In space rectangular coordinate system, equation 3x-4y-12z-14 = 0 represents plane, P (0,0,1) represents point By analogy with the formula of the distance from the midpoint to the straight line in the plane rectangular coordinate system, we can get that the distance from the point P to the plane is

In space rectangular coordinate system, equation 3x-4y-12z-14 = 0 represents plane, P (0,0,1) represents point By analogy with the formula of the distance from the midpoint to the straight line in the plane rectangular coordinate system, we can get that the distance from the point P to the plane is

The distance from P (0,0,1) to the plane 3x-4y-12z-14 = 0 is
d=|3*0-4*0-12*1-14| / √(3^2+4^2+12^2)= 2 .

The vertex of the parabola is the center of the hyperbola where the square of 16 x minus the square of 9y equals 144, and the focus is the left vertex of the hyperbola?
16x²-9y²=144
x²/9-y²/16=1
a=3,b=4,c=√(a²+b²)=5
（1）
Hyperbolic eccentricity: e = C / a = 5 / 3
Hyperbolic standard equation: X & sup2 / 9-y & sup2 / 16 = 1
（2）
Left vertex of hyperbola: (- 3,0)
Let the standard equation of parabola be y & sup2; = 2px
Then, P / 2 = - 3, P = - 6
So the parabolic equation is Y & sup2; = - 12x
Why let the standard equation be y & sup2; = 2px
Weak question Y & sup2; = 2px
What does P stand for? What does Y stand for? What does x stand for? If the right vertex becomes the focus, what does the formula become?

The focus is the vertex of the hyperbola
The parabola is determined as y ^ 2 = 2px
Left vertex
Determine the parabola form as: y ^ 2 = - 2px

Is there a sign for the countdown? Thank you

According to my experience, certainly not

Let loga (x) = logb (y) = 2, a + B = 2, then the value range of X + y is?

Obviously, x = A & # 178;, y = B & # 178;
x+y=(a+b)²-2ab=4-2ab
a+b=2
And the base a > 0, b > 0
SO 2 = a + b > = 2 √ ab
√ab2

If the solution set of the inequality ax ＾ 2 + BX + C ＜ 0 about X axis is empty, then A.A > 0, B ＾ 2-4ac > 0, b.a0, B ＾ 2-4ac > 0, b.a0, and B ＾ 2-4ac is less than or equal to 0
D.a0
How to do it, write the process

Let f (x) = ax ^ 2 + BX + C. from the title, we know that f (x) > or = 0 is always true on R. therefore, we can draw the image of F (x) according to this, then we can know that only a > 0 and B ^ 2-4ac

Can I omit the multiplication sign before and after the brackets? For example: (80 + x) × 3.2 = 480 can be written as (80 + x) 3.2 = 480

It seems that we can't omit the multiplier. The unknowns should be before the numbers. It can be written as 3.2X + 3.2x80 = 480 Baidu map

The usage difference of the three pronunciations of tired

I've been working all day and I'm very tired
Lei three voices: he has been scarred, don't blame him
Lei two voices: this year's orchard is really fruitful. It's a big harvest!
The difference is four tones and three tones and two tones

If real numbers x and y satisfy x2 + y2-2x + 4Y = 0, then the maximum value of x-3y is 0______ ．

Let x-3y = t, then | 1 − 3 × (− 2) − t | 10 ≤ 5 is changed to | t − 7 | ≤ 52, and the solution is 7 − 52 ≤ t ≤ 7 + 52, and the maximum value of | x-3y is 7 + 52

75 written math problems in Volume 1 of grade 4
Please! I'm in a hurry to use it! If I don't do well in the exam, I'd better bring the answers! Please help me!

145×13= 147×12= 258×46= 325×26= 237×83=
322×35= 54×145= 36×254= 83×217= 32×164=
25×328= 12×124= 85×215= 28×153= 85×142=
16×134= 34×246= 160×30= 220×40= 160×60=
180×50= 290×30= 460×80= 360×12= 390×14=
350×15= 320×16= 280×15= 430×26= 36×120=
18×230= 26×320= 23×340= 27×150= 87×410=
106×30= 206×40= 956×30= 305×50= 108×90=
209×6= 145×12= 135×12= 176×46= 325×26=
237×83= 322×35= 54×145= 36×254= 83×217=
43×129= 32×164= 25×328= 12×124= 85×215=
28×153= 85×142= 16×134= 34×246= 160×30=
220×40= 160×60= 180×50= 290×30= 460×80=
360×12= 390×14= 350×15= 320×16= 280×15=
430×26= 36×120= 18×230= 26×320= 23×340=
27×150= 87×410= 106×30= 206×40= 208×30=
305×50= 108×90= 209×60= 73×207= 26×108=
640÷80= 15×10= 12×11= 160×30= 220×40=
104×5= 4500÷50= 120×2= 90÷30= 270÷30=
270×30= 66÷7= 84÷21= 76÷9=

The number of roots of equation x & # 178; + 2x-1 = 0 can be regarded as the number of intersections of straight line y = x + 2 and hyperbola y = 1 / X
It can be inferred that the number of roots of the equation x & # 178; - 1 = 1 / X is several ()

Y = x & # 178; - 1 is a parabola with the opening upward, the vertex (0,1), the inverse scale function y = 1 / X and y = x & # 178; - 1 have no intersection in the third quadrant, but have an intersection in the first quadrant
There is only one root of the equation x & # 178; - 1 = 1 / X