Answer:
LCM of 42 and 63 is 126.
Step-by-step explanation:
Find the prime factorization of 42
42 = 2 × 3 × 7Find the prime factorization of 63
63 = 3 × 3 × 7Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 3 × 3 × 7LCM = 126
Pretty sure its D. because it is not a one to one ratio but it doesn't necessarily have to pass through the origin.
It its normal form its 48/100 but in its simplest form it is 12/25. Your welcome!<span />
Answer: In problem 8, the lines are not parallel. In problem 10, the lines are parallel.
To determine if the lines are parallel. You need to check if the segments form on each side are proportion.
#8 check to see if: 2/1 = 3/1.2
If you cross multiply, you get 3 = 2.4 which is not true, so the lines are NOT parallel.
#10 check to see if: 6/5 = 9/7.5
If you cross multiply, you get 45 = 45 which is true, so the lines are parallel.
If the airport is located at the origin, for units of miles and hours, we can write the equations of position for airplanes "a" and "b" in rectangular coordinates as
a = (-30 +250t, 0)
b = (0, -40 +300t)
The distance between these (moving) points can be computed in the usual way using the Pythagorean theorem.
d = √((-30 +250t - 0)² +(0 - (-40 +300t))²)
d = √(2500 -39000t +152500t²)
Then the rate of change of d is the derivative of this.
d'(t) = (-19500 +152500t)/√(2500 -39000t +152500t²)
At the present time (t=0), the rate of change of distance between the planes is
d'(0) = -19500/√2500 = -390
The distance between the planes is decreasing at 390 mi/h.
