You need to hang seven pictures in a straight line. In how many ways may
his be accomplished?

The seven pictures can be hanged in 5040 ways in a straight line.

Step-by-step explanation:

It is given that, there are seven pictures that are to be hanged in a straight line in many ways.

The seven pictures can be arranged in several ways which can be found using the factorial.

Since there are 7 different pictures, the number of ways it can be arranged is 7 factorial ⇒ 7!

if we are filling the 7 pictures at a time, we have seven options to fill the first position.

And then, there are 6 options to fill the second position and followed by the third position which as 5 options to filled and it continues till the seventh position which will have only 1 option to be filled.

Therefore, it is calculated as :

⇒  7! = 7×6×5×4×3×2×1

⇒ 5040 ways.

The seven pictures are hanged in 5040 ways.

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).