The area is given by:
A = x * y = 834
The cost equation is given by:
C = 6 * (2x) + 3 * (y)
We express the equation in terms of a variable:
C (x) = 6 * (2x) + 3 * (834 / x)
Rewriting:
C (x) = 12x + 2502 / x
We derive the equation:
C '(x) = 12 - 2502 / x ^ 2
We match zero:
0 = 12 - 2502 / x ^ 2
We clear x:
x = root ((2502) / (12))
x = 14.4 feet
We look for the other dimension:
y = 834 / x
y = 834 / 14.4
y = 57.9 feet
Answer:
The dimensions of the enclosure that can be erected at minimum cost are:
x = 14.4 feet
y = 57.9 feet
Width = 20 feet
length = 2(20) = 40 feet
then the perimeter equals 2width+ 2length = 2(20)+ 2(40) = 40+80 = 120 feet
Answer:
radius = 16 cm
diameter = 32 cm
Step-by-step explanation:
radius is shown in diagram
diameter is two times the radius
Answer:
y = - x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m =
with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (8, 2 )
m = = = - 1 , then
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 4 ) , then
4 = - 6 + c ⇒ c = 4 + 6 = 10
y = - x + 10 ← equation of line