Question

1. Mandeep’s parents want to build a rectangular ice rink in the family’s back yard with an area of 200m²
2. What are the dimensions that will minimize the amount of material required to build the boards around the rink?
3. If the material for the boards can be bought for $1.75 a linear foot, how much will it cost to build the boards?

1. Trevor was given 15 square concrete stones with a 1 ft. side length. He decides to make a slab for a fire pit and put a garden around the outer edge of the concrete. What are the dimensions for his new fire pit that will minimize the amount of garden?

Answer 1

Answer:-

Given That:-

Mandeep’s parents want to build a rectangular ice rink in the family’s back yard with an area of 200m2.

What are the dimensions that will minimize the amount of material required to build the boards around the rink?

Given,

Let the length and breadth of rink be 'l' and 'b' respectively.

Then,

Area = lb = 200 m²

b = 200/l

Now,

perimeter of b rink = p = 2(l + b)

p = 2 (l + (200/l))

dp/dl = 2[1 - (200/l²)]

For maxima or minima

dp/dl = 0

2[1 - (200/l²)] = 0

Now,

  

Therefore,

is point of minima

For minima material

and

  

If the material for the boards can be bought for $1.75 a linear foot, how much will it cost to build the boards?

Total perimeter of rink =

  

= 185.598 foot

Therefore,

Lost of material = 1.75 * 185.598

= $ 324.797

Trevor was given 15 square concrete stones with a 1 ft. side length. He decides to make a slab for a fire pit and put a garden around the outer edge of the concrete. What are the dimensions for his new fire pit that will minimize the amount of garden?

Trevor has toal 15 square concrete

Therefore total Area = 15 square feet

A = l x b = 15

b = 15/l

perimeter = 2(l + b)

p = 2(l + 15/l)

Therefore,   is point of minima

Dimensions are length = feet

and

Breadth = 15/l

= 15/

= feet

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