Answer:
a) 5units
b) (4.5, 4)
Step-by-step explanation:
Let the coordinate of P and Q be P(3, 2) and Q(6, 6)
PQ can be gotten using the distance formula;
PQ =√(6-2)²+(6-3)²
PQ = √4²+3²
PQ =√16+9
PQ =√25
PQ = 5units
Midpoint M is expressed as;
M(X, Y) = {(x1+x2)/2, y1+y2/2}
X = x1+x2/2
X = 3+6/2
X= 9/2
X = 4.5
Similarly;
Y = y1+y2/2
Y = 2+6/2
Y = 8/2
Y = 4
Hence the midpoint of PQ is (4.5, 4)
Answer:
25000m/s
Step-by-step explanation:
The following formula is used to calculate the speed or velocity of a wave.
V = f * w
Where V is the velocity (m/s)
f is the frequency (hz)
w is the wavelength (m)
First, determine the frequency.
Calculate the frequency of the wave.
Next, determine the wavelength.
Calculate the wavelength of the wave.
Finally, calculate the wave speed.
Using the formula above, calculate the wave speed.
Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle
Answer:
86400 ways
Step-by-step explanation:
Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.
Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.
After picking the places for the women, we will now fill each gap between two women with a man.
We have 6 men. Thus, number of ways to arrange the men is 6!
Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways
