A square is divided into three rectangles of the same size, one of which has a circumference of 16 cm. How many square centimeters is the original square area

A square is divided into three rectangles of the same size, one of which has a circumference of 16 cm. How many square centimeters is the original square area

Let the side length of a square be 3x
Then the length of the rectangle is 3x and the width is X
(3x+x)*2=16
x=2
So the side length of the square is 6 cm and the area is 36 square cm

Given the function f (x) = 2 ^ X-2 ^ - x, the sequence {an} satisfies f (log2an) = - 2n
(1) Find the formula of sequence {an}
(2) It is proved that the sequence {an} is a decreasing sequence

f(log2an)=2^(log2an)-2^(-log2an)=an-1/an=-2n
=>an^2+2n*an-1=0
Because log2an makes sense
So an > 0
So an = √ (n ^ 2 + 1) - n
an =√(n^2+1) -n =1/[√(n^2+1) +n]
So obviously there is a (n + 1)

Jinzhou taxi charging standards are as follows: within 2 kilometers (including 2 kilometers) 5 yuan; more than 2 kilometers, 1.2 yuan per kilometer
(1) Write out the functional relationship between Y (yuan) and X (km);
(2) How much will you pay if you drive 4 km by taxi?
(3) If someone pays 11 yuan, how many kilometers does the taxi drive?

1. When 0 ＜ x ≤ 2, y = 5
When x > 2, y = 5 + 1.2 (X-2)
2. When x = 4, y = 5 + 1.2 × 2 = 7.4
3. When y = 11, 5 + 1.2 (X-2) = 11
x=7
The distance of taxi is more than 6 km and less than or equal to 7 km

What are the changes in the height and area of a rectangle nailed by a wooden bar into a parallelogram? Why?

Both the height and the area are smaller
Because the area of the parallelogram = base * height, and because the height of the rectangle becomes smaller in order to keep the perimeter unchanged in the process of drawing into the parallelogram, the area becomes smaller

Given x + 3x + 1 = 0, find the value of X + 1 / X and X + 1 / 4

x^2+3x+1=0
x^2+1/x^2=((-3x-1)^1+1)/(-3x-1)
=(9x^2+6x+2)/(-3x-1)
=(-27x-9+6x+2)/(-3x-1)=7
x^4+1/x^4=(x^2+1/x^2)^2-2=7^2-2=47

1. If the real number x, y satisfies the square of X + the square of Y - 2x + 4Y = 0, then what is the maximum value of x-2y
2. Point P is on the square of a: x + the square of y-8x-4y + 11 = 0, point q is on the square of B: x + the square of Y + 4x + 2Y + 1 = 0, then what is the minimum value of | PQ |
3. If the real number x, y satisfies the square of (X-2) + the square of y = 1, then what is the maximum value of Y divided by X

1. Method 1: let t = x-2y, the problem is transformed into the maximum value problem when the circle x ^ 2 + y ^ 2-2x + 4Y = 0 and the straight line t = x-2y have a common point. The method can be solved by the distance from the center of the circle to the straight line is not greater than the radius
Method 2: substituting X or Y in t = x-2y into the equation x ^ 2 + y ^ 2-2x + 4Y = 0 to obtain the quadratic equation of one variable about X or Y, and using the discriminant greater than or equal to 0 to find the maximum value of T
Method 3: from x ^ 2 + y ^ 2-2x + 4Y = 0, let x = √ 5cos θ + 1, y = √ 5sin θ - 2. Substitute x-2y into trigonometric function to get the maximum
Answer: the maximum value is 10
2. From geometric knowledge, the minimum value of | PQ | is the center distance of two circles minus the radius of two circles
3. Method 1: let k = Y / x, then the problem is transformed into the problem of the maximum slope of the line between the point and the origin on the circle (X-2) ^ 2 + y ^ 2 = 1
Method 2: substituting y = KX into the equation (X-2) ^ 2 + y ^ 2 = 1, eliminating y to get the quadratic equation of one variable about X, and using the discriminant greater than or equal to 0 to get the maximum value
Answer: √ 3 / 3

As shown in the figure, if the perimeter difference between △ AOB and △ AOD is 8, and ab: ad = 3:2, what is the perimeter of ▱ ABCD?

∵ quadrilateral ABCD is a parallelogram, ∵ ob = OD, ∵ the perimeter of AOB is 5 larger than that of △ AOD, ∵ OA + ob + AB) - (OA + od + AD) = ab-ad = 5; and ∵ AB: ad = 3:2, ∵ AB = 15, ad = 10

It is known that a * 3 / 4 = 11 / 12 * b = 4 / 3 * C =, and a, B, C, D are not equal to zero. Please arrange a, B, C, D from large to small, 3Q
And explain the reason for this arrangement

A / D = 4 / 3, B / D = 12 / 11, C / D = 3 / 4, D / D = 1 4 / 3 > 12 / 11 > 1 > 3 / 4, so a > b > d > C

In order to speed up the modernization of teaching methods, a school plans to purchase a batch of computers. It is known that the quotation of company a is 5800 yuan per computer, and the preferential condition is to buy more than 10 computers, then 70% of the quotation will be calculated from the 11th computer. The quotation of company B is 5800 yuan per computer, and the preferential condition is 85% of the quotation. If you are the person in charge of the school, you should pay more attention to the computer brand and quality And after-sales service, how do you choose? Please give reasons

If the number of computers purchased is less than 11, it is obvious that company B has a discount, but company a has no discount, so company B chooses company B. if the number of computers purchased is more than 10, the school needs to purchase x computers, then it needs to pay [10 × 5800 + 5800 (X-10) × 70%] yuan to company a, and 5800 × 85% X Yuan to company B (X-10) × 70% < 5800 × 85% & nbsp; X solution: x > 20; 2) if company B offers preferential treatment: 10 × 5800 + 5800 (X-10) × 70% > 5800 × 85% & nbsp; If the two companies have the same preference, then 10 × 5800 + 5800 (X-10) × 70% = 5800 × 85% x = 20. A: when the number of computers purchased is less than 20, company B is more favorable; when the number of computers purchased is just 20, either company will choose; when the number of computers purchased is more than 20, company a is more favorable

Cut the largest circle on a square piece of paper with a circumference of 24 cm. Is the circumference of this circle 12.56

A square with a circumference of 24 cm has a side length of 24 / 4 = 6 cm
The maximum radius of the circle is 6 / 2 = 3cm
The circumference of the circle is 2 * pi * 3 = 18.84 cm