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a_sh-v [17]
2 years ago
7

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

s. Find the dimensions of the tank with minimum weight.
Mathematics
1 answer:
marishachu [46]2 years ago
4 0

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

V = s^2h = 5324

h = 5324 / s^2

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top s^2

Side area 4sh

Total surface area A = s^2 + 4sh

We can substitute h = 5324 / s^2

A = s^2 + 4s\frac{5324}{s^2}

A = s^2 + 21296/s

To find the minimum of this function, we can take the first derivative, and set it to 0

A' = 2s - 21296/s^2 = 0

2s = 21296/s^2

s^3 = 10648

s = \sqrt[3]{10648} = 22

h = 5324 / s^2 = 5324 / 22^2 = 11

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kow [346]

The height of Radon plant is 6.3 meters

<em><u>Solution:</u></em>

Given that, Allies plant has a height of 6 meters

Radon’s plant grows \frac{3}{10} meters higher

To find: Height of Radon plant

From given information,

Height of Allies plant = 6 meters

Height of radon plant = \frac{3}{10} + Height of Allies plant

Substituting the known value,

\text{ Height of radon plant} = \frac{3}{10} + 6\\\\\text{ Height of radon plant} = \frac{3+60}{10}\\\\\text{ Height of radon plant} = \frac{63}{10}\\\\\text{ Height of radon plant} = 6.3

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2 years ago
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled b
abruzzese [7]

Answer:

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8 0
2 years ago
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Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is
Liula [17]

Answer:

The variance in weight is statistically the same among Javier's and Linda's rats

The null hypothesis will be accepted because the P-value (0.53 ) > ∝ ( level of significance )

Step-by-step explanation:

considering the null hypothesis that there is no difference between the weights of the rats, we will test the weight gain of the rats at 10% significance level with the use of Ti-83 calculator

The results from the One- way ANOVA  ( Numerator )

with the use of Ti-83 calculator

F = .66853

p = .53054

Factor

df = 2  ( degree of freedom )

SS = 23.212

MS = 11.606

Results from  One-way Anova ( denominator )

Ms = 11.606

Error

df = 12 ( degree of freedom )

SS = 208.324

MS = 17.3603

Sxp = 4.16657

where : test statistic = 0.6685

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             level of significance ( ∝ ) = 0.10

The null hypothesis will be accepted because the P-value (0.53 ) > ∝

where Null hypothesis H0 = ∪1 = ∪2 = ∪3

hence The variance in weight is statistically the same among Javier's and Linda's rats

7 0
1 year ago
The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under;
docker41 [41]

Answer:

a) 51.4

b) answer attached

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Step-by-step explanation:

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b) answer attached below

c) probability that out of 20-64 group a randomly selected sample is female

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= 48.59% chance of her being a female

Download docx
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