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Kobotan [32]
3 years ago
15

A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs

0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
Mathematics
1 answer:
LenKa [72]3 years ago
3 0

Answer:

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

Step-by-step explanation:

Volume of the Cylinder=400 cm³

Volume of a Cylinder=πr²h

Therefore: πr²h=400

h=\frac{400}{\pi r^2}

Total Surface Area of a Cylinder=2πr²+2πrh

Cost of the materials for the Top and Bottom=0.06 cents per square centimeter

Cost of the materials for the sides=0.03 cents per square centimeter

Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)

C=0.12πr²+0.06πrh

Recall: h=\frac{400}{\pi r^2}

Therefore:

C(r)=0.12\pi r^2+0.06 \pi r(\frac{400}{\pi r^2})

C(r)=0.12\pi r^2+\frac{24}{r}

C(r)=\frac{0.12\pi r^3+24}{r}

The minimum cost occurs when the derivative of the Cost =0.

C^{'}(r)=\frac{6\pi r^3-600}{25r^2}

6\pi r^3-600=0

6\pi r^3=600

\pi r^3=100

r^3=\frac{100}{\pi}

r^3=31.83

r=3.17 cm

Recall that:

h=\frac{400}{\pi r^2}

h=\frac{400}{\pi *3.17^2}

h=12.67cm

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

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Answer:

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Step-by-step explanation:

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Answer:

The confidence interval is (24116.3878,24883.6122).

Step-by-step explanation:

We are given the following information in the question:

Population mean, \mu = $23,500

Sample mean,\bar{x} = $24,500

Sample standard deviation,s = $2,800

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Confidence interval:

\bar{x} \pm t_{critical}\frac{s}{\sqrt{n}}  

Putting the values, we get,

t_{critical}\text{ at}~\alpha_{0.05} = \pm 1.655436

24500 \pm 1.65543(\frac{2800}{\sqrt{146}} ) = 24500 \pm 383.6122 = (24116.3878,24883.6122)

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Three-quarters of a pound of candy cost 66 cents. Find the cost of one pound<br> of candy.
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Step-by-step explanation:

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Read 2 more answers
One bar of candy A and two bars of candy B have 774 calories. Two bars of candy A and one bar of candy B contains 786 calories.
vampirchik [111]
◆ Define the variables:

Let the calorie content of Candy A = a
and the calorie content of Candy B = b

◆ Form the equations:

One bar of candy A and two bars of candy B have 774 calories. Thus:

a + 2b = 774

Two bars of candy A and one bar of candy B contains 786 calories

2a + b = 786

◆ Solve the equations:

From first equation,
a + 2b = 774
=> a = 774 - 2b

Put a in second equation
2×(774-2b) + b = 786
=> 2×774 - 2×2b + b = 786
=> 1548 - 4b + b = 786
=> -3b = 786 - 1548
=> -3b = -762
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◆ Find caloric content:

Caloric content of candy B = 254 calorie

Caloric content of candy A = a = 774 - 2b = 774 - 2×254 = 774 - 508 = 266 calorie
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