# If the garden is to be 1250 square feet, and the fence along the driveway costs \$6 per foot while on the other three sides it costs only \$2 per foot, find the dimensions that will minimize the cost.

So, the minimum cost is \$400.

### Area of the rectangle:

The area of a rectangle is the region occupied by a rectangle within its four sides or boundaries.

And the formula is,

Given that,

Area of the garden=1250 square feet.

Let, the length be and the breadth be then,

The total cost of the fence is,

Now, differentiating the obtained equation we get,

Therefore the length is 25 ft

And breadth is 50ft

Now, calculating the minimum cost,

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Dimensions of rectangular garden:

x = 25 feet   ( sides along the driveway)

y = 50 feet

Step-by-step explanation:

Rectangular area is:

A(r)  = x*y           (1)

if we call x one the driveway side the cost of that side will be

6*x

The cost of the other side parallel to driveway side is 2*x and cost of the others two sides are 4*y

Total costs:  C = 6*x + 2*x  * 4*y     (2)

From equation (1)

A(r)  = 1250 = x*y      ⇒⇒   y = 1250/ x

Plugging that value in equation (2) we get costs as a function of x

that is:

C(x) = 6*x + 2*x +  4* 1250/x

Taking derivatives on both sides of the equation

C´(x)  = 6 + 2 - 5000/x²

C´(x)  = 8 - 5000 /x²

C´(x) = 0       ⇒       8 - 5000 /x² = 0

8*x² -5000 = 0

x² = 5000/8

x² = 625

x = 25 feet

and    y = 1250/ 25

y = 50 ft

C(min) = 50*2*2 + 6*25 + 2*25

C(min) = 200 + 200

C(min) = 400 \$

## Related Questions

FACTOR COMPLETELY:
y^3 - 5y^2 - 17y + 21
HINT: one of the factors is (y-1)

7,300 meters

Step-by-step explanation:

7.3×1000 = 7300

Step-by-step explanation:

The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hour while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function. a. The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
b. The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours..
c. The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.
d. The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.

Please select the best answer from the choices provided.​

If hours is represented as h, your distance is therefore 3*h (due to that for every hour, you walk 3 miles. For example, in one hour you'd walk 3 miles, in 2 hours you'd walk 3+3=3*2=6 miles,etc.). If distance is represented by d, we get 3*h=d. Since you have to figure out the distance from the equation (that's the purpose of it!), the distance is the dependent variable. In addition, since you can't have 2 separate variables in one equation, h is the independent variable due to that you have to put a number for h in to figure out the distance

So basically the answer is A.

How to solve -2x-10x12=18

x  =  −69

Step-by-step explanation:

1: Simplify

−2x−(10)(12)=18

−2x+−120=18

−2x−120=18

2: Add 120 to both sides.

−2x−120+120=18+120

−2x = 138

3: Divide both sides by -2.

-2x ÷  -2 = 138 ÷  -2

x = −69

x=-69

Step-by-step explanation:

I believe it is m < 5 I could be wrong sorry.

Compact and oversized tires are produced on two different machines. The table shows the number of each type of tire produced, y, depending on the number of hours, x, the machines work.

OPTION B: 57x - 3

Step-by-step explanation:

Total tires produced is the sum of number of over-sized tires and the number of compact tires.

So, we have when x = 1, tires, y = 23 + 31 = 54

When x = 2, total tires y = 48 + 63  = 111

When x = 3, total tires y = 73 + 95  = 168

When x = 4, total tires y = 98 + 127 = 225

We can substitute the options to check which one will be the correct representation.

Option A: 55x - 1

When x = 1, y = 55(1) - 1    = 54

When x = 2, y = 55(2) - 1  = 109        111

So, this option is eliminated.

Option B: 57x - 1

When x = 1, y = 57(1) - 3    =   54

When x = 2, y = 57(2) - 3  =   111

When x = 3, y = 57(3) - 3  =   168

When x = 4, y = 57(4) - 3  =   225

These values exactly match with the values from the table. So, Option B is the right answer.

Option C: 110x - 2

When x = 1, y = 110(1) - 2 = 108    54

Hence, this option is incorrect.

Option D: 114x - 6

When x = 1, y = 114(1) - 6  54

Hence, this option is also eliminated.

Option B is the required answer.

Step-by-step explanation:

the person above me was on the right track but needed to multiply the sum of the y values by 2. Therefore the answer should be D

A circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle? Check all that apply.(x – 12)2 + y2 = 12
(x – 6)² + y² = 36
x² + y² = 12
x² + y² = 144
(x + 6)² + y² = 36
(x + 12)² + y² = 144

Options 2 and 5.

Step-by-step explanation:

The standard form of a circle is

... (1)

where, (h,k) is center and r is radius.

We need to find the circle that has a diameter of 12 units, and its center lies on the x-axis.

So, radius of required circle must be 6 and center is in the form of (a,0).

The first equation is

.... (2)

On comparing (1) and (2) we get

Center of the circle is (12,0) and radius is . So, option 1 is incorrect.

Similarly,

For equation 2, center of the circle is (6,0) and radius is . So, option 2 is correct.

For equation 3, center of the circle is (0,0) and radius is . So, option 3 is incorrect.

For equation 4, center of the circle is (0,0) and radius is . So, option 4 is incorrect.

For equation 5, center of the circle is (-6,0) and radius is . So, option 5 is correct.

For equation 6, center of the circle is (-12,0) and radius is . So, option 6 is incorrect.

Therefore, the correct options are 2 and 5.

its the 2nd and the 5th