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Marina86 [1]
3 years ago
14

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

Mathematics
1 answer:
vaieri [72.5K]3 years ago
7 0

Answer:

<u><em>Dimension of box:-</em></u>

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

                 500=x^2y

Therefore, y=\dfrac{500}{x^2}

It is open box. The surface area of box, S .

S=x^2+4xy

Put  y=\dfrac{500}{x^2}

S(x)=x^2+\dfrac{2000}{x}

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

S'(x)=2x-\dfrac{2000}{x^2}

For critical point, S'(x)=0

2x-\dfrac{2000}{x^2}=0

x^3=1000

x=10

Put x = 10 into y=\dfrac{500}{x^2}

y = 5

Double derivative of S(x)

S''(x)=2+\dfrac{4000}{x^3} at x = 10

S''(10) > 0

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

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What is the area of this square?
bogdanovich [222]

Answer:

6.25 mm squared

Step-by-step explanation:

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8 0
3 years ago
What is the area of this composite figure?<br>A. 135 cm2<br>B. 207 cm2<br>C. 249 cm2<br>D. 279 cm2
mariarad [96]

Answer:

249 cm^2

Step-by-step explanation:

This problem becomes easier if we subdivide the figure, find the areas of the resulting figures and then sum them up.

Draw a vertical line straight down from the edge marked "4 cm" towards the edge marked "18 cm."  The resulting rectangle on the left is 15.5 cm long and (18 - 7.5) cm wide, or 15.5 by 10.5 cm.  Its area is 162.75 cm^2.

Next, find the area of the rectangle on the right of the line we drew.  Its width is 7.5 cm and its height (15.5 - 4) cm, resulting in an area of 86.25 cm^2.

Last, add together these two subareas:  combine 86.25 cm^2 and 162.75 cm^2.  The total area of the composite figure is then 249 cm^2 (answer).

7 0
3 years ago
A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rec
lisov135 [29]

The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

<h3>What is the area of the rectangle?</h3>

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²

Let x be the width of the rectangle.

As the area of track along the walls of the gym is 7000ft²

(x - 12)(3x - 12) = 7000

After simplifying:

3x² - 48x + 6856 = 0

Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

Learn more about the rectangle here:

brainly.com/question/15019502

#SPJ1

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