Ind the last 7 digits in the binary expansion of $27^{1986}$. (give your answer in binary.)

Since 1986 = 62*32 + 2, we have

by Euler's theorem, since . Then

which tells us the 7th digit from the right is 1.

Then

so the next digit must be 0;

so the next digit is 1;

so the next digit is 1;

so the next digit is 0;

so the next digit is 0; and

so the last digit is 1.

So the last 7 digits of this number in binary are 1011001.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

.19875994384

step-by-step explanation:

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