Answer:
Step-by-step explanation:
Use the <u>Slope Formula</u> to determine the slope of two given points:
First Point: 
Second Point: 
-Substitute both points:
First Point: 
Second Point: 
-Solve for the slope:
Therefore, the slope is 
Answer:
Speed of boat in still water is 6km/h
Speed of current is 4km/h
Step-by-step explanation:
We know speed = distance / time
Let the speed of boat in still water be x
Let the speed of current be y
Hence the speed of boat, down stream = 
Distance downstream = 20km
Time taken = 2 hours
We have
......(1)
Speed of boat upstream = 
Distance upstream = 4
Time taken = 2
We have
...(2)
Adding (1) & (2)
Substituting in (1) we get
Answer:
1/12,000
Step-by-step explanation:
Data provided in the question:
Size of a population of mustard plants = 6,000
Now,
According to genetic drift theory
The probability that a newly-arisen mutation will become fixed is given using the formula
⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]
⇒ 1 ÷ [ 2 ×6,000 ]
⇒ [ 1 ÷ 12,000 ]
Hence,
probability that a newly-arisen mutation will become fixed in this population is 1/12,000
Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then
tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2) ===> sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)
We also know that
sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1 ===> sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))
Recall the double angle identities:
cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1
sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)
Then
cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)
sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)
