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3 years ago

You are asked to construct a rectangular crate with a square

Mathematics

2 answers:

BigorU [14]3 years ago

6 0

Answer:

2.13 ft x 2.13 ft x 2.66 ft

Step-by-step explanation:

If W is the width of the square base, and H is the height, then:

12 = W²H

The cost of the crate is:

C = 8W² + 2W² + 4(4WH)

C = 10W² + 16WH

Solve for H in the first equation:

H = 12 / W²

Substitute into the second equation:

C = 10W² + 16W (12 / W²)

C = 10W² + 192 / W

Take the derivative with respect to W.

dC/dW = 20W − 192 / W²

Set to 0 and solve:

0 = 20W − 192 / W²

20W = 192 / W²

20W³ = 192

5W³ = 48

W = ∛(48/5)

W ≈ 2.13 ft

Find H:

H = 12 / W²

H ≈ 2.66 ft

guajiro [1.7K]3 years ago

4 0

Answer:

2.125 ft square by 2.657 ft high

Step-by-step explanation:

Let x represent the side length in feet of the square base. Then the height is found from ...

V = Bh

V/B = h = 12/x²

The cost of material is the sum of costs of top, bottom, and sides. That is ...

cost = 8x² +2x² +4(4xh) = 10x² +192/x

The cost is minimized when its derivative with respect to x is zero.

d(cost)/dx = 20x -192/x² = 0

x³ = 9.6 . . . . . . multiply by x²/20 and add 9.6

x = ∛9.6 ≈ 2.125 . . . . feet

h = 12/x² ≈ 2.657 . . . . feet

The dimensions of the crate are 2.125 feet square by 2.657 feet high.

_____

<em>Comment on the answer</em>

You may notice that the cost of top and bottom together is $10 per square foot. The cost of opposite sides together is $8 per square foot. That is, the ratio of costs is ...

base : sides = 10 : 8

You may also notice that the ratio of dimensions is ...

height : base side = 2.657 : 2.125 = 10 : 8

That is no accident. The dimensions of the lowest-cost crate are such that any pair of opposite sides costs the same.

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The Los Angeles Times regularly reports the air quality index for various areas of Southern

Troyanec [42]

Answer:

Range = 32 ; IQR = 13 ; Variance = 92.75 ; Standard deviation = 9.63

Step-by-step explanation:

Given the data:

28, 42, 58, 48, 45, 55, 60, 49, 50

Reorderd data: 28, 42, 45, 48, 49, 50, 55, 58, 60

The range: maximum - minimum

Range = 60 - 28 = 32

Interquartile range (IQR) : Q3 - Q1

Q3 = 3/4(n+1) th term. ; n = sample size

Q1 = 1/4(n+1)th term.

Using calculator :

Q3 = 56.5 ; Q1 = 43.5

IQR = 56.5 - 43.5 = 13

The variance :

Σ(X - m)^2 / n-1

m = Σx / n

Mean, m = 435 / 9 = 48.33

Variance :

[(28-48.33)^2 + (42-48.33)^2 + (45-48.33)^2 + (48-48.33)^2 + (49-48.33)^2 + (50-48.33)^2 + (55-48.33)^2 + (58-48.33)^2 + (60-48.33)^2] / 8

= 742.0001 / 8

= 92.75

Standard deviation = sqrt(Variance):

Sqrt(92.75) = 9.63

C.)

Sample mean are very close with a slightly greater Variability in the air quality of Anaheim over Pomona

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3 years ago

Kayla spent half her weekly allowance buying pizza. To earn more money her parent let her weed the garden for 10 dollars. What i

chubhunter [2.5K]

$18 - 10 = $8
$8 is weekly allowance

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3 years ago

9.) express the area of this triangle as a polynomial. (Remember A=1/2B H

schepotkina [342]

Plug in the values for b = $4ab^2c^7$ and h = $3a^2b^5$

A = $\frac{1}{2} (4ab^2c^7)(3a^2b^5)$
Simplify....
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5 0

3 years ago

Read 2 more answers

Find the measure of the indicated angle to the nearest degree.

ELEN [110]

Answer:

Step-by-step explanation:

Adjacent to the undetermined angle is 6, and the hypotenuse has been given. We can conclude, after looking at our SOHCAHTOA, that we will be using cosine(CAH) to solve this problem.

Let the unspecified angle be $\theta\\$ (This sign is called theta, which is just a sign for angle)

Lets start!

cos $\theta\\$ = adj/hyp

cos $\theta\\$ = 6/13

$\theta\\$ = $cos^{-1}$ (6/13)

$\theta\\$ = 62.5

$\theta\\$ = 63

Hope that helped!

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3 years ago

A plumber charges $10 for transportation and $37 per hour for repairs.

Ganezh [65]

Answer:

10+37h

Step-by-step explanation:

10 is the flat fee so only happens once

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3 years ago