. The infinite dihedral group D[infinity] is a subgroup of permutations of the integers generated by f(n) = −n and g(n) = 1 − n, which reflect the integer number line over the point 0 and 1/2 respectively. (a) Give a presentation of D[infinity]. (b) Demonstrate a surjective homomorphism to each finite dihedral group ϕ : D[infinity] → Dn for n ≥ 3.

312312

step-by-step explanation:

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .