Inverse proportional functions and practical problems in mathematics in the second year of junior hi

1. Solution: (1) Let the area of the funnel mouth be s, the depth of the funnel is d and the volume of the funnel is 1 liter (known) according to the volume of the cone = 1 3 The bottom area is high, and 1 1 3 s d is obtained: the functional relationship between the area s and the depth d of the funnel is:

s=3 d(2)s=100cm2=1dm2 (known) According to: s=3 d, obtain: d=3 s=1dm=10cm

1. Funnel volume v=sd 3 Therefore, s=3v d=3 d2 100 square centimeters, i.e. 1 square decimeter, d=3v s=3 s=3 1=3 dm, 1 total time, t=dt d=t=2x10, 4 t2 t=10 d=2x10 4 10=2000 days, i.e., 5 years and 175 days.

1.(1) 3/s d

2) 100 square centimeters 1 square decimeter.

When s 1.

d 32, (1) :d 2 t/10 to the power of 4.

2): When t 10.

d＝2000

If I wasn't in junior high school, I wouldn't know where the picture 、、、

1.(1) 3/s d2) 100 square centimeters 1 square decimeter.

When s 1 d :d 2 t/10 to the power of 4 (2): when t 10 d 2000、、、 if I wasn't in the second year of junior high school, I wouldn't know where the graph 、、、

I forgot to separate the numbers I just had.

1）v=s*d/3

2) d=3*v s=30cm I haven't thought about the second question yet.

1.OAB translates 6 3 units to the right, and the coordinates of each point of the shape are translated 6 3, that is, the ordinate is unchanged, and the abscissa is 6 3 units, then the point A'(3√3，3)

If the point a falls exactly on the inverse proportional function y=k x, then the horizontal and vertical coordinates in the point a satisfy the inverse proportional function, and the horizontal and vertical coordinates of the point a are substituted to obtain k=9 3

9√3/x2.According to the formula of the distance between two points, ob=6=oa

Rotate the OAB in a counterclockwise direction, i.e., its trajectory is "a circle with O as the center of the circle r=6 as the radius", then the equation is: x 2

y 236 can find the intersection point of the garden and the inverse proportional function.

Solution: x1 = 3

x2=-√3

x3=3√3 x4=

y1=9y2=-9 y3=

3 y4=-3

Because the angle of rotation is less than 90°, the two intersections must be located in the third quadrant, that is, the horizontal and vertical coordinates are both negative, and a can be obtained'(-√3,-9),b

After rotation, point A to A', so the angle of rotation.

aoa'Connect AA', oa', to get the new oaa', which can be obtained by the formula for the distance between two points: oa

oa'=aa

6 so oaa'

aa'o∠a'oa

Rotation angle a = 60°

1. Move to the right.

6 3 units, the coordinates of a are (3 3, 3), and bringing the coordinates into the analytic formula gives k = 9 3 , so y = 9 3 x

The trajectory of point 2,,a is a circle, the equation is x 2 + y 2 = 36, the intersection of this circle and y = 9 3 x is c(-3 3,-3), d(-3,-3 3).

The triangle formed by these two points and the triangle OAB are congruent, so it is possible to calculate a=60°

Since the ordinate of one of the intersections is 6, 3x-2k=(k-3) x=6, and the above equation is equivalent to a system of equations, which is solved to x=-4 3 (the abscissa of one of the intersections), k=-5.

y1=3x+10,y2=-8/x.

I won't draw on this, I can only answer:

3x+10<-8 x, the square of x on both sides, and the inequality does not change.

3x to the power + 10x to the square + 8x<0

x(x+2）(3x+4)<0

x<-2 or -4 3

All I can say is that I didn't even graduate in math.

This seems to be a question about coordinate values, bring in the 6, 6x1=3x-2k : 6x2=(k-3) x

3x 》6 x》2

When x is equal to 2, k = 0.

Left and right: 1:2

I'm sorry, I'm really bad at math, it's normal to be wrong, please weigh it yourself. The figure is gone、,

Such questions can only be used on the test paper, and are not useful at all in practice, and may be useful, but rarely

I really don't understand why those teachers have to call us useless things, a lot.

Education in China is to teach us useless knowledge, but to ignore useful things, such as our morality, politics, etc

o(∩_o~

By question: 3x-2k=(k-3) x

The ordinate is 6, substituting 6 into y1 to get 6=3x-2k to get x=(6+2k) 3 Substituting the obtained x into the top equation can find k

The analytic formula of the two functions is solved.

If you need a diagram, I can draw it and send it to you.

Other than that. You're wrong about the one upstairs ...

Solution: It takes X minutes for Xiao Ming to complete the entry task.

120x=24000

x=200A:.

2. t=v/24000

3.There are 60 minutes in an hour, and 180 minutes in three hours, and 24000 180 is about 133 but 134 words per minute should be entered to complete the task.

(1) 24000 120 = 200 minutes (2) v = 24000 t (3) v = 24000 180 = cycle So at least 134 words should be entered.

(1) 24000 divided by 120 equals 200, i.e. he needs 200 minutes to complete.

2) It should be t=24000/v

3) 3 hours = 10800 minutes.

When t = 10800, v = 20/9 is approximately equal to at least 3 words that he should record.

I don't know if you want to define a domain... I'll not write about it yet.

Hope...

(1) Bring a set of values in and find out.

Analytic formula for proportional function: y=[-(root number2) 2] x inverse proportional function analytical formula: y=(-2 root number2) x

2) Since x=a, y=negative root number 2 is a set of corresponding values of the proportional function, then it is easy to find x=a=-2 by substituting the analytic formula

Because y=(-2 root number 2) x

So substitute x=-2 and y=negative root number 2.

Negative root number 2 = (-2 root number 2) -2

Obviously, the above formula does not hold.

So this set of values is not the corresponding value of the inverse proportional function.

1. The other branch of the image must be in the fourth quadrant, and this image and the image of the second quadrant are symmetrical with respect to the origin. Because the image is in the first.

2. Four quadrants, so n+7<0, i.e., n<7;

2. Because the images of this function are monotonically increasing in the second and fourth quadrants, that is to say, the images in these two quadrants increase with the increase of x, and the number of images in y also increases, so:

When a, when 0, when a<0b1

Finish <>

(1) Because y=n+7 x is in the second quadrant, n+7>0 n>-7 because the inverse proportional function image has 2 k>0 inverse proportional in one. The inverse proportional function of the three-quadrant k<0 is in two. Four quadrants.

So the other is in the fourth quadrant.

2) Because k < 0, y increases with the increase of x.

Because a< a1, so b

The other branch of the image must be in the fourth quadrant, and the images of this function are monotonically increasing in the second and fourth quadrants, respectively, you have to think about it.