A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?

A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?

(1) From the question meaning: y = 60-x10 (2 points) (2) z = (200 + x) (60-x10) = - 110x2 + 40x + 12000 (3 points) (3) w = (200 + x) (60-x10) - 20 × (60-x10) (2 points) = - 110x2 + 42x + 10800 = - 110 (x-210) 2 + 15210. When x = 210, w has the maximum value. At this time, x + 200 = 410, that is to say, when the price of each room is 410 yuan per day, w has the maximum value, and the maximum value is 15210 yuan

A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?

(1) From the question meaning: y = 60-x10 (2 points) (2) z = (200 + x) (60-x10) = - 110x2 + 40x + 12000 (3 points) (3) w = (200 + x) (60-x10) - 20 × (60-x10) (2 points) = - 110x2 + 42x + 10800 = - 110 (x-210) 2 + 15210. When x = 210, w has the maximum value. At this time, x + 200 = 410, that is to say, when the price of each room is 410 yuan per day, w has the maximum value, and the maximum value is 15210 yuan ．

Find the area of a triangle whose sides are 8 and 6
One root of x ^ 2 - (3K + 1) x + 2 (k ^ 2 + k) = 0 is larger than the other root. 4. Two sides of a triangle are 8 and 6 long, and the third side is a real root to calculate the triangle area

The two equations are 2K, K + 1. I don't know which one is bigger or which one is smaller
Suppose 2K = K + 1 + 4, then k = 5,
Or 2K + 4 = K + 1, k = - 3,
And because one root of the equation is the side length of the triangle, it is the first case
K = 5, the root is 10,6. Both sides may be the third side of the triangle, which also meets the condition that the third side is in the range of 2-14, so the area of the triangle is 24 or 8 * root 5

Lie equation: (5.3 + 2.7) x divided by 2

4/5

The radius of a circle is 12 decimeters. How many decimeters are the diameter and perimeter of the circle, and how many square decimeters are the area

Diameter = 12 × 2 = 24 (decimeter)
Perimeter = 3.14 × 24 = 75.36 (decimeter)
Area = 3.14 × 12 & # 178;
=3.14×144
=452.16 (square decimeter)
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1. Fill in the number in brackets. 2. Simplify the ratio below first, and then calculate the ratio
（1） 2 / 5 * 2 / 3 = 2 / 5 * 1 / 3. B.4/3 divided by 5 / 8 * 5 / 8 = 4 / 3 divided by (5 / 8 * 8 / 5) = 4 / 3. C.8 * 11 / 5-2 * 11 / 5 = (8 + 2) * 11 / 5. D.11/9 divided by 3 / 5-2 / 9 divided by 3 / 5 = (11 / 9-2 / 9) divided by 3 / 5 = 1 * 5 / 3 = 5 / 3 2, (2) 1.0.3 km: 75 M. 2.12 Min: 3 / 4 h

（1） 1. BD 2. A
（2） 1.0.3km: 75m
Simplify 300m: 75m = 12:3 = 4:1
12 minutes: 3 / 4 hours
Simplify 12 points: 45 points = 4:15

As shown in the figure, let o be a point in △ ABC, connect Ao, Bo and Co, and extend the intersection of BC, Ca and ab at points D, e and F. s △ is known AOB:S △ BOC:S If △ AOC = 3:4:6, then odao · oebo · ofco equals ()
A. 235B. 435C. 635D. 835

∵ s △ AOB: s △ BOC: s △ AOC = 3:4:6, ∵ s △ AOB: s △ ABC = 3:13, s △ BOC: s △ ABC = 4:13, s △ AOC: s △ ABC = 6:13, ∵ OFCF = 313, odad = 413, oebe = 613, ∵ ofco = 310, odao = 49, oebo = 67, ∵ odao · oebo · ofco = 310 × 49 × 67 = 435

When is the time to prove the equality sign
For example, "if a, B, C are positive real numbers, and a * B + b * C + C * a = 0, use Cauchy inequality to prove that a + B + C is greater than or equal to the root sign 3", it is not necessary to prove when the equal sign holds;
And "when we know that a and B are positive real numbers, we have to prove the value of a, B and C when we want to prove that 1 + 1 + B is greater than or equal to 4 (a + b)"?

The first question is wrong, it should be ab + BC + Ca = 1
As far as these two problems are concerned, there is no need to discuss the equal sign
No matter what method is used, it can be proved that a + B + C ≥ 3 and 1 / A + 1 / b ≥ 4 / (a + b)
If the topic itself requires discussion of the conditions for the establishment of the equal sign, of course there is nothing to say
If there is no such requirement, there is no need to discuss it
But most of the questions can get equal sign. If the equal sign can't be set up at the same time, let it go
Therefore, the condition of equal sign often indicates the direction of expansion and contraction
In addition, if the first question to change the argument, requires a + B + C minimum, it is necessary to verify that the equal sign can be established
Because the minimum value needs to be available
If it has been scaled, for example, by 4A & # 178; + B & # 178; ≥ 4AB, 4b & # 178; + C & # 178; ≥ 4bc, 4C & # 178; + A & # 178; ≥ 4CA,
We get 5 (A & # 178; + B & # 178; + C & # 178;) ≥ 4 (AB + BC + Ca) = 4, then (a + B + C) &# 178; = A & # 178; + B & # 178; + C & # 178; + 2 (AB + BC + Ca) ≥ 4 / 5 + 2 = 12 / 5
It is proved that a + B + C ≥ 2 √ 15 / 5. Although the conclusion is correct, 2 √ 15 / 5 is not the minimum, because the equal sign cannot be established
However, it is not necessary to discuss all the equal cases in the problem of finding the maximum value, unless the problem requires finding all the maximum value points (sometimes not unique)

Trapezoid bottom is 4cm, add a bottom is 3cm, area is 3cm2 triangle can be put together into a parallelogram, trapezoid area is how many square meters?

Bottom = 4 + 3 = 7
Height = 2 * 3 / 3 = 2
Area of trapezoid = (4 + 7) * 2 / 2 = 11cm ^ 2

The following groups of functions are the same function ()
A. f(x)=x-1，g(x)=(x-1)2B. f(x)=|x-3|，g(x)=(x-3)2C. f(x)=x2-4x-2，g(x)=x+2D. f(x)=(x-1)(x-3)，g(x)=x-1•x-3

In option a, the domain of F (x) is r, and the domain of G (x) is [1, + ∞). If the domain of F (x) is different, their corresponding rules are different, so they are not the same function. In option B, the domain of F (x) is r, and the domain of G (x) is r, G (x) = (x-3) 2 = | x-3 |