A landscape architect plans to enclose a 2600 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the north side.
Find the minimum total cost.

$4,265.90

Step-by-step explanation:

-Let X and Y be the two sides of the rectangle and C be the cost function.

-The cost function can then be expressed as:

C=25(2y+x)+10x

C=50y+35x                   ...(i)

#The region's area is equated as:

xy=2600                        ...(ii)

#We make Y the subject of the formula in i and substitute in ii;

y=2600/x

=>C=50y+35x

C=50(2600/x)+35x

C=130000/x+35x

#We get the first derivative to determine the critical points:

dC/dx=-130000/x^2+35

#Set dC/dx=0

130000/x^2=35

x=60.94 ft

y=2600/x=2600/60.94=42.66 ft

-The minumum is therefore calculated as:

C=50y+35x

=50(42.66)+35(60.94)

=$4,265.90

Hence, the minimum cost is $4,265.90

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

move it to the other side

step-by-step explanation: