In the quadrilateral ABCD, ab = ad = CD = 1, BD = radical 2. BD ⊥ CD. The quadrilateral ABCD is folded into tetrahedral a'bcd along the diagonal BD Let plane a 'BD ⊥ plane BCD, then the following conclusion is correct () A. The angle between a'c ⊥ BD B, Ca 'and plane a'bd is 30 ° C, and the angle ba'c = 90 ° D. the volume of tetrahedral a'bcd is 1 / 3

Because BD ⊥ CD plane a'bd ⊥ plane BCD, so CD ⊥ plane a'bdcd ⊥ a'dcd = 1, a'd = 1, so a'c = radical 2, a'B = AB = 1, BD = radical 2, CD = 1, according to Pythagorean theorem, we get BD = radical 3, so a'B & # 178; + a'c & # 178; = BC & # 178; that is, angle ba'c = 90 ° so C pairs
The correct answer is: B
After drawing, make a vertical line to BD through a ', and the vertical point is e
Link CE
It can be seen that angle a'ce is the angle formed by Ca 'and plane a'bd
In triangle a'ce
We can calculate a'e = √ 2 / 2, CE = √ 6 / 2
tan∠A'CE=√3
30 degree
[if you have any help, please adopt]
The correct conclusion is C
A:A'B⊥A'C
B: For a'e ⊥ BD in E, even CE
Then a'e ⊥ plane BCD
∴A'E⊥CE
∵AB=AD=1，BD=√2
∴∠BAD=90°
∴A'E=√2/2
∵ plane a'bd ⊥ plane BCD
Plane a'bd ∩ plane BCD = BD, CD ⊥ BD
⊥ CD ⊥ plane a'bd
∴CD⊥A'D
∵ a'd = ad = 1 =... Expand
The correct conclusion is C
A:A'B⊥A'C
B: For a'e ⊥ BD in E, even CE
Then a'e ⊥ plane BCD
∴A'E⊥CE
∵AB=AD=1，BD=√2
∴∠BAD=90°
∴A'E=√2/2
∵ plane a'bd ⊥ plane BCD
Plane a'bd ∩ plane BCD = BD, CD ⊥ BD
⊥ CD ⊥ plane a'bd
∴CD⊥A'D
∵A'D=AD=1=CD
∴A'C=√2=2A'E
∴∠A'CE=60°
C:BD=√2,CD=1，CD⊥BD
∴BC=√3
A'B=1，A'C=√2
∴∠BA'C=90°
D:S△BCD=√2/2
h=√2/2
V = 1 / 6 "stowed
It's a fraction of one plus nine
It can't be 1 / 18 + 1 / 18 = 1 / 9
1/12+1/36=1/9
1/90+1/10=1/9
How to find the velocity harmonic motion of the oscillator when it moves to half of the amplitude
The kinetic energy of the work done by the average force is conserved
If the restoring force F from the maximum displacement to half displacement is obtained, the average force F from the maximum displacement to half displacement is 1 / 2F,
Furthermore, from the conservation of kinetic energy, f ` s = 1 / 2mV ^ 2
Then V can be solved
In tetrahedral a-bcd, the projection o of vertex a in bottom BCD is perpendicular to triangle BCD, so AB AC ad is perpendicular?
In addition, there are ab vertical CD AC vertical BD
Can you deduce these two conclusions? Are these two conclusions true at the same time?
1. If vertex A is a projection on the bottom BCD and is the perpendicular of triangle BCD, then ab ⊥ CD, AC ⊥ BD, ad ⊥ BC
[AB, AC and ad will not be vertical]
2. In addition, if ab ⊥ CD, AC ⊥ BD, then we can get that point O is the perpendicular of triangle BCD. That is to say, the inverse proposition of the first question is also correct
Let AB, AC in a-bcd,
The projection of ad two vertical a on the bottom BCD is o
Because ab ⊥ AC, ab ⊥ ad,
So ab ⊥ plane ACD
So ab ⊥ CD, Ao ⊥ CD
So CD ⊥ surface ABO,
CD⊥BO
Similarly, BC ⊥ do, BD ⊥ Co
So o is BCD and perpendicular
Five fractions add up to one
Choose from the natural numbers from 1 to 100, which cannot be repeated
1/2+1/4+1/8+1/9+1/72=1
Isn't the sum of five fifths equal to one?
1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+1/5
=1/2+1/5+1/6+1/12+1/20
In simple harmonic motion, can the maximum acceleration be increased by increasing the amplitude? What other ways?
It's free vibration
sure
The recovery coefficient can also be increased
incorrect.
If it is forced vibration, there is no necessary connection between them.
If there is a specific vibration equation, the specific relationship can be analyzed.
From the point of view of kinematics, it can be defined as "the law that the displacement X of the particle leaving the equilibrium position changes with time t, and the vibration that can follow the cosine function (or sine function) is called simple harmonic vibration.". That is, x = ACOS (ω T + α). The above two statements are the two most commonly used definitions of simple harmonic vibration. The essence is the same.
Through the above formula x = ACOS (ω T + α), it is obvious that the displacement x... Expansion of simple harmonic vibration body is made
incorrect.
If it is forced vibration, there is no necessary connection between them.
If there is a specific vibration equation, the specific relationship can be analyzed.
From the point of view of kinematics, it can be defined as "the law that the displacement X of the particle leaving the equilibrium position changes with time t, and the vibration that can follow the cosine function (or sine function) is called simple harmonic vibration.". That is, x = ACOS (ω T + α). The above two statements are the two most commonly used definitions of simple harmonic vibration. The essence is the same.
Through the above formula x = ACOS (ω T + α), it is obvious that the change law of displacement X of simple harmonic vibration object with time t follows cosine function (or sine function). If the relationship between X and t is expressed vividly by the curve shown in Fig. 1-29 (abscissa is t, ordinate is displacement x), it is to describe simple harmonic vibration by vibration graph line method.
There is also a vector diagram method, or reference diagram method, which can more intuitively understand the relationship between the displacement and time of simple harmonic vibration, and deeply understand the meaning of the three physical quantities a, ω and α of simple harmonic vibration.
To sum up, there are three ways to express a kind of vibration
1. Trigonometric function method: x = ACOS (ω T + α).
2. Vibration diagram line method.
3. Vector graphic method. Put it away
If we know that the volume of a square circumscribed sphere is 3 / 32 (PAI), then the edge length of a cube is ?
The center of mass (i.e. the center) of the cube and the circumscribed sphere coincide, so the length from the center of mass to any vertex of the cube = radius r of the sphere. According to the formula (volume of the sphere = 4 / 3 * π * r cube), the value of R can be calculated. Then you can imagine making two straight lines from the center of mass to two vertices of an edge line of the cube, just forming an equilateral right triangle, The length of the bottom edge of a triangle (that is, the length of the edge line) is the edge length, and the length of the other two lines of the triangle is R. according to the Pythagorean theorem, the edge length can be calculated
Ten fractions add up to one
Choose from the natural numbers from 1 to 100, which cannot be repeated
3 4 8 9 16 27 54 32 48 96
(96+48)+32+16+8+4+54+27+9+3
=32+32+16+8+4+18+9+3
=16+16+8+4+6+3
=8+8+4+2
=4+4+2
=2+2
=1
In simple harmonic motion, the weight, period and energy of a body are known, and its amplitude is calculated
The total energy is equal to the kinetic energy of the vibration passing through the equilibrium point. Let the velocity be v0:1 / 2 m * V0 ^ 2 = E
The relationship between velocity V0 and amplitude and angular velocity: v = w * a
Relationship between period and angular velocity: T = 2 pi / W
The solution is a = sqrt (E / 2 / M) * t / π
Sqrt is the root sign
The volume ratio of the inscribed sphere to the circumscribed sphere of a cube is______ .
Let the edge length of a cube be a, then the radius of its inscribed sphere is 12a, and the radius of its circumscribed sphere is 32a, so the ratio is 1:3, so the answer is 1:3

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