Called ultimate addition, u(x) is defined to be the sum of all digit of an integer until the result is single digit integer. if m is a two-digit integer, how many possibility of m such that u(m) = u(50654)? a. 2 b. 5 c. 8 d. 10 e. 12

Work Shown:

u(50654) = 5+0+6+5+4 = 20

u(20) = 2+0 = 2

u(50654) = 2

We want to find all possible values of m such that u(m) = 2 and also m is some two-digit integer.

Possible values of m are: m = 11, m = 20

u(m) = u(11) = 1+1 = 2

u(m) = u(20) = 2+0 = 2

and that's it. There are no other ways to have two positive integers add up to 2.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

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step-by-step explanation: