Solve a math problem of inverse proportional functions

Solution: (1) Because the primary function y=2x-1 passes through the point (a,b)(a+1,b+k)b=2a-1

b+k= 2（a+1）-1 ②

Let - get b-(b+k)=2a-1-2(a+1)-1, k=2 The analytic formula of the inverse proportional function is y=2 2x

2) Point a(m,1) on an inversely proportional function image.

1=2 2m, m=1, the coordinates of point a are (1,1)3) exist. 1. When ao=ap, (point p on the positive half axis of the x-axis), point p(2,0). Analysis: Passing point A to do Al X-axis, AO=PO, OAP is an isosceles triangle, Al X-axis (isosceles triangle three lines in one, that is, bottom midline = height = apex bisector), OL = PL=1 (OL is the abscissa of point A), OP=2 (OL + OP=1+1=2), point P on the X axis. , point p(2,0).

2. When op=ap, (point p is the isosceles right angle of the ap vertex), point p(1,0). Analysis: Al x-axis is known by 1, al=1 (point a ordinate), op=1 (point a abscissa), so point p(1,0).

1) The slope of the primary function k=2;

According to the slope, k=(x-x1) (y-y1), that is, k={b-(b+k)} {a-(a+1)} k is the slope of the primary function, k is the unknown of the inverse function).

The solution yields k=2

So the analytic formula of the inverse function is y=2 2x=1 x2) and substitutes point a (m,1) into the primary function.

The solution is m=1

So the coordinates of point A are (1,1).

3) There are p-points (2,0) and (— 2,0).

a（x，y）

ab=1, b=60° y=(root number 3) 2, and a on the image of the inverse proportional function y = root number 3 x.

Therefore x=2a(2, root number 3 2).

Let c(x,0)ac = root number 3

Use the Pythagorean theorem, or the AC two-point distance formula.

x-2) 2+(root3 2-0) 2=(root3) 2x-2=+-3 2

x1=7/2

x2=1/2

c(,0) or (,0).

1) Because most of the image limbs of the jujube are inversely proportional functions y=x -2a and primary functions y=kx+2 over the point p(a,2a), so.

2a=-1 2 2a=ak+2 so a=-1 4, k=10

2) The vertical volume of apostulous history rock of APO = OA*PA 2=(1 4*1 2) 2=1 16

1) Bring p into the original two functions to obtain 2a=-2 2a=ak+2 to solve which beam a=-1 k=4

2) Area of APO = 1 2 (1*2) = 1

Solution: From the known, -2a=-2a a, then a=-1, -2=-k+2, k=4, so p(-1, -2), then opa=2

Solution: (1) Bringing the point p(a,2a) into the inverse proportional function is: 2a=-2a a, a=-1

So point p(-1,-2).

Then bring the point p(-1,-2) into y=kx+2, there is: -2=-k+2, and get: k=4

So the point a(-1,0).

The area of the APO is: s=|oa|×|ap|/2=1×2/2=1

Because it is inversely proportional, it |m|-2=-1,∴|m|=1, i.e. m=plus or minus 1

However, because it is an inverse proportional function, m-1 cannot be equal to 0, so m=1 is rounded off, and the final answer can only be m=-1

On the third floor, don't say the first floor and the second floor, the three of you are copied and the answers are all wrong, this question doesn't need any images, you copied the original words of the original link author, but unfortunately that one is simply wrong.

The correct answer is given below: (solemnly declare that personal originality is absolutely correct!) ）

1) According to the title, when the material is heated, the functional relationship between y and x is y=ax+b

This is the real one-time functional relationship, and they all give proportional functions that I can't understand. )

Obviously, this function passes two points (0,15) and (5,60) and substitutes these two points into y=ax+b

b=15 --1)

5a+b=60 --2)

Simultaneous solution (1)(2) gives a=9, b=15

According to the idea, when the material is stopped from heating, the functional relationship between y and x is y=c x, and the point (5,60) is substituted on the image of this function, and 60=c 5 is solved, and the solution is c=300

In summary, when the material is heated, the function of y and x is y=9x+15 (0 x 5).

When the material is stopped from heating, the relationship between y and x is y=300 x (x 5).

2) The problem is to find how much x is equal to when the material is reduced to 15 degrees, and then the function is on the second image, substitute y=15, and solve x.

15=300 x, solution x=20

Therefore, a total of 20 minutes elapsed from the start of heating to the cessation of operation.