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frozen [14]
2 years ago
9

Consider all rectangles with an area of 256 cm squared. let x be the length of one side of such a rectangle. express the perimet

er as a function of x and determine the dimensions of the rectangle that has the least perimeter
Mathematics
1 answer:
Leya [2.2K]2 years ago
5 0

Answer:

- P = 2x + 512/x

- 16cm by 16cm

Step-by-step explanation:

The formula for calculating the area of a rectangle = Length * width

Area = LW

256 = xy .... 1

y = 256/x

x is the length

y is the width

Perimeter of the rectangle = 2(x+y)

P = 2x + 2y

P = 2x + 2(256/x)

P = 2x + 512/x

Hence the perimeter as a function of x is P = 2x + 512/x

For the rectangle to have a least perimeter, this means dP/dx = 0

dP/dx = 2 - 512/x²

0 = 2 -512/x²

2 = 512/x²

2x² = 512

x² = 256

x = √256

x = 16

Since xy = 256

y = 256/16

y = 16

Hence the dimensions of the rectangle that has the least perimeter is 16cm by 16 cm

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Answer:

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Step-by-step explanation:

From the question we are told that

   The function is  f(x, y) =  9sin(xy) \ \ \

    The point considered is  (0,8 )

Generally the maximum rate of change of f at the given point and the direction is mathematically represented as

            \Delta f(x,y) =  [\frac{\delta  f(x,y)}{\delta x } i + \frac{\delta  f(x,y)}{\delta y } j  ]

             \Delta f(x,y) =  [\frac{\delta  (9sin(xy))}{\delta x} i  + \frac{\delta  (9sin(xy))}{\delta y} i   ]

            \Delta f(x,y) = [9y cos (x,y) i +  9xcos (x,y) j]

At  (0,8 )

            \Delta  f (0,8) =  [9(8) cos(0* 8)i  + 9(8) sin(0* 8)j  ]

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Answer:

z=1.64

And if we solve for a we got

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Step-by-step explanation:

Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:

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And if we solve for a we got

a=14.4 +1.64*1.1=16.204

The 95th percentile of the hip breadth of adult men is 16.2 inches.

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