠0 is m≠-1, and the function is a straight line, which does not meet the topic.

So m 1 and m ≠-1 satisfies the condition.

2. A zero point is at the origin point when x=0 when y=0

i.e. y=0=2m-1

The solution is m=1 2

The quadratic function has two intersections with the x-axis, and the discriminant formula is required to be greater than zero.

That is, (4m) squared - 8 (m+1) (2 m-1) = 8-8 m> 0 is solved to obtain m<1, when the function f(x) is a one-time function, the function is a straight line, and there is only one intersection point with the x-axis, that is, 2 (m+1) cannot be equal to 0, that is, m is not equal to -1

So when m<1 and not equal to -1, the function image has two intersections with the x-axis.

The zero point of the function is originally described, and when x=0, f(x)=2m-1=0 is solved to m=1 2

a = [ 2 +（2h+2）] h * 1/2 = h^2 + 2h = （h+1）^2 -1

a = (h+1) 2 -1 gives 2 times the parabola a is fixed (-1,-1) so.

a is increasing within (-1, positive infinity).

Define the domain 0 <= h <= and the value range 0 <= a <= + =

Fig... I didn't give it out, I saw the picture.

h<= 2=

Does this require a function?

It can be solved directly

Hello! Answer 1: Let the original profit margin be x, because **price = purchase price (1 + profit) original ** price = original purchase price * (1 + x).

The current purchase price is reduced to the following.

**Price = (1 + 10% + x) * original purchase price * ((1-8%) Since ** price remains unchanged, there is.

1+10%+x）*（1-8%）=1+x）

x = i.e. the original profit margin is 15%.

So p=15

Answer 2: From "the hound runs 5 steps, the rabbit runs 9 steps", it can be seen that when the hound is a meter per step, then the rabbit is 5 9 meters per step. From the time when the hound runs 2 steps, but the rabbit can run 3 steps, it can be seen that at the same time, the hound can run 2a meters, and the rabbit can run 5 9a * 3 5 3a meters.

Thus, it can be seen that the speed ratio of the hound to the rabbit is 2a:5 3a 6:5, that is to say, when the hound runs 60 meters, the rabbit runs 50 meters, and the difference of 10 meters is just after the chase.

1.Solution: Set the original purchase price to X yuan.

According to the meaning of the topic, the price is invariant, and the equation can be listed:

1+p%)x=(1+p%+10%)(1-8%)x Since the purchase price will not be 0, we should reduce x on both sides of the equation at the same time.

100+p=

Then the speed of the hound: the speed of the rabbit = (9 3) :(5 2) = 6:5, that is, in the same time, the hound runs 6 steps equal to the rabbit runs 5 steps.

Then the distance the hound runs = 10 (6-5) 6 = 60 steps.

Hope mine can help you solve the problem.

1. Divide each small square into quarters, then there are a total of 9*4=36 small parts, and choose 6 small parts arbitrarily (which has many methods), then it is one-sixth.

1 6 1 divided by 6 No sign on the phone, sorry.

For 90 days, the number of A is x, and the number of B is y

x+320=y

3x=y+460

The solution gives x = 390 y = 710

31 days in January, 14 days in February, 11 days in March, 7 days in April, 6 days in May, 5 days in June, 4 days in July, 3 days in August, 3 days in September, 3 days in October, 2 days in November, 2 days in December.

A total of 91 days.

A is x, B is y, x+320=y

y+460=3x

Equations can be solved.

x=390，y=710。

There are only 10 days in March......A total of 90 days, bar ......

y=4 (x-1 2)-a*2 x+(a 2) 2+1=(1 2)*(2 x) 2-a*2 x+(a 2) 2+1 so that t=2 x,1=4, y(min) = y(t=4)=(a 2) 2-4a+9

In the second question, your condition is a bit blind, f(x)=2 x-2 (-x), when x (-1,1), there is f(1-t)+f(1-t 2)<0-1<1-t<1,-1<1-t 2<1,0 to make a mark, and answer it tomorrow when you wake up.

Let t=1 x, and bring in the relation to get the expression a as follows:

f(1/t)+2f(t)=1/t；

f(x) is the function, let t=x, bring in a to get the expression bf(1 x)+2f(x)=1 x

Combine the expression b with the original analytic formula and subtract f(1 x) to obtain the f(x) analytic formula.

f(x)=—x；

3x 3 2.Because according to the definition of parity: for any x within the definition domain, f(-x) = -f(x) or f(x).

It can be seen that for any x in the defined domain, f(-x) is defined, so -x is also in the definition domain, so it is symmetrical.

Let x=tf(t)+2f(1 t)=t

Let x=1 t

f(1/t)+2f(t)=1/t

Solve the system of equations: f(t)=(2 t -t) 3

Is. f(x)=(2/x - x)/3

1.Use the orthogenomic theorem to find the angle c

6/sina=3/sin30°

sina = 1, angle a = 90°, angle c = 90 - angle b = 60°. c = 3 3, right triangle abc area = 1 2 * b * c = 9 3 2

d=2, the general formula of the number series {an}; an=1+2(n-1).