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lesantik [10]
2 years ago
8

box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am

ount of material used. sides of base
Mathematics
1 answer:
Naya [18.7K]2 years ago
6 0

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

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A rectangle is 3 times as long as it is wide, and its perimeter is 80 centimeters. Find its dimensions
Free_Kalibri [48]

Say the width is W and the length is L

L=3W (and of course W=W)

Now you use the perimeter formula P=2L+2W

80=2(3W) + 2W)

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W=10

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L=3(10)

L=30

The dimensions are length: 30 cm and width: 10 cm

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3 years ago
Graph x^4-3x^2+x. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the inte
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Functions, equations and tables can be represented using graphs

  • The x-intercepts are: 0, 0.35 and 1.53
  • The local maximum is at point (0.17, 0.08), and the local minimum is at point (1.13, -1.07)

The expression is given as:

x^4-3x^2+x

Rewrite the expression as a function

f(x) =  x^4-3x^2+x

See attachment for the graph of the function.

<h3>The x-intercepts</h3>

This is the point where the graph cross the x-axis.

From the attached graph, the x-intercepts are: 0, 0.35 and 1.53

<h3>The local maximum</h3>

From the attached graph, the local maximum is at point (0.17, 0.08)

<h3>The local minimum</h3>

From the attached graph, the local minimum is at point (1.13, -1.07)

<h3>Intervals</h3>
  • The graph increases at interval (-1.30, 0) and (1,13, infinity)
  • The graph decreases at interval (- infinity, 1.30) and (0.35, 1.13)

Read more about graphs and functions at:

brainly.com/question/13136492

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frozen [14]
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of the 80 guests invited to a wedding, 28 attended the wedding. What percent of the invited guests attended the wedding?
klasskru [66]

Answer:

35%

Step-by-step explanation:

% of guests who attended the wedding is number of guests who attended the wedding divided by the number of invited guests and the result multiplied by 100%

Therefore

28/80 x 100%

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35%

35% of the invited guests attended the wedding

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