A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $12 per foot and on the other three sides by a metal fence costing $4 per foot. If the area of the garden is 200 ft, find the dimensions of the garden minimizing the cost. (Let x be the length of the brick wall and y be the length of an adjacent side in feet.)

The dimensions of the garden that will minimize the costs are: x=10ft, y=20ft

Step-by-step explanation:

Let x be the length of the brick wall. Let y be the length of the adjacent sides.

Area of the garden = 200 ft

Therefore: xy=200

Perimeter of the Fence = Length of

brick wall+Length of Opposite Metal Fence + Length of Other Adjacent Metal Fence

=x + x + 2y

Costing of brick wall= $12 per foot Cost of Metal =$4 per foot.

Cost of the Fence=12x+4x+4(2y)

=16x+8y

Recall:

Therefore, the cost in terms of x is:

The minimum costs C(x) occur when its derivative equals zero.

Thus:

x=10ft

Recall that:

y=200/10=20 ft

The dimensions of the garden that will minimize the costs are: x=10ft, y=20ft

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct