An inverse proportional math problem, a math inverse proportional function problem

The coordinates of point e are: 5+1 2, 5-1 2 or (5-1 2, 5+1 2).

According to the description of the stem, the diagram is probably this:

Let the point b(x,y) and the point b be on the function y=1 x(x 0).

y=x (b is a vertex of a square).

y=x=1, i.e. b(1,1).

a coordinate is (1,0);

Let AD=A, then there is de=a(A 0), the coordinates of point D are (1+A,0), and the coordinates of point E are (1+A,A).

Again, point e on the function y=1 x (x 0).

a=1 (1+a), i.e., a +a=1 is solved to get a= -1 2 5 2a 0a= ( 5-1) 2

So the coordinates of point e: 5+1 2 , 5-1 2 .

When a is on the y-axis, the method is the same as above, i.e. e" ( 5-1 2, 5+1 2) in the figure

So the coordinates of point e are: 5+1 2, 5-1 2 or (5-1 2, 5+1 2).

(1) Over (k, 5).

i.e. y=52k-1=5

2k=6k=3 analytical: y=3 x

2)3/x=2x-1

3=2x²-x

2x²-x-3=0

2x-3)(x+1)=0

Point A is in the first quadrant.

x>0 so x=

y=2a(,2)

I was asked if I didn't understand.

(1) Substituting (k,5) into a linear equation.

2k-1=5

k=3 is parsed as y=3 x

2)y=3/x=2x-1

2x²-x-3=0

x=3 2 or -1

Since a is in the first quadrant, x>0

x=3 2 coordinates (3 2,2).

Bring (k,5) into y=2x-1 2k-1=5 k=3, so through the point coordinates (3,5), bring (3,5) into y=k x 5=k 3 k=15(1) inversely proportional analytic formula y=15 x

The two functions intersect, so 15 x=2x-1 (x-3)(2x+5)=0 x=3 or x=-5 2

Because in the first quadrant, x=3 brings y=2x-1 y=5 so a(3,5).

Determine whether the two quantities in each of the following questions are inversely proportional and explain why.

1) The total number of meters of weaving is constant, the number of meters of weaving per hour and the time spent.

Yes, the time to weave is equal to the total number of meters divided by the number of meters per hour of weaving, and the faster the number of meters per hour, the less time it takes.

2) The circumference of the rectangle is certain, its length and width.

Not (3) the volume of the cuboid is certain, its base area and height.

Yes, the volume is equal to the base area multiplied by the height and the larger the base area, the smaller the height.

4) The distance Xiao Gang has traveled from home to school and the rest of the journey.

Not (5) the area of the triangle, its base and height.

Not because the area of the triangle is fixed.

2.Use your brain and fill it in.

1) In the ratio.

The divisor) is certain, and the (dividend) is (positively) proportional to the (quotient);

The dividend) is certain, and the (divisor) is (inversely) proportional to the (quotient);

quotient) certainly, (the dividend) is (positively) proportional to (the divisor);

2) In the fraction.

The denominator is certain, and the (numerator) is (inversely) proportional to the (ratio);

ratio) is certain, (denominator) is (positive) proportional to (numerator);

numerator) is certain, (denominator) is (proportional) to (ratio);

The distance is constant, and time and speed are inversely proportional.

The total price is fixed, and the unit price is inversely proportional to the quantity.

The total number of pages is constant, and the average number of pages read per day is inversely proportional to the number of days after reading the book.

The total number of words is constant, and the typing speed is inversely proportional to the time taken.

The total amount of juice is certain, the number of cups divided is inversely proportional to the amount of juice per glass, and the total number of people in line is inversely proportional to the number of people in each row.

The area of the rectangle is fixed, and the length and width are inversely proportional.

The volume of the box is constant, and the base area and height are inversely proportional.

The total amount of coal is certain, the amount of coal burned per day is inversely proportional to the number of days burned in Changchang, and the total number of trees planted in each row is inversely proportional to the number of rows.

A pile of goods is certain, and the ones that are shipped out are inversely proportional to the rest.

The total amount of coal is fixed, the amount of coal burned per day is inversely proportional to the number of days burned, and the total number of trees planted in each row is inversely proportional to the number of rows.

The work is always stupid and slow, and the ergonomics are inversely proportional to the time.

One. What is the proportion of each of the following?

The radius and circumference of the circle (

proportional) 2.The fraction of the newspaper order and the amount of money payable (

proportional) 3.The flour used and the remaining flour (

Disproportionate) II. Application:

1.On a map with a scale of 1:25000000, the actual distance between A and B is 4500 kilometers, how many centimeters are the distance between the two places on the map?

Solution: Let the two places be separated by xcm

4500km=450000000cm

x:450000000

Solution. x=18

2.On a map with a scale of 1:40000, the distance between the two places is 5 centimeters, and if the scale is 1:25000, what is the distance between the two places?

Solution: The distance between the two places is x centimeters.

x:(5*40000)=1:25000

Solution. x=8

Determine whether the two quantities in each of the following questions are inversely proportional and explain why.

1) The total number of meters of weaving is constant, the number of meters of weaving per hour and the time spent.

Be. The time to weave is equal to the total number of meters divided by the number of meters per hour of weaving.

The faster the number of meters of fabric per hour, the less time it takes.

2) The circumference of the rectangle is certain, its length and width.

No. (3) The volume of the cuboid is certain, its base area and height.

Be. The volume is equal to the base area multiplied by the height.

The larger the base area, the smaller the height.

4) The distance Xiao Gang has traveled from home to school and the rest of the journey.

No. (5) The area of the triangle, its base and height.

No. Because the area of the triangle is fixed.

2.Use your brain and fill it in.

1) In the ratio.

The divisor) is certain, and the (dividend) is (positively) proportional to the (quotient);

The dividend) is certain, and the (divisor) is (inversely) proportional to the (quotient);

quotient) certainly, (the dividend) is (positively) proportional to (the divisor);

2) In the fraction.

The denominator is certain, and the (numerator) is (inversely) proportional to the (ratio);

ratio) is certain, (denominator) is (positive) proportional to (numerator);

numerator) is certain, (denominator) is (proportional) to (ratio);

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

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.

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