Digital reading How to read the numbers 110-119, For example, can the number 111 be read as 111, 111, or both?

Digital reading How to read the numbers 110-119, For example, can the number 111 be read as 111, 111, or both?

The latter is generally used

The formula of point relation and line symmetry
A point (x, y) is symmetric with respect to the line y = KX + B

Let me give you an example. It'll take a look
Find the symmetric point of point (3,2) about 3x + 5Y + 3 = 0
Let (3,2) be (a, b) with respect to 3x + 5Y + 3 = 0
Then (3,2) and the midpoint of (a, b) ((3 + a) / 2, (2 + b) / 2) are on the straight line
3*(3+a)/2+5*(2+b)/2+3=0 (1)
Because the vector (A-3, b-2) from (3,2) to (a, b) is perpendicular to the straight line, and the direction vector of the straight line can take (- 5,3), there is an equation
-5*(a-3)+3*(b-2)=0 (2)
By solving a and B simultaneously (1) and (2), we can get the symmetric point (a, b)
For a general point (x, y), the symmetric point (a, b) of a given line can be obtained by the same method

Give as much as you have!
There are two types of calculation in 100 questions: off form calculation and column vertical calculation

The number of real roots of the equation x-e ^ (- x) = a is discussed

Let f (x) = x-e ^ (- x),
Since f '(x) = 1 + e ^ (- x) > 0,
So f (x) is an increasing function of R,
When x → - ∞, f (x) → - ∞; when x → + ∞, f (x) → + ∞,
Therefore, for any real number a, the equation f (x) = x-e ^ (- x) = a has a unique real root

Find the largest area of the inscribed rectangle ABCD (points ABCD are all on the ellipse) of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0)?

Let any point (x, y) on the ellipse form an inscribed rectangle with (x, - y), (- x, y), (- x, - y) because it is symmetric on the ellipse. The two variable lengths of the rectangle are 2x and 2Y respectively. So the area of the rectangle is 4xy. 4xy = 2Ab * [2 (x / a) (Y / b)] ≤ 2Ab * [(x / a) &# 178; + (Y / b) &# 178;] = 2

Simple calculation of Volume 2 of grade 4 of primary school
I do my homework! And it's urgent! It's urgent! It's urgent, it's urgent!

8×(125－25) 48＋52÷4 160＋40÷4
(19－11)×125 (12＋42÷7)×5 26×8÷26×8
498＋397 502－399 63－45－55＋137
125×56 302×99＋302 145×89＋145×21
14×500 280÷280 2400÷80 33×20
198＋36 250×400 96÷6 900÷1
80÷16 432－198 125×24 24×5
14.15＋5.87＋5.85 8.07－5.8 ＋0.93 28.93－7.46－5.54
6.38＋5.4＋4.6＋3.62 12.6－3.28＋7.4－5.72 15.047＋8.92－5.047
80－(8.24－6.3＋1.76) 27.62－(7.62＋4.85)
32.74＋12.39－12.74 48.63－12.46－17.54 1437×27＋27×563

Given the function f (x) = {(2b-1) x + B-1, x > 0. - x ^ 2 + (2-B) x, X ≤ 0. If it is an increasing function on R, then the value range of real number B is obtained

A:
x>0,f(x)=(2b-1)x+b-1
x0
x=0
So:
b>1/2
b

The focus and vertex of the ellipse are the focus and vertex of the hyperbola 16x-9y = 144 respectively

Square of 16x - square of 9y = 144
The standard equation is
x^2/9-y^2/16=1
a^2=9,b^2=16
c^2=a^2+b^2=25
Focus (± 5,0), vertex (± 3,0)
So for ellipses
a=5,c=3,b=4
So the elliptic standard equation is
x^2/25+y^2/16=1

A few simple calculation problems
1 and 1 / 4-0.78 + 2.75 5 and 2 / 5 + 2 and 7 / 9-4.4 4.8 + 3 and 5 / 6-1 / 6 + 5 and 1 / 5

1 and 1 / 4-0.78 + 2.75 = 1 + 0.25 + 2.75 - 0.78 = 4 - 0.78 = 3.225 and 2 / 5 + 2 and 7 / 9-4.4 = 5 + 0.4-4.4 + 2 + 7 / 9 = 3 and 7 / 9, 4.8 + 3 and 5 / 6-1 / 6 + 5 and 1 / 5 = 4.8 + 3 + (5 / 6 - 1 / 6) + 5 + 1 / 5 = 4.8 + 0.2 + 8 + 2 / 3 = 13 and 3

Let f (x) be a differentiable function, f (x) > 0, and obtain the derivatives of the following functions. (1)
1. Let f (x) be a differentiable function, and f (x) > 0, find the derivatives of the following functions
（1）y=lnf（2x）
（2）y=f^2（e^x）

（1）y=lnf（2x）
y'=1/f(2x)*[f(2x)]'=f'(2x)*2/f(2x)
=2f'(2x)/f(2x)
(2)y'=2f(e^x)*[f(e^x)]'
=2f(e^x)*f'(e^x)*e^x
=2e^x*f(e^x)*f'(e^x)