Answer:
.
Step-by-step explanation:
Dilate a point by a scale factor of
with
as the center, and the resultant point would be at
.
In this question:
Point to dilate: .
Scale factor: .
Center of dilation: .
The resultant point would be:
, which simplifies to
.
Answer:
Population of mosquitoes in the area at any time t is:
Step-by-step explanation:
assume population at any time t = P(t)
population increases at a rate proportional to the current population:
⇒dP/dt ∝ P
----(1)
where k is constant rate at which population is doubled
solving (1)
---- (2)
initial population = 400,000
population is doubled every week
⇒P(1)=2P(0)
Using (2)
In presence of predators amount is decreased by 50,000 per day
Then amount decreased per week = 350,000
In this case (1) becomes
---(3)
solving (3) by calculating integrating factor
Multiplying I.F with all terms of (3)
Integrating w.r.to t
at t=0
So, population of mosquitoes in the area at any time t is