Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
θ = the angle
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
Answer:
First on is 0.75
Second is 22/52 (not sure about this one though)
Step-by-step explanation:
For the first one:
P(aUb) = p(a) + p(b) - p(a^b)
0.6 = 0.4 + 0.5 - p(a^b)
p(a^b) = 0.3
P(a/b)= p(a^b)/p(a)
P(a/b)= 0.3/0.4
P(a/b)= 0.75
For the second one:
Total of the cards are 52
Diamonds are 13 out of that 52
Face cards are 12 out of that 52
Diamond OR face cards means p(aUb)
And that equals p(a)+p(b)-p(a^b)
p(a^b) means the intersection between the two, there are three common cards between diamonds and face cards, so p(a^b)=3
13/52 + 12/52 - 3/52= 22/52
Answer: Tigers: Linear Function
Narwhals: Linear Function
