Monotone decreasing interval of function y = log (2 ^ 2) x-log (2) x

Monotone decreasing interval of function y = log (2 ^ 2) x-log (2) x

The power exponent of the logarithm base can be reduced to its reciprocal and removed as a coefficient
y=log(2^2)x-log（2）x=[log（2）x] /2 - log（2）x = - [log（2）x] /2
Y = log (a) x increases monotonically on (0, + ∞) when a ＞ 1, obviously 2 ＞ 1
Y = log (2) x increases monotonically on (0, + ∞)
If y = f (x) increases monotonically, then y = KF (x) decreases monotonically when k ＜ 0, obviously - 1 / 2 ＜ 0
Y = - [log (2) x] / 2 decreases monotonically on (0, + ∞)
That is to say, the monotone decreasing interval of the original function is (0, + ∞)

Let f (x) = ax / (x ^ 2 + b) be defined as R, and the extremum at x = 1 is 2
/f(x2)-f(x1)/

∵ the domain of definition is r, ∵ b > 0
F ′ (x) = (AX & # 178; + ab-2ax & # 178;) / (X & # 178; + b) = # 178; = 0  AB ax & # 178; = 0  x = 1, get the extremum 2  AB-A = 0  a ≠ 0, B = 1
∵f(1)=a/(1+1)=2∴a=4,∴f(x)=4x/(x²+1)
(1)|f(x2)-f(x1)|≤|f(x2)|+|f(x1)=|4x2/(x2²+1)|+|4x1/(x1²+1）|
∵x2²+1≥2|x2|, x1²+1≥2|x1|
∴|4x2/(x2²+1)|≤4|x2|/2|x2|=2, |4x1/(x1²+1)|≤4|x1|/2|x1|=2
∴|f(x2)-f(x1)|≤2+2=4
(2)

In the quadrilateral ABCD, BC > Ba, ad = DC, BD is the bisector of the angle ABC
The quadrilateral graph is trapezoid, with a and B on the left and D and C on the right. The graphs on both sides seem to be symmetrical, and D and B are connected as straight lines to divide the quadrilateral into two triangles

Because ad is equal to DC, BD is the bisector of angle ABC, so angle abd is equal to angle DBC, that is, angle ADB is equal to angle BDC, and because do is equal to do, triangle ADO is similar to triangle doc. So their two angles add up to 180 degrees!

When the orbit radius of a man-made earth satellite increases by four times, its cycle will increase by 5.6 × 10 to the fourth power second

The answer is to the fourth power of 5.6 * 10
List Newton's second law twice and the equation comes out

A calculation problem of intelligence
Lao Wang uses a small round stove to bake cakes, but the stove is too small. He can only bake two cakes at a time, and the front and back sides of each cake need to be baked. The time required for each side is half a minute. Now Lao Wang only has one and a half minutes, but he has to bake three cakes. Q: what should he do?

It's simple
Let these three cakes be a, B and C, with 1 and 2 sides
① It took half a minute to bake cake a and cake B at the same time
② Bake 2 cakes a and 1 cake C at the same time, and put the cake B aside for half a minute
③ Finally, a cake baked, and then baked B cake 2 and C cake 2 at the same time, took half a minute
④ At this time, B cake, C cake also baked, used 0 minutes
It's a minute and a half!

The perimeter of a rectangle is 130 cm. If its width increases by 15 and its length decreases by 18, a new rectangle with the same perimeter will be obtained. Find the area of the original rectangle

From the meaning of the title: the length of the original rectangle is 130 ／ 2 ／ (8 + 5) × 8 = 40 (CM), the width is 130 ／ 2-40 = 25 (CM), then 25 × 40 = 1000 (square cm); answer: the area of the original rectangle is 1000 square cm

Simplify the third power of root 8a and the fifth power of root B

√（8a³b^5)
=√(2²×a²×2a×b^4×b)
=2 | a | B & sup2; √ (2Ab), (a, B are the same sign)

An iron bridge is 1000 meters long. A train passes through the bridge. It takes one minute for the train to get on the bridge and then completely cross the bridge. The time for the whole train to be completely on the bridge is 40 seconds (from the rear of the train to the front of the train about to get off the bridge). How about the speed and length of the train?

1 minute = 60 seconds, all pass: S1 = l bridge + L, T1 = 60s, all on the bridge: S2 = l bridge - L, T2 = 40s, let the speed of the train be v m / s, the length of the train be l m, then 60s × v = 1000m + l40s × v = 1000m − L, the solution is: v = 20m / s, l = 20m. That is, the length of the train is 200m, and the speed is 20m / s. answer: the speed of the train is 20m / S; the length is 200m

Cut a round piece of paper and put it together into an approximate rectangle with the width equal to the radius and the area equal. The circumference of the rectangle is 33.12 cm, and the circle is 33.12 cm
What is the area of the paper?

Two lengths are circles and two widths are radii
R = 4 is obtained from 2 π R + 2R = 33.12
The area is π R ^ 2 = 50.24 square centimeter

What's the number of 2 to the power of 2010

The single digit of 2 ^ (4N + a) is the same as that of 2 ^ a~
In fact, any positive number is like this. M ^ (4N + a) is the same as the single digit of m ^ a
So it's 2 ^ 2010 -- 2 ^ 2 = 4
So the single digit is 4