The minimum value of the function y = 2tan α + cos α sin α, α ∈ (0, π 2) is___ ．

The minimum value of the function y = 2tan α + cos α sin α, α ∈ (0, π 2) is___ ．

First, the original function is changed into y = 2tan α + 1tan α ≥ 22, the minimum value of the function is 22

The maximum value of function y = sin * x + acosx + 5 / 8a-3 / 2 on [0, ～] is 1
The "~" in [0, ~] means: Pai, which is 3.14

Let t = a ＾ x, then f (x) = t ＾ 2 + 2t-1 = (T + 1) ＾ 2-2, opening upward, symmetry axis t = - 1, when a ＾ 1 / a ＾ t ＾ a, so when t = a, i.e. x = 1, f (x) gets the maximum value, so (a + 1) ＾ 2 -

Given that the maximum value of function f (x) = sin square x + acosx + 5 / 8a-3 / 2 on X belonging to [0,2 faction] is 1, find a

Because (cosx) ^ 2 + (SiNx) ^ 2 = 1
So f (x) = sin square x + acosx + 5 / 8a-3 / 2 = - (cosx) ^ 2 + acosx + 5A / 8-3 / 2 = - (cosx-a / 2) ^ 2 + A ^ 2 / 4 + 5A / 8-1 / 2
And because the maximum value of function f (x) on X belongs to [0,2 school] is 1, if and only if cosx = A / 2, the function obtains the maximum value 1, and the solution is a = 3 / 2 or - 4
Since cosx = A / 2, a = 3 / 2

Given the function f (x) = Sin & # 178; X + acosx + 5 / 8a-3 / 2, when a = 1, find the maximum value of the function

f(x）=sin²x+cosx+5/8-3/2
=1-cos^2 x+cosx+5/8-3/2
=-(cosx-1/2)^2+3/8
The maximum value is 3 / 8

How to solve those math problems with equations
1. The square of equation (A-2) x + ax + 3 = 0 is a linear equation of one variable with respect to X. Find the solution of this equation?
2. Xiao Wang mistakenly regards - 2x as + 2x when he solves the linear equation 3a-2x = 15 with respect to X. he obtains the solution of the equation as x = 3 and asks for the solution of the original equation.
3. Many places in China have the custom of the first hundred years of the lunar new year. In one area, the custom is as follows: each family has one person and only visits the neighbors once. In this area, there is a village with only one horizontal row of households and one room for each household. During the Spring Festival of 2009, there were 54 visits. How many households are there in this village?
4. Use two tractors of different sizes to plough 30 mu per hour. It is known that the efficiency of a large tractor is 1.5 times that of a small tractor. How many mu of arable land can a small tractor cultivate per hour?
The above questions should be solved by equations as far as possible, and it's better to write the process of solving the problem.
I want to solve the equation, and I want to solve the whole process of the equation, OK?

1. Because the square + ax + 3 = 0 of equation (A-2) x is a linear equation of one variable, the square term is 0, that is, A-2 = 0. The equation of a = 2 becomes 2x + 3 = 0. The solution is x = - 3 / 2
2. From the meaning of the question, the solution of 3A + 2x = 15 is x = 3. After substituting 3A + 6 = 15, a = 3 is obtained, so the original equation is 3 * 3-2x = 15, that is - 2x = 6, and the solution is x = - 3
3. There are x households. From the meaning of the question, we can see that the number of visits to each household is 2, that is, we should visit 2x. We also know that the households at the second end of the street can only visit one, so the equation is 2x-2 = 54, and the solution is x = 28
4. If a small tractor has x mu of arable land per hour, then a large tractor has 1.5x mu of arable land per hour

1. The price of a commodity is 1000 yuan and the purchase price is 600 yuan. In order to ensure that the profit is not less than 10%, how much discount is the minimum?
2. For discount goods, if they are sold at 60% discount, they will lose 20 yuan. If they are sold at 80% discount, they will earn 15 yuan?

1. Solution: 600 * (1 + 10%) = 660 yuan
1000x=660
x=0.66
Therefore, the minimum discount is 60%
2. Let the commodity be x yuan
0.6x+20=0.8x-15
20+15=0.8x-0.6x
0.2x=35
X = 175 yuan

Xiao Ming ran a lap on the 400 meter track. It is known that he ran 5 meters per second in the first half of the time and 3 meters per second in the second half of the time. How much time did he spend in the second half of the distance? (hint: find out the total time first, and then calculate the time for the second half of the distance.)
This is the original.

First of all, we need to make clear the concept of half time and half distance in the question stem. In fact, it is the time taken by the ball to half the distance 200 meters. If the whole journey takes x seconds X / 2 * 5 + X / 2 * 3 = 400 x = 100, then the first 50 seconds walk 50 * 5 = 250 meters, and the second 50 seconds walk 50 * 3 = 150 meters, then the last half of the journey should take time from the front

Uncle Zhou sold 180 weekly newspapers and some evening newspapers yesterday. It is known that one weekly newspaper costs 1.5 yuan and one evening newspaper costs 0.8 yuan. He earned 235 yuan in total. How many copies of the evening newspaper have been sold

Suppose that the evening paper has sold x copies 1.5 * (180-x) + 0.8x = 235 270-0.7x = 235 35 = 0.7x x = 50 answer: if the evening paper has sold 50 copies, if you are satisfied with this question, please click on the top right corner and "adopt it as a satisfactory answer" ~ if there are any new questions, please don't ask

Solve the mathematical master equation with 2 variables within 10 minutes
When a new batch of goods is ready for sale, it can be sold out in 10 days and make a profit of 10000 yuan. When it is sold out in 8 days, it can make a profit of 8000 yuan. When the goods are stored in 1 day, it costs 100 yuan. How much is the cost and the total price of pre-sale

Suppose the cost is X Yuan and the total pre-sale price is y yuan. From the meaning of the question, we can get the equations: 0.8y-x-100 * 10 = 10000 (1) 0.75y-x-100 * 8 = 8000 (2) (1) - (2), then we can get: 0.05y-200 = 2000, that is: 0.05y = 2200, then: y = 44000

Let's buy an X-box
Unit price plus boxes equals total price
28y=308
Solution: 28y / 28 = 308 / 28
y=11
checking calculation
28y = 308;
still
Check the calculation and write it anywhere

Checking calculation: when y = 11, 28y = 28 times 11 = 308
A: I bought 11 boxes