The equivalence

means that n-5 is a multiple of 12.
that is
n-5=12k, for some integer k
and so
n=12k+5
for k=-1, n=-12+5=-7
for k= 0, n=0+5=5 (the first positive integer n, is for k=0)
we solve 5000=12k+5 to find the last k
12k=5000-5=4995
k=4995/12=416.25
so check k = 415, 416, 417 to be sure we have the right k:
n=12k+5=12*415+5=4985
n=12k+5=12*416+5=4997
n=12k+5=12*417+5=5009
The last k which produces n<5000 is 416
For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,
thus there are 417 integers n satisfying the congruence.
Answer: 417
f(0) = ( f(k) +f(-k) ) / 2
f(0) = (16 - 4) / 2
f(0) = 12 / 2
f(0) = 6 → ANSWER
*Remember that f(0) = m(0) + n = n
If we have f(x) = mx + n, then:
f(k)= mk + n and f(-k)= -mk + n
If we add them:
f(k) + f(-k)
= mk + n -mk + n
= 2n
= 2f(0)
So we conclude that:
f(0) = [f(k) + f(-k)] / 2
Answer:
Identify all points and line segments in the picture below.
This image has the potential for visual bias, so there is no alternative text.
Select one:
a. Points: A, B
Line segments: bar(AB)
b. Points: A, B, C, D
Line segments: bar(AB)
c. Points: A, B, C, D
Line segments:
bar(AB), bar(BC), bar(CD), bar(AD), bar(BD), bar(AC)
d. Points: A, B, C, D
Line segments: bar(AB), bar(AC), bar(BD)
Step-by-step explanation:
Answer:
1440π squared mm.
Step-by-step explanation:
Given is the radius of base of cylinder, r = 12mm.
The altitude is five times the base radius, h = 5 times 12mm = 60mm.
The lateral area of the cylinder is the curved surface area of the cylinder.
The formula for curved surface area of cylinder is as follows:-
Curved Surface Area = Circumference of base x altitude of cylinder.
SA = 2πrh = 2π•12•60 = 1440π sq. mm.
Hence, Lateral area of cylinder is 1440π squared mm.