What’s the least common multiple of each group of numbers? A. 5 and 6 b. 2 and 9 c. 6 and 8 d. 2, 5, and 6
2 answers:
For this case we have that by definition, the LCM of two or more natural numbers is the smallest natural number that is a common multiple of all of them.
So:
A. 5 and 6
The LCM of 5 and 6 is the smallest positive integer that divides the numbers 5 and 6 without leaving a residue.
multiples:
5: 10,15,20,25,30,35,40,45
6: 12,18,24,30,36
B. 2 and 9
Multiplos:
2: 4,6,8,10,12,14,16,18
9: 18,27
C. 6 and 8
6: 12,18,24,30,36
8:16, 24
D. 2,5 and 6
Multiplos:
2: 4,6,8,10,12,14,16,18 ..., 30
5: 10,15,20,25,30,35,40,45
6: 12,18,24,30,36
Answer:
a.30
b.18
c.24
d.30
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The given equation is
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm