When the length and width of a rectangle are expanded three times at the same time, the perimeter is 72 cm. What is the original perimeter of a rectangle? Who knows the answer, When the length and width of a rectangle are expanded three times at the same time, the perimeter is 72 cm. What is the perimeter of the original rectangle?

Circumference of rectangle = (length + width) × 2
Three times the length is equal to 3 × length; three times the width is equal to 3 × width
The perimeter of the expanded rectangle is: (3 × length + 3 × width) × 2 = 3 × [2 × (length + width)], which indicates that the perimeter of the expanded rectangle is three times of the original perimeter
The original circumference of the rectangle is: 72 △ 3 = 24 cm

For a three digit number, the sum of the three digits is 17, the number on the hundred digit is 7 times larger than the number on the ten digit number, and the number on the one digit is 3 times of the number on the ten digit number

Let X be the number of ten, then the number of one is 3x, and the number of hundred is (x + 7). From the meaning of the question, we can get: 3x + X + (x + 7) = 17, and the solution is: x = 2, then we can get the number of one is 6, the number of ten is 2, and the number of hundred is 9. A: this three digit number is 926

A 240 meter long train passes through an 884 meter long tunnel at a speed of 1500 meters per minute. How many minutes does it take for the train to enter the tunnel from the front to leave the tunnel from the rear? (two decimal places reserved)

(240 + 884) △ 1500, = 1124 △ 1500, ≈ 0.75 (minutes); a: it takes 0.75 minutes from the front to the rear to leave the tunnel

There is a rectangle, its length and width increased by 8 cm, the area of this rectangle increased by 208 square cm, the original rectangle circumference is () cm
A. 144B. 36C. 72D. 18

As shown in the figure, (208-8 × 8) △ 8 × 2, = (208-64) △ 8 × 2, = 144 △ 8 × 2, = 36 (CM)

Given the function f (x) = 2x-12x, the sequence {an} satisfies f (log2an) = - 2n. (1) find the general term formula of the sequence {an}; (2) prove that the sequence {an} is a decreasing sequence

(1) ∵ f (x) = 2x-12x, f (log2an) = - 2n, ∵ 2log2an-2-log2an = - 2n, an-1an = - 2n, ∵ an2 + 2nan-1 = 0, the solution is an = - n ± N2 + 1, ∵ an & gt; 0, ∵ an = N2 + 1-N, n ∈ n *; (2) prove that an + 1An = (n + 1) 2 + 1 - (n + 1) N2 + 1-N = N2 + 1 + n (n + 1) 2 + 1 + (n + 1)

The taxi fare standard in Hangzhou is as follows: 10 yuan for the part within 3 km (including 3 km), 2 yuan for the part over 3 km, 50% for the part over 10 km, i.e. 3 yuan for each km. (less than 1 km is calculated as 1 km)
How much is Xiao Ming's first 4.3km taxi fare? (4.3km)
If Xiao Ming takes a taxi for 15.2km, how much is the fare?
3 Xiaoming's home is 13.3km away from the school. Xiaoming has 32 yuan with him at the weekend. Is it enough for Xiaoming to take a taxi from the school? If so, how much money is left? If not, how many kilometers must he walk first?

14 yuan;
42 yuan;
3. It's not enough. You can only take 12km, the fare is 30 yuan, the remaining two yuan, and the remaining distance is 1.3km;
If you need to know the detailed process, please ask, please adopt, thank you!
But the actual car need to add one yuan fuel!

As shown in the figure on the right, ABCD is a right angled trapezoid. Take CD as the axis and rotate the trapezoid for one circle to get a revolving body. What is the volume of this revolving body?

First, find a square at 3cm, and its volume is 3 ^ 2 * 3.14 * 3, which is the bottom area multiplied by the height. Then the upper part is a cone, and its volume is a third cylinder, 3 ^ 2 * 3.14

Factorization factor: the third power of a, the second power of X - the third power of a, the second power of y =?

The third power of a, the second power of X - the third power of a, the second power of Y
=The third power of a (the second power of X - the second power of Y)
=The third power of a (x + y) (X-Y)

Given the set a = {x | - 2 ≤ x ≤ 5}, B = {x | m + 1 ≤ x ≤ 2m-1}, if B &; a, find the value range of real number M

A={x|-2≤x≤5}
① If B is an empty set, then M + 1 ＞ 2m-1, that is, m ＜ 2 holds
② When B is not an empty set, M + 1 ≤ 2m-1, m ≥ 2
If B is a subset of a, then M + 1 ≥ - 2 and 2m-1 ≤ 5
The result is - 3 ≤ m ≤ 3
In this case, 2 ≤ m ≤ 3
Therefore, it can be concluded from (1) and (2)
The value range of real number m: m ≤ 3

As shown in the figure, in the pyramid p-abcd, plane PAB ⊥ plane ABCD, BC ⊥ plane pad, ∠ PBC = 90 ° and ⊥ PBA ≠ 90 ° are proved: (1) ad ⊥ plane PBC; (2) plane PBC ⊥ plane PAB

It is proved that: (1) because BC ⊂ planar pad, and BC ⊂ planar ABCD, planar ABCD ∩ planar pad = ad, so BC ⊂ ad. because ad ⊄ planar PBC, BC ⊂ planar PBC, so ad ⊂ planar PBC. (2) from P as pH ⊥ AB in H, because planar PAB ⊥ planar ABCD, and planar PAB ∩ planar ABCD = AB, so pH