What is the meaning of the quantity expressed by positive and negative numbers A lesson of rational numbers

What is the meaning of the quantity expressed by positive and negative numbers A lesson of rational numbers

There are many things that can be expressed, such as:
1. The contrast is poor. No matter the height, size, weight, mass, temperature, etc., you can find any benchmark. If you compare others with him, the positive means that they are much higher or heavier than him, and vice versa;
2. Directionality: determine a positive direction, positive in the same direction, negative in different directions;

In order to express two opposite quantities, such as above zero (), height and (), income and (), we introduce negative numbers

Such as above (below zero), height and weight, income and expenditure

|lgx|

|lgx|

A bamboo pole is several meters long, and it is 1.8 meters longer with a rope. If the rope is folded in half and then measured again, it is 1.2 meters shorter. How long is the rope?

(1.2 + 1.8) × 2 = 3 × 2, = 6 (m)

(within 1 hour) it is known that 3 / a = 7 / b = 2 / C ≠ 0 (1) find the value of 2a-b + 4C / A + 2b-3c
(within one hour) a = 7 / 3 B = 2 / 2 C ≠ 0
(1) If AX = by = CZ ≠ 0, find the value of X ∶ y ∶ Z

11/7 3:7:2

According to the measurement, the three sides of a triangular wheat field are 13m, 5M and 12m respectively, so what is the area of this wheat field?

It's all about asking!
Use the Helen formula!

A = 5 / 3, B = log (1 / 2) (1 / 3), compare the size of AB!

a=5/3
b=-ln3/(-ln2)=ln3/ln2=log2(3)
b-a=log2(3)-5/3=[3log2(3)-5]/3=[log2(27)-log2(32]/3

The utility model relates to a rectangular water tank on a watering cart, which measures 2.5 meters long, 2 meters wide and 4 meters from the inside. How many tons of water can it hold at most? (1 cubic meter weighs 1 ton)
If you sprinkle 7 liters per minute, how many hours does it take to finish sprinkling a car?

1. 2.5 × 2 × 1.4 = 7m3
7 × 1 = 7 tons
A. It can hold up to 7 tons
2. 7 m3 = 7000 L
7000 ÷ (7 × 60) = 50 / 3 hours
A: it takes 50 / 3 hours

It is known that in an equilateral triangle ABC with side length 2, P and Q are points on AB and AC in turn, and the segment PQ divides the triangle ABC into two parts with equal area, let AP = x, AQ = t, PQ = y
Find: 1) the function relation of T with respect to X
2) The functional relation of Y with respect to X
3) The minimum and maximum of Y
Hope to have a specific process!

(1) Because PQ bisects the area of triangle, if (AP * AQ) / (AB * AC) = 1 / 2, then 2XT = 4, XT = 2, then t = 2 / X (2) by cosine theorem: y ^ 2 = x ^ 2 + T ^ 2-xt = x ^ 2 + 4 / x ^ 2-2, then y = under the root sign (x ^ 2 + 4 / x ^ 2-2) (3) by means inequality, it is easy to get that x ^ 2 + 4 / x ^ 2 is greater than or equal to 4, then the minimum value of Y is

When passing through the fixed point P (1,4) and making the parabola C: y = 2x2 at two points a and B, and passing through a and B and making the tangent of parabola C at point m, the trajectory equation of point m is______ ．

Let the linear equation AB be y-4 = K (x-1); the simultaneous linear equation and y = 2x2 get: 2x2-kx + K-4 = 0, let a (x1, Y1), B (X2, Y2) get X1 + x2 = K2, x1x2 = k − 42 ∵ y = 2x2 ∵ f ′ (x) = 4x by Weida's theorem, let the tangent through a and B as parabola C be L1 and L2 respectively, then kl1 = 4x1, kl2 = 4x2