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a_sh-v [17]
3 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]3 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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Plz help pe with this guys, thank you.
Burka [1]
31.+ addition
32. - subtraction
7 0
3 years ago
Which of the following fractions equal to 1/4
shutvik [7]

Answer:

D

Step-by-step explanation:

A  no   = 1/5

B no   = 4

C  no   = 1/3

D   yes

E     no = 17/50

4 0
2 years ago
Read 2 more answers
Please help with question 20! Thanks<3
kkurt [141]

Answer:

Population of Town A = 19,575

Population of Town B = 52,200

Population of Town C = 20,880

Step-by-step explanation:

The ratio of..

A : B = 3 : 8

B : C = 5 : 2

Both A : B and B : C have B in their ratios. What we can do is make B the same in both ratios and then create a ratio between all three towns.

A : B = (3 : 8) x 5 = 15 : 40

B : C = (5 : 2) x 8 = 40 : 16

A : B : C

15 : 40 : 16

Now, to find the population of each town we can write the following equation using the numbers from our ratio between all three towns and set it to the given population.

15x + 40x + 16x = 92,655

Solve for x.

71x = 92,655

x = 1,305

Finally, we can use the value of x to find the population of each town.

Population of Town A = 15x

Population of Town A = 15(1,305)

Population of Town A = 19,575

Population of Town B = 40x

Population of Town B = 40(1,305)

Population of Town B = 52,200

Population of Town C = 16x

Population of Town C = 16(1,305)

Population of Town C = 20,880

~Hope this helps!~

3 0
3 years ago
The average size of 8 farms in Indiana County, Pennsylvania, is 191 acres with standard deviation of 38 acres. The average size
Grace [21]

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. it is a two-tailed test. Let μ1 be average size of farms in Indiana County, Pennsylvania and μ2 be the average size of farms in Greene County, Pennsylvania.

The random variable is μ1 - μ2 = difference in the average size of the farms in Indiana County and the average size of the farms in Greene County.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(μ1 - μ2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 191

μ2 = 199

s1 = 38

s2 = 12

n1 = 8

n2 = 10

t = (191 - 199)/√(38²/8 + 12²/10)

t = - 0.57

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [38²/8 + 12²/10]²/[(1/8 - 1)(38²/8)² + (1/10 - 1)(12²/10)²] = 37986.01/4677.36142857143

df = 8

We would determine the probability value from the t test calculator. It becomes

p value = 0.58

Let us assume a significance level of 0.05

Since alpha, 0.05 < than the p value, 0.58, then we would accept the null hypothesis. Therefore, at a significance level of 5%, there is not sufficient evidence to conclude that the average size of the farms in Indiana County and the average size of the farms in Greene County are different.

4 0
3 years ago
Whats 9 divide by 6.5
dezoksy [38]
It's an irrational number which means the number never ends and has no pattern in its decimal. So you would round it:
9/6.5= 1.384615384615385
but the answer would be 1.384
8 0
3 years ago
Read 2 more answers
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