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Answers to the 13th Beijing Senior High School Mathematics Knowledge Application Competition
One,

(1), the other cars he will meet are: No.82 to No.49 * * * No.80, but he hasn't arrived yet! There is still half the distance between the car and the car. She walked half the distance in 9 seconds, so if you add 9, you get 729 seconds.

(2), 1 12 Cable cars come and go once * * The length of two cable cars (the distance in the station is not recorded), and the cars go half a car interval every nine seconds, so 18 seconds goes one car interval. Therefore,1200 * 2/12/18 =1.19m/s.

Second,

Y = 7/3 * arcsin (1-x/140), (x is speed and y is angle). Get 19. 16.

When x=0; y=2 10

When x=40; y= 106

When x = 70; y=70

When x= 100; y=38.7

x = 120; y= 19. 16

Fold a piece of paper in half, and then seal the other three sides to form a hollow box, so the really usable part is 17*( 18-0.5)/2.

If the width of the bottom surface is x, the length is 8.75-x and the height is17-x.

So the volume v is: V=x*(8.75-x)*( 17-x).

According to the formula:

The unary cubic equation ax 3+bx 2+CX+d = 0, (a, b, c, d∈R, a≠0).

Multiple root discriminant:

a=b^2-3ac;

B = 9ad BC

C=c^2-3bd,

Total discriminant:

δ=b^2-4ac。

When A=B=0, jinsheng formula ① (when A=B=0, jinsheng formula ①):

x 1 = X2 = X3 =-b/(3a)=-c/b =-3d/c .

When δ = b 2-4ac >; 0, golden formula ② (when δ = b 2-4ac > 0, Jinsheng formula ②):

x 1=(-b-(y 1^( 1/3)+y2^( 1/3)))/(3a);

x2,3=(-2b+y 1^( 1/3)+y2^( 1/3)3 ^( 1/2)(y 1^( 1/3)-y2^( 1/3))i)/(6a);

Where y 1, 2 = ab+3a (-b ((b 2-4ac) (1/2))/2, I 2 =-1.

When δ = b 2-4ac = 0, Formula ③ (when δ = b 2-4ac = 0, Jinsheng Formula ③):

x 1 =-b/a+K; X2=X3=-K/2,

Where K=B/A, (A≠0).

When δ = b 2-4ac

x 1 =(-b-2(acos(θ/3))^( 1/2))/(3a);

X2,3 =(-b+((a)^( 1/2))*(cos(θ/3)((3)^( 1/2))*sin(θ/3))/(3a);

Where θ=arccosT, t = (2ab-3ab)/(2a (3/2)), (a >;; 0,- 1 & lt; T & lt 1)

Solution: When x= 1.8375, the maximum value of y is about 248.520.

Fourth,

Because, when it becomes a circular orbit, it is at the equatorial radius of the earth, and the radius of the earth is: 637 1.3.

So the distance from the spacecraft to the center of the earth is 6371.3+343 = 6714.3.

Let the maximum distance be x.

From cosine theorem: 6714.3 * 6714.3 = 6371.3 * 6371.3+x * x+2 * 6371.3 * x * cos.

Let the maximum deflection angle be y.

From cosine theorem: x * x = 6371.3 * 6371.3+6714.3 * 6714.3+2 * 6371.3 * 67/.

X is about 1600.

Y is about 3 1.

So * * * need to set up 12 monitoring stations.

Five,

(1), the inflexible things are the necessities of life: food, salt and water. ...

There are also elastic things: durable goods such as plasma TVs and high-end cars.

Food, salt and other condiments, water and other necessities of life, even if the price changes a lot, the per capita demand for goods will remain basically unchanged for a month, while the population will remain basically unchanged for a period of time, so the sales volume will not change much.

Gold, TV, luxury cars, if you don't explain them at home now, there is no need. If the price goes up, they can be bought after the price goes down, so when the price changes, these unnecessary things will change greatly.

(2)、(xy)' = xy '+x ' y = ey+y =(e+ 1)y =(e+ 1)f(x)