Exercise of "if there is no dust" in Lesson 12 of Chinese for Grade 5 of PEP

Exercise of "if there is no dust" in Lesson 12 of Chinese for Grade 5 of PEP

Features: small, wet, light wavelength. Function: weaken the intensity of sunlight, make the sky blue

If there is no dust?
where?

That's what's in

Let a and n be any natural numbers, and prove that a ^ (4N + 1) - a can be divisible by 30
Or prompt some ideas, because my wealth is little, so can't reward, forgive me!

A (a ^ 4-1) divising a ^ (4N + 1) - A
a(a^4-1)
=a(a^2-1)(a^2+1)
=a(a-1)(a+1)(a^2+1-5+5)
=a(a-1)(a+1)(a-2)(a+2)+5a(a-1)(a+1)
=(a-2)(a-1)a(a+1)(a+2)+5a(a-1)(a+1)
The above formula is the sum of two continuous products. The first is the product of five consecutive integers, which is certainly a multiple of 30. The second is the product of five and three consecutive integers, which is also a multiple of 30

If the image of exponential function y = f (x) passes through (2,9), then f (- 1)=

The exponential function must be y = a ^ x, (a > 0 and a is not equal to 1);
From the title: A ^ 2 = 9, so a = 3;
So: y = f (x) = 3 ^ X
So: F (- 1) = 1 / 3

You want to know what someone will do next
Help me!

You want to know what someone is going to do next

How to factorize x ^ 2-mx + 4 how to factorize x ^ 2 - (M + 1 / M) x + 1

x²-mx+4
=（x-（m+√（m²-16）/2））（x-（m-√（m²-16）/2））
x^2-（m+1/m）x+1
=（x-1/m）（x-m）

Problems in application of quadratic equation of one variable
(6) The ratio of length to width of a cuboid is 5:2, the height is 5cm, and the surface area is 40cm & sup2;. Draw this trapezoid
(7) How can a 50m long fence be used to form a rectangular field with an area of 50cm & sup2?
(8) After two recent interest rate cuts, a bank has reduced the annual interest rate of one-year deposits from 2.25% to 1.98%. What is the average percentage of each interest rate cut (the result is written in the form of a%, where a retains two decimal places)?
(10) How can a 40cm long rope form a rectangle with an area of 75cm & sup2;? Can it form a rectangle with an area of 191cm & sup2;? If so, explain the enclosure method; if not, explain the reason

6) The ratio of length to width of a cuboid is 5:2, the height is 5cm, and the surface area is 40cm & sup2;. Draw this trapezoid
(7) How can a 50m long fence be used to form a rectangular field with an area of 50cm & sup2?
(8) After two recent interest rate cuts, a bank has reduced the annual interest rate of one-year deposits from 2.25% to 1.98%. What is the average percentage of each interest rate cut (the result is written in the form of a%, where a retains two decimal places)?
(10) How can a 40cm long rope form a rectangle with an area of 75cm & sup2;? Can it form a rectangle with an area of 191cm & sup2;? If so, explain the enclosure method; if not, explain the reason

The swimming pool is 50m long and 16m wide. 1m3, which can hold 1000 liters of water. If the water level rises by 3cm, how many liters of water should be injected

3 cm = 0.03 m
50 × 16 × 0.03 = 24 M3
24 m3 = 24000 L

One third of an hour can walk one and a fifth of a kilometer. According to this calculation, it takes () hours to walk four fifths of an hour and () kilometers to walk three fourths of an hour

According to this calculation, it takes (2 / 9) hours to walk four fifths of an hour and (2 / 7 / 10) kilometers to walk three fourths of an hour
4 / 5 △ 1 / 5 △ 1 / 3) = 2 / 9 (hours)
(1 and 1 / 5 △ 1 / 3) × 3 / 4 = 2 and 7 / 10 (km)

Ancient poems, sayings, proverbs and idioms about bridges

As the saying goes: on the rocking single wooden bridge, the intense undercurrent makes the strength of both sides reach the extreme. The unbalanced strength will call for the destructive storm, and the time of sadness is coming. When the boat arrives at the bridge, it will go straight. On the Wei bridge, it will go to xiliutun to watch the troops