In a given geometric sequence gn, g(4) = 5 and g(6) = 11.25.

英语翻译
Our last example is also a geometric one,but here the “divisions”,i.e.the boxes,are not
whole parts of the given geometric figure,indeed,they are points in it.The difficulty is
realizing that it is these precise points that will help (or having a hunch of what those
points are by making a few drawings).
We are given a square and 9 lines cutting through it.Each line cuts the square
into two quadrilaterals,and the ration of the areas of those quadrilaterals is 2:3.
Prove that at least three of these 9 lines pass through the same point.
Since each line divides the square in two quadrilaterals,each line cuts the square
at two non consecutive edges.The figures obtained are trapezoids with two right angles,
and their area is equal to their base (here the side of the square)
multiplied by the height of their “midline”,the line perpendicular to
their two parallel edges and at equal distance from those two edges.
Since for any of those trapezoids their base is the same,the ration of
their midlines must be 2:3.But there are only two possible midlines
for the trapezoids,so we get four different points,call them
midpoints,two on each midline,where the midline of two
trapezoids intersects with one of the 9 given lines.Every one of those lines must pass
through one of these midpoints.We have 4 points and 9 lines,so there is at least one
point through which pass three lines.
We have shown that,given 9 lines,each cutting a square into two trapezoids
whose areas are in the ratio 2:3,at least three of the lines pass through the same point.
We now move on to more difficult problems,which generally necessitate a little
more twist,or work,before applying the pigeonhole principle

in a certain geometric sequence the first term exceeds the second term by 32 and the sum of the second and third is 48,find the infinite sum of rhe sequence

英语翻译
However,geometric rigor shrinks from even so small an error,and this objection would be simply too great were any force granted to it

1.What is the next term in the geometric sequence 16,–4,1,– 1/4,…

Suppose X has a geometric distribution with parameter p.Show that if n and k are positive
integers,then
P(X = n + kjX > n) = P(X = k):

有一道sat的试题麻烦解答一下 The 3rd term of a geometric seq
uence is -3,and the 6th term is （八分之三.）what is the 4th term of the sequence?

想问一道a
a geometric series has first term a and common ratio r,where 0

简单英文数学问题(geometric sequence)
find the sum to infinity of a geometric sequence whose sum to three terms is 3968 with a second term of 640
please process,thanks

sat数学题 The 3rd term of a geometric sequence is -3
,and the 6the term is 八分之三.what is the 4th term of the sequence?

英语翻译
geometry of shallow curves
to establish the geometric relationships required to derive the differential equation of the elastic curve,we will consider the deformations of the cantilever beam in Fugure9.1a.
the deflected shape is represented in Figure9.1b by the displaced position of the longitudinal axis(also called the elastic curve).as reference axes,we estabilsh an x-y coordinate system whose origin is located at the fixed end.for clarity,vertical distances in this figure are greatly exaggerated.slopes,for example,are typically very small--on the order of a few tenths of a degree.if we were to show the deflected shape to scale,it would appear as a straight line.
to establish the geometry of a curved element,we will consider an infinitesimal element of length ds located a distance x from the fixed end.as shown in Figure9.1c,we denote the radius of the curved segment by p.angle between these tangents is denoted by dФ.since the tangents to the curve are perpendicular to the radii at points A and B,it follows that the angle between the radii is also dФ.the slope of the curve at point A equals
if the angles are small(tanФ≈Ф radians),the slope can be written
from the geometry of the triangular segment ABO in figure9.1c,we can write
dividing each side of the equation above by ds and rearranging terms give
where dФ/ds,representing the change in slope per unit length of distance along the curve,is called the curvature and denoted by the symbol Ф.since slopes are small in actual beams,ds≈dx,and we can express the curvature in equation9.3 as

英语翻译
The first term in a geometric sequence is 2,and the commom ratio is 3.The first term in an arithmetic sequence is 3,and the commom difference is 3.Let set X be the set containing the first six terms of the geometric sequence and set Y be the set containing the frist six terms of the arithmetic sequence.What is the sum of the elements in X∩Y?

什麽是Arithmetic and Geometric Sequences
请解释一下两者的分别...
可以的话请例举一些例子,

英语翻译
Hamiltonian cycles in fault random geometric network
In a network,if Hamiltonian cycles exist,the fault tolerance is better.
不要google直译,

pockets是机械中什么意思
机械专业英语中有一句 For example,geometric design deals with lines,splines,circles ,and arcs whereas manufacturing talks about pockets ,chamfers,holes,and so on .中的Pockets 无论如何也理解不了 大家帮帮忙 应该不是口袋的意思 呵呵

一道数学题.find the sum of the n consecutive geometric terms which can be inserted between 1 &
continue.......
inserted between 1 and 2.
上面没打完整。