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<> set pb=1, pa=2, pc=3

Because cq=2, pc=3, pq=1

The length of BC can be obtained.

a<> rotate the triangle apc 60 degrees clockwise to get the triangle bp c, because pc=p c= 3, pcp =600, pcp is an equilateral triangle, pp = 3, bp =ap=1,bp=2, bpp is a right triangle, bp p=900,bpp =300, bpc=600+300=900 pcb is a right triangle bp=2, pc= 3, bc= 7

Connect the three vertices with that point, and form three small triangles inside, the total area of the three of them is equal to the area of the equilateral triangle, let the side length be r and the three areas are , and the root number is three xr, which adds up to the total area. The side length is r, the area of the equilateral triangle is the root number of the quarters, and the root number is three, xrxr, and you can make a quadratic equation to solve it, and the side length is 2+2x, and the root number is 3

Set the public than the wisdom hand for x, hail Bijing.

then a1+a1x+a1x =3a1x

1+x+x source prudence = 3x

2x²-x-1=0

2x+1)(x-1)=0

x1=-1/2，x2=1

So the common ratio is -1 2 or 1

The common ratio is 1 or 1 for laughing silver.

Let the collapse ratio be n.

n 2 + n + 1) * a1 = 3 * n 2 * a1 to get 2n 2 - n -1 = 0

Solve the group to promote with 1 or.

If the speed of the fast train is x, the speed of the slow train is 5/7x.

Column equation: 4x-48 = 4 * 5/7 x + 48. This can be solved to x= 84.

Let AB and the two places be separated by S kilometers.

s=（4*84-48）*2=476

a:b:c= 1:2:3

The sum of the three corners of the triangle is 180 degrees, so.

The angles are 30, 60, 90 degrees.

So a:b:c=1:3:2

1 to 3 to 2....For the second question, just replace c with 180-(a+b) and then use the formula.

The big side is against the big corner, and the small side is against the small corner

I see, are you still puzzled?

Any vector e in the plane can be linearly represented by k1*e1+k2*e2, that is, e=k1*e1+k2*e2, (k1, k2 are any real numbers), so e1, e2 can be used as the basis for representing all vectors in the plane where they are located.

Not necessarily, are you sure you're right?

It is 16 connection oe,of

Because OA=OB=OC, EAO=OCE=90°, OE=OE, OAE is all equal to OCE

So ae=ce

So PE+CE=PE AE 8

The same can be said for CF BF

So PE CF=PF+BF 8

So the circumference of the pef is 8 8 16

Use your brains! ＾－

Solution: fb,fc is the tangent of the circle o.

fc=fbeb,ec is the tangent of the circle o.

ec=eapb, and pa is the tangent of the circle O.

pb=pa=8cm

So the circumference of PEF = PF + PE + CE + CF = PA + PB = 8 + 8 = 16cm

First of all, let's clarify a few concepts of proportional series:

1.The formula for the general term of the proportional series is: n-1 power of an=a1 q (n-m power of an=am q);

where it is a subscript, as long as n+m=p+q, you can use this formula).

to the n-m power.

Then review the question, 1The a1a9=64 given by the title can be known as a1a9=a3a7=64 according to the second concept.

2.Yes, because a3 + a7 = 20.

From the above, we can get a3=4, a4=16 or a3=16, a4=4 (because there is no telling whether the proportional series is increasing or decreasing, there are two sets of solutions).

Then according to the third concept, we can calculate q=4 or q=1 4

Finally, we can count a11, so according to the second concept, we know that a11=a3 (q-8 power).

The solution is that a11 = 4 to the 8th power of 4 = 9th power of 4 or 8th power of a11 = 16 (1 4) = 6th power of 1 4.

Since typing is inconvenient, it can only be like this! Hope. ）

Hint: There are a lot of formulas to learn math!