Find the range of function y = Sin & sup2; X + cosx + 1, X ∈ [- π / 3, π / 3]

Find the range of function y = Sin & sup2; X + cosx + 1, X ∈ [- π / 3, π / 3]

y=1-cos²x+cosx+1
=-cos²x+cosx+2
Let cosx = t, then t ∈ [1 / 2,1]
So, y = - T & # 178; + T + 2, t ∈ [1 / 2,1]
For quadratic function with opening downward, the axis of symmetry is t = 1 / 2
Therefore, when t = 1 / 2, y has a maximum value of 9 / 4;
When t = 1, y has a minimum value of 2
Therefore, the range is [2,9 / 4]

Finding the range of function y = sin X-2 / cos X-2

y(cosx-2)=sinx-2
ycosx-sinx=2y-2
√ (Y & # 178; + 1) sin (x-t) = 2y-2, where Tan = y
So sin (x-t) = (2y-2) / √ (Y & # 178; + 1)
Because | sin (x-t)|

How many square meters is 7 * 10 minus 7 square millimeter equal to

0.00000000000001 square meters

Xiao Ming's father plans to deposit the balance of RMB 10000 in the bank and withdraw it in three years
(1) How many different storage methods are there if the storage period is at least one year? Please write as many as possible
(2) According to the current one-year, two-year and three-year interest rates and interests, please work with some students to work out the real interest of different storage methods, and compare which method has the most real interest

(1) There are four different ways to save at least one year. One is to save for one year, three times; two is to save for one year, then two years; three is to save for two years, then one year; four is to save for three years
(2) According to the current one-year, two-year and three-year interest rates and interest tax, the interest earned by different storage methods is as follows. The fourth method has the most interest
The interest rates of one-year, two-year and three-year are 2.25%, 2.79% and 3.33% respectively, and the interest tax is zero
1. Deposit for one year, three times respectively, with interest of 690.30;
2. One year first and two years later, the interest is 795.56;
3. The interest is 795.56 for two years and one year later;
4. For three years, the interest is 999

As shown in the figure, Xiao Hong cuts a 4 cm wide strip from a square, and then cuts a 5 cm wide strip from the remaining rectangular paper along the direction parallel to the short side. If the area of the strips cut twice is exactly the same, what is the area of each strip? What is the area of the original square?

Suppose the side length of the square is xcm, then according to the meaning of the question: 4x = 5 (x-4), the solution is: x = 20. Then 4x = 80 (cm2), 20 × 20 = 400 (cm2). Answer: the area of each strip is 80cm2, the area of the original square is 400cm2

[please describe the steps in detail] in △ ABC, three sides a > b > C, and 2b = a + C, the coordinates of vertex A and C are respectively
(ellipse) in △ ABC, three sides a > b > C, and 2b = a + C, the coordinates of vertex A and C are (- 1,0), (1,0), respectively. Find the trajectory of vertex B
I don't know how to find the standard equation after reading the answer, and finally get rid of the magic horse

B = 2A + C = 2B = 4 ellipse note that half of the ellipse needs to dig out 3 points intersecting with the XY axis, which should be C = 1 of the ellipse. Then when a, B, C = 2 (of course, this is only the equation, which actually needs to dig out this point), B = root 3 of the ellipse, so the equation of a = 2 of the ellipse is (x ^ 2) / 4 + (y ^ 2) / 3 = 1, and the condition is XB > C, that is | B

A math problem of grade seven
The room temperature of a cold storage in a freezing factory is - 12 ℃. There is a batch of food that needs to be refrigerated at - 28 ℃. If the temperature drops by 4 ℃ every hour, how many hours can it reach the required temperature?

[(- 12) - (- 28)] 4 = 4 hours

Cut out the largest circle on a square piece of paper with an area of 81 square decimeters. What's the area of this circle
The side length of a square is 9. I know, but how can I get it?
I'm hungry for other formulas~

Let the side length of a square be X,
From the question: X & sup2; = 81, x = 9
If the area of the circle is the largest, the side length of the square is equal to the diameter of the circle,
The radius of the circle is r = 9 / 2 = 4.5
The area of the circle is s = Πr & sup2; = 63.6 square decimeters

As shown in the figure, in RT △ ABC, ∠ C = 90 ° and AC = 12ab. Verification: ∠ B = 30 °. Please fill in the blanks to complete the following proof. Proof: as shown in the figure, make the center line CD on the hypotenuse of RT △ ABC, then & nbsp; CD = 12ab = ad (???????????) ∵ AC = 12ab, ∵ AC = CD = ad & nbsp; that is, ∵ ACD is an equilateral triangle=______ °．∴∠B=90°-∠A=30°．

It is proved that: as shown in the figure, if we make the middle line CD on the hypotenuse of RT △ ABC, then CD = 12ab = ad (the middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse). ∵ AC = 12ab, ∵ AC = CD = ad & nbsp; that is, ∵ ACD is an equilateral triangle. ∵ a = 60 °. ∵ B = 90 ° - a = 30 °. So the answer is: the middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse; 60

An insurance calculation problem,
If the net premium income of the company is 2 million yuan and the compensation incurred is 1.6 million yuan, then the compensation ratio is ()
A．60％ B．75％ C．80％ D．50％
23. Next to question 22, the compensation accepted by the company should be ()
A. RMB 50000, RMB 51000, RMB C2000 and RMB d300
24. Next to question 22, if the compensation incurred is 2.7 million yuan, the compensation accepted by the company should be ()
A. 1 million yuan b.1.2 million yuan c.8 million yuan d.6 million yuan
25. Next to question 22, if the compensation incurred is 2.7 million yuan, the compensation paid out of the company should be ()
A. 1.2 million yuan b.1.5 million yuan c.1.6 million yuan D.1 million yuan

According to the contract, only when the compensation ratio exceeds 75% can the accepting company be responsible for the compensation. The upper limit of the compensation ratio of the accepting company is 50%, and the upper limit of the compensation amount is 1.2 million yuan