Awinding river is modeled br r(x)=x^3+4x^2+4x+12. bridges will be built along the x axis, as needed, to cross the river. how many bridges will need to be built?

The Winding river is modeled by r(x)=

As bridges will be built along x-Axis to cross the river.

so,the bridges work as a tangent to river.

r'(x)=

So , r'(x)=0

→=0

→3x²+6 x+ 2 x+4=0

→3 x(x+2)+2(x+2)=0

→(x+2)(3 x+2)=0

x=-2, x= -2/3

As there are two values of x, from where we can draw tangents or bridges to the river.So there are maximum of two bridges that we  need to  built.

find out the value of b

step-by-step explanation:

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: