Can a number of and the unmber of add uncountable nouns?

Can a number of and the unmber of add uncountable nouns?

A number of refers to a large number, so it can be followed by an uncountable noun, while the unmber of means The number of people has a number of people has a number of people has a number of people has a number
Amount of plus countable noun or uncountable noun
An amount of + uncountable noun
Amount of is wrong. It should become amounts of or an amount of + uncountable noun
Amount of + n
Amount to + V
It means something different
Is the predicate after neither of singular or plural?
Look at the noun after of,
1. Uncountable nouns and singular predicates
2. Plural noun, predicate can be singular or plural
Given function f (x) = LG (x ^ 2 + 2x + a)
(1) If the domain of F (x) is r, find the range of real number a
(2) If the range of F (x) is r, find the range of real number a
1. The logarithmic true number should be > 0, that is, X & # 178; + 2x + a = (x + 1) &# 178; + A-1 > 0
Where (x + 1) &# 178; + A-1 is a parabola with the opening upward and the axis of symmetry x = - 1, so as long as the lowest point is greater than 0, that is, the domain of definition is r when the parabola does not intersect the X axis. In conclusion, A-1 > 0, that is, a > 1 is required
2. The range of value is required to be r, because X & # 178; + 2x + A is a parabola with the opening upward, so x & # 178; + 2x + A is required to take all the values in (0, + ∞). From the image, the parabola and X axis should have an intersection point, that is, A-1 ≤ 0, that is, when a ≤ 1, the range of F (x) is r
1) If r = > x ^ 2 + 2x + A is greater than 0, then (x + 1) ^ 2 + A-1 > 0 = = > A-1 > 0 = = > a > 1
2) If the range is r, then x ^ 2 + 2x + a
The collective noun staff is the subject, and the predicate verb is singular or plural. Why?
Staff refers to a whole, not a single person. If a company is a staff, two companies are two staff
We & nbsp; want & nbsp; more & nbsp; staff
Staff is a collective noun, not plural, when it is used to refer to "staff". When it is used as the subject, if it emphasizes the whole, the predicate verb is singular; if it emphasizes the individual member, the predicate verb is plural
For example: the & nbsp; Staff & nbsp; wore & nbsp; big & nbsp; sunny & nbsp; smiles
&The & nbsp; teaching & nbsp; Staff & nbsp; of & nbsp; this & nbsp; College & nbsp; is / are & nbsp; excellent
Given the function y = LG (AX2 + 2aX + 1): (1) if the domain of definition of the function is r, find the value range of a; (2) if the domain of definition of the function is r, find the value range of A
(1) When a ≠ 0, there should be a ＞ 0 and △ = 4a2-4a ＜ 0, and the solution is a ＜ 1. Therefore, the value range of a is [0,1). (2) if the value range of the function is r, then AX2 + 2aX + 1 can take all positive integers, a ＞ 0 and △ = 4a2-4a ≥ 0. The solution is a ≥ 1, so the value range of a is [1, + ∞)
What's the difference between each and every?
Every student in our school works hard. Every student may have one book
Given the point a (1,0), let P (x, y) be the function f (x) = 2x / (x + 1) (x)
F (x) = 2x / (x + 1), let P (x, 2x / (x + 1)), in fact, only the value of X is required
|AP | = √ (x-1) ^ 2 + 4x ^ 2 / (x + 1) ^ 2, from the inequality a ^ 2 + B ^ 2 ≥ 2Ab, we can see that
|AP | get the minimum if and only if (x-1) ^ 2 = 4x ^ 2 / (x + 1) ^ 2, x = ± √ 2-1, x = ± √ 2 + 1
Therefore, there are four points to meet the requirements, namely (√ 2-1,2 - √ 2), (- √ 2-1,2 + √ 2)
（√2+1,√2）,（-√2+1,-√2）
Because of X
Just write the answer
Is every, each, and each of singular or plural
(1) Every always modifies a singular noun followed by a singular verb
(2) Each is used as an adjective to modify a singular noun followed by a singular verb. As a pronoun, it is used alone, followed by a singular verb. After a plural noun and pronoun, it is used as an appositive, followed by a plural verb
(3) Each of + noun plural as the subject, after the predicate verb with the singular
Given that f (x) = 2x / (1 + x ^ 2) (x ∈ R), this paper discusses the properties of the function f (x), makes a graph and writes out the concrete process
First of all, we can judge that f (x) is an odd function & nbsp; because f (- x) = - 2x / (1 + x ^ 2) = - f (x), the graph is symmetrical about the origin, f (0) = 0f '(x) = (2-2x ^ 2) / (1 + x ^ 2) ^ 2 = 2 (1-x ^ 2) / (1 + x ^ 2) ^ 2F' (x) = 4x (x ^ 2-3) (x ^ 2 + 1) / & nbsp; (1 + x ^ 2) ^ 4 (we can ignore the equations that are always greater than 0, so I will not write those, only write the equations related to the key inflection point, When you write questions, don't forget to add) Let f '(x) = 0 & nbsp; solve X1 = - 1, X2 = 1 & nbsp; find the slope of function f (x) is 0, two points (- 1, - 1), (1,1) Let f' (x) = 0 & nbsp; solve X3 = - radical 3, X4 = radical 3 for f '(x) (negative infinity, - 1) and (1, positive infinity) on f' (x) & lt; 0 & nbsp; function f (x) monotonically decreases (- 1,1) on f '(x) & gt; 0 function f (x) monotonically increases for f' (x) (negative infinity, We can see that f '(x) is monotonically increasing (negative root 3, root 3) & lt; f' (x) & lt; 0 & nbsp; we can see that f '(x) is monotonically decreasing. Considering 1, we can find the limit of F (x) on negative infinity first & nbsp; which can be obtained as 02 & nbsp; (negative infinity, negative root 3) & lt; 0 & nbsp; function f (x) monotonically decreasing & nbsp;, f' '(x) & gt; 0 & nbsp; It is known that f '(x) is monotonically increasing & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; f (x) monotonically decreasing shape is convex & nbsp; 3 & nbsp; (negative radical 3, - 1) & nbsp; & nbsp; f' (x) & lt; 0 & nbsp; function f (x) monotonically decreasing & nbsp; & nbsp; f '' (x) & lt; 0 & nbsp; it is known that f '(x) monotonically decreasing shape is concave & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; f (x) monotonically decreasing shape is concave & nbsp; 4 & nbsp; (- 1,0) f '(x) & gt; 0 function f (x) monotonically increasing & nbsp; f' (x) & lt; 0 & nbsp; we can see that f '(x) is monotonically decreasing & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; f (x) monotonically increasing shape is concave & nbsp; & nbsp; & nbsp; we can draw the left figure, and then draw the right half according to the parity (figure I try my best, to this extent, if you don't understand it, you can hi me)