Scientific Mathematics (1)

Reference answer

1、B

2. A.

3. A.

4、B

5. A.

6、B

7、B

8、C

9. Answer

10、D

1 1、55,

12、 1,

13、,

14、90,

15、,

16、9,

17、48.6

17 Question Tip: Imagine a robot walking, which means that if the first step is set to 1.9 meters, the time for the first step to cross is 0 seconds; Then the second step is carried out after the interval of 1.9 seconds, and the time used is still 0 seconds. That is, it took 1.9 seconds to stride two steps, and so on: it took 25 * 1.9 = 47.5 seconds to walk 26 steps (49.4 meters), and after 1.9 seconds, the last step instantly exceeded 50 meters, so it took 49.4 seconds. So the correct answer should be that the first step is set to 1.8m, so the answer is 48.6 seconds.

18. solution: from, that is.

(1) order,

Therefore, the monotonic increasing interval of is.

(2) because, so, that is because again.

So, according to the cosine theorem,

So, again, so, so

19. Solution: (1) Let the tolerance of arithmetic progression be,

Because that's

solve

So ...

So the general formula of the series is.

(2) because,

So the sum of the previous paragraphs in this series

.

Suppose there is a positive integer,, and,, in geometric series,

Then.

Namely.

So ...

Because so

That is to say, because, therefore.

Because so

At this time.

Therefore, there are positive integers that satisfy the meaning of the question, and there is only one set of solutions, that is,.

20.

Solution:

(1) proves that a quadrilateral is a rectangle with a midpoint,

Is the midpoint,

In, it is the midpoint, so

∵ plane, plane, plane;

(2) according to the meaning of the question.

and

Aircraft

Aircraft, aircraft,

∵ is the midpoint, ∴

Combined, quadrilateral is parallelogram.

∴,

And, ⅷ

∴, namely

and

∴ Aircraft,

∫ plane,

∴

(3): As shown in the figure, establish a spatial rectangular coordinate system with a straight line as the axis.

That is all right

It is easy to know that the normal vector of the plane is,

Let the normal vector of the plane be

So, that is

Let's order then.

∴,

According to the meaning of the question,

In an instant, the sharp dihedral angle between planes is

2 1.

Solution: (1) can be obtained from the problem: e =.

∵

A circle with the origin as the center and the length of the minor axis of ellipse C as the radius is tangent to the straight line x+y+=0.

∴

=b, then the solution is b = 1.

Zaiyou

A2=b2+c2, which can be solved as: A = 2.

∴

The standard equation of ellipse:.

A (-2) From (1), we can know that: A (-2,0), B (2 2,0), the equation of the straight line L is: x = 2.

Let G(x0, y0)(y0≠0), then Q(x0, 2y0),

Also, 4y02 = 4-x02.

∴

The equation of straight line AQ is,

pass by

Solution: that is,

∴

.

∴

The slope of the straight line QN is:

∴ The equation of straight line QN is:

that is

∴ The distance from point O to straight line QN is

∴

The straight line QN is tangent to the circle o with the diameter AB.

22. Solution:

(1), ∫ held by Neiheng.

If it is based on internal invariance, it is based on internal invariance.

Settings,

,,,,

Therefore, the function is monotonically increasing and decreasing,

∴,∴

(2) Orders

Then, ∵ Neiheng was established.

∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴875

Yes, zero, ∴

At that time, that is,

When,,,

that is

∴,

∴