Answer:
1. x=3 x=1
2. x=0
Step-by-step explanation:
We want f(x) to equal g(x)
f(x)=g(x)
1/(x-2) = (x-2)
Using cross products
1 = (x-2) * (x-2)
1 = x^2 -2x-2x+4
Subtract 1 from each side
1-1 = ^2 -2x-2x+4-1
0 = x^2 -4x+3
Factoring
What number multiplies to 3 and adds to -4
-3*-1 = 3
-3+-1 = -4
0= (x-3) (x-1)
Using the zero product property
x-3 =0 x-1=0
x=3 x=1
2. f(x)=x^2+4x+2
g(x)=(1/2)^ x+1
From the graph,we can see they intersect at x=0
Answer:
The number of mosquitoes is maximum for 6.5 inches rainfall.
Step-by-step explanation:
The given function is
.... (1)
where, M(x) is number of mosquitoes in millions and x the June rainfall in inches.
We need to find the rainfall that produces the maximum number of mosquitoes.
Differential the above function with respect to x.
.... (2)
Equate first derivative equal to 0.
Differential function (2) with respect to x.
Double derivative is negative. So, the value of function is maximum at x=6.5.
Therefore, the number of mosquitoes is maximum for 6.5 inches rainfall.