Arectangular area adjacent to a river is fenced in; no fence is needed on the river side. the enclosed area is 1000 square feet. fencing for the side parallel to the river is $ 8 per foot, and fencing for the other two sides is $ 4 per foot. the four corner posts are $ 20 each. let x be the length of one of the sides perpendicular to the river.
(a) write a function c(x) that describes the cost of the project.
(b) what is the domain of c?

C(x)  =  8*x  +  8* (1000)/x  + 80

C(x)  Domain  x > 0

Step-by-step explanation:

enclosed area     1000 ft²

let   x be side perpendicular to the river

and  y  parallel to the river

Then:

A = x*y               y  =  A / x           y  =  1000/x

Cost of one side (x)    4*x  $   then two sides     cost = 4*2*x    cost = 8*x

Cost of one side (y)    8*y  $      8* (1000/x)

Cost of four cornes posts   4*20 = 80 $

Total cost  C(x)

C(x)  =  8*x  +  8* (1000)/x  + 80

R {   x > 0}

Taking derivatives both sides of the equation

C´(x) = 8  - 8000/x²       C´(x) = 0        8  - 8000/x² = 0

8x² -8000 = 0     x²  = 1000

x = 100

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation: