On the words of quantity in English There are some words for quantity in English For example: a number of; the number of; a great many; little; fee There are a lot more that we don't list What are the words of quantity? Whether they modify countable nouns or uncountable nouns; what about the singular and plural predicates And the singular and plural of the predicate!

1. A good / great deal of + uncountable V single three a large / small sum of money V single three large / small sums of money V single three a large / small amount of uncountable V single three large / small amounts of uncountable V single three 2
What are the words of quantity and degree in English?
Please arrange them in order of size
There are many phrases in English, which can be divided into the following three categories according to their usage: 1. Modifier nouns: many, a number of, a few, many a, vertical, etc
1. A good / great deal of + uncountable V simple three
A large / small sum of money V
Large / small sums of money V
A large / small amount of uncountable V single three
Large / small amounts of uncountable V single... Expansion
1. A good / great deal of + uncountable V simple three
A large / small sum of money V
Large / small sums of money V
A large / small amount of uncountable V single three
Large / small amounts of uncountable V single three
2. A number of plural nouns V plural
Numbers of noun plural V plural
The number of noun plural V simple three
A good / great many + noun plural V simple three
A good / great many of + the / these / those / one's + noun plural V simple three
3. A variety of plural nouns / uncountable nouns V simple three
A supply of plural noun / uncountable noun V simple three
A quantity of plural noun / uncountable noun V simple three
A mass of plural noun / uncountable noun V simple three
A measure of plural noun / uncountable noun V simple three
Measures of plural / uncountable plural
Masses of noun plural / uncountable noun V plural
Supplies of plural noun / uncountable plural noun V
Quantities of plural noun / uncountable noun V plural
Variations of plural noun / uncountable plural noun V
Plural of noun V plural
Plury of uncountable noun V single three denotes quantity:
1、 There are many phrases in English, which can be divided into three categories according to their usage
1. Modifier nouns: many, a number of, a few, many a, several, etc. Many a means many, but many a is followed by a countable noun singular
Many a student has such a question.
A number of students have passed the exam.
Several days ago, I met him in the park.
2. Modify uncountable nouns: much, a great deal of, a large amount of, etc.
We can get a great deal of (a large amount of) information from Internet.
3. It can modify both countable nouns and uncountable nouns: a lot of (lots of); plenty of; a large quantity of, etc.
Plenty of the water is polluted.
Many rivers are polluted.
2、 The usage of "a fee, a little"
1. Both "fee" and "a fee" modify countable nouns. "Few" means "almost none", which means negative; a "few" means "some, a few", which means positive; and "quite a few = many" means "many". For example:
I have eaten a few apples today.=I have eaten many apples today.
He has few friends.
2. Little and a little both modify uncountable nouns. "Little" means "very few" and "a little" means "some". For example:
I have little money.
I have a little work to do
"Quite a little = many" means "many".
3、 The difference between a number of and the number of:
A number of is equivalent to some, a few; a great / large number of is equivalent to many, quite a few; the number of refers to " "The number of people.". For example:
The number of the students in our school is 5000.
A number of students have passed the exam.
also:
Three of good / degree
A large / small sum of money V
Large / small sums of money V
A large / small amount of uncountable V single three
Large / small amounts of uncountable V single three
2. A number of plural nouns V plural
Numbers of noun plural V plural
The number of noun plural V simple three
A good / great many + noun plural V simple three
A good / great many of + the / these / those / one's + noun plural V simple three
3. A variety of plural nouns / uncountable nouns V simple three
A supply of plural noun / uncountable noun V simple three
A quantity of plural noun / uncountable noun V simple three
A mass of plural noun / uncountable noun V simple three
A measure of plural noun / uncountable noun V simple three
Measures of plural / uncountable plural
Masses of noun plural / uncountable noun V plural
Supplies of plural noun / uncountable plural noun V
Quantities of plural noun / uncountable noun V plural
Variations of plural noun / uncountable plural noun V
Plural of noun V plural
Plenty of uncountable noun V single three
There are many ways to express degree. Generally, adjectives and adverbs can express degree.
He is a good student
What are the words in Business English for increasing number
increase
push up
elevate
skyrocket
roaring
high gear.
Ask: there are many more, please find as many as you can
The function f (x) = Log1 / 2 (x ^ 2 + 4x + 4) is an increasing function in the interval
First, define the field: x ^ 2 + 4x + 4 > 0, (x + 2) ^ 2 > 0, X is not equal to - 2
Let t = x ^ 2 + 4x + 4 be an internal function, t = (x + 2) ^ 2, t be a decreasing function on (negative infinity, - 2), and an increasing function on (- 2, positive infinity)
Y = log0.5 (T), because 0
As shown in the figure, there are three points a, B, C, ab = 1 / 2Ac on the known number axis, and the corresponding number of point C is 200
(1) If BC = 300, find the number corresponding to point a; (2) under the condition of (1), the moving points P and Q move to the left from two points a and C respectively, and the moving point R moves to the right from point a. the velocities of points P, Q and R are 10 unit length per second, 5 unit length per second and 2 unit length per second respectively. Point m is the midpoint of line PR, and point n is the midpoint of line RQ, (3) under the condition of (1), if the corresponding numbers of points E and D are - 800 and 0 respectively, the moving points P and Q start from E and D and move to the left at the same time. The velocities of points P and Q are 10 unit length per second and 5 unit length per second respectively. Point m is the midpoint of line PQ, and point Q moves from point d to point a, Is the value of qc-am changed? If not, calculate the value; if not, explain the reason
This is from Xuezhi newspaper. I did it right myself. Here is the correct solution
1.∵BC=300,AB=AC/2,∴AB=600
The point C corresponds to 200
A 200-600=-400
2. Set X seconds
MR=（10+2）*x/2
RN=600-(5+2)*x/2
MR=4RN
Solution x = 60
3. Let the elapsed time be y
Then PE = 10Y, QD = 5Y
So the PQ point is [0 - (- 800)] + 10y-5y = 800 + 5Y
Half is (800 + 5Y) / 2
So the AM point is (800 + 5Y) / 2 + 5y-400 = 15y / 2
QC = 200 + 5Y
So 3qc / 2-AM = 3 (200 + 5Y) / 2-15y / 2 = 300 is the fixed value
It is known that f (x) is a monotone function in its domain of definition. It is proved that f (x) has at most one zero point
How to prove it!
Counter proof: suppose there are two zeros X1 and X2, such that f (x1) = f (x2) = 0, let x1
It can be disproved by assuming that there are two zeros, and then negating the hypothesis according to the definition of monotone function
If the function y = f (x) has an inverse function, then the equation f (x) = C (c) is a constant
How many real roots does the equation have
The answer to this question is that there is at most one real root,
There is an inverse function, which is a one-to-one function y = ax + B
y=k/x
There may or may not be one
So can it be understood that there is no real root
C=0,
If y = K / x, there is no solution, and there is no real root
So there is at most one root
A root
Because a function has an inverse function, it is monotone.
A function has an inverse function
Then each Y corresponds to only one X
And every x corresponds to only one y
So there is at most one real root
There are no real roots
For example, y = f (x) is one of the hyperbolas
Then f (x) = 0 has no real root
But there are still inverse functions
You can see it by drawing
Y = f (x) can be infinitely close to the x-axis, but there is no intersection.
As shown in Figure 1, there are three points a, B and C on the given number axis, AC = 2Ab, and the corresponding number of point a is 400
(1) if AB = 600, find the distance from point C to the origin;
(2) under the condition of (1), the moving points P, Q and R start from C and a at the same time, where P and Q move to the right and R move to the left, as shown in Figure 2. It is known that the velocity of point q is 2 times that of point R, less than 5 unit length / s, and the velocity of point P is 3 times that of point R. after 20 seconds, the distance between points P and Q is equal to that between points Q and R, so the velocity of moving point q is calculated
(3) Under the condition of (1), O is the origin, and the moving points P, t and R start from C, O and a at the same time, where P and t move to the left and R to the right, as shown in Figure 3. The velocities of points P, t and R are 20 unit length / s, 4 unit length / s and 10 unit length / s respectively. In the process of movement, if point m is the midpoint of line Pt and point n is the midpoint of line or, Then, does the value of PR + ot divided by Mn change? If it does not change, find the value; if it changes, explain the reason
Understand the newspaper do not do (1) ∵ BC = 300 AB = AC / 2 ∵ AB = 600 ∵ C point corresponding to 200 a 200-600 = - 400 2. In x seconds Mr = (10 + 2) * x / 2 RN = 600 - (5 + 2) * x / 2 Mr = 4rn solution x = 60 3. After time set Y PE = 10 years
The known function f (θ) = cos ^ 2 θ + 2msin θ - 2m-2, m ∈ R
If cos ^ 2 θ + 2msin θ - 2m-2
Let sin θ = t, then the problem is transformed into: "T ^ 2-2mt + 2m + 1 ＞ 0, when - 1 ≤ t ≤ 1, the value range of the real number m is determined." the following discussion is divided into three cases. For convenience, we remember that f (T) = T ^ 2-2mt + 2m + 1 = (T-M) ^ 2-m ^ 2 + 2m + 1 (1) if M > 1, we want to make T ^ 2-2mt + 2m + 1 ＞ 0, when - 1 ≤ t ≤ 1, the value range of the real number m is determined
cos^2θ+2msinθ-2m-2
Inverse function of y = (Log1 / 2) 2-4 (x ≥ 2)
() is quadratic
x≥2,log1/2 x≤-1,( log1/2 )^2≥1,y=( log1/2 )^2-4≥-3.
The domain of inverse function y = (Log1 / 2) ^ 2-4 is [- 3, + ∞)
After changing the logarithm into index, we can get: y = (1 / 2) ^ (- √ x + 4)
（x≥-3）.

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