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Tcecarenko [31]
1 year ago
13

An open-topped glass aquarium with a square base is designed to hold 13.513.513, point, 5 cubic feet of water. what is the minim

um exterior surface area of the aquarium?
Mathematics
1 answer:
ExtremeBDS [4]1 year ago
3 0
Suppose the aquarium's shape is a square prism, with each side of the square having length x, and the aquarium's height is y, so we have: 
<span> x^2 * y = 13.5
</span> <span>y = 13.5/(x^2) 
</span><span> The area of each side is xy, and there are four sides, so that totals 4xy 
</span><span> The area of the bottom is x^2 
</span><span> Total surface area: 
</span><span> A = x^2 + 4xy 
</span><span> A = x^2 + 4x(13.5/(x^2))
</span> <span>A = x^2 + 54x^(-1) 
</span><span> dA/dx = 2x - 54x^(-2) 
</span><span> Set the derivative to zero: 
</span><span> 2x - 54x^(-2) = 0 
</span><span> 2x = 54/(x^2) 
</span><span> 2x^3 = 54 
</span><span> x^3 = 54/2 
</span><span> x^3 = 27 
</span><span> x = cbrt(27) = 3, assuming x is a real number 
</span><span> A = 3^2 + 54*3^(-1) 
</span><span> A = 9 + 18
</span><span> A = 27 square feet</span>
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Answer:

First person: $107

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Third person: $93

Step-by-step explanation:

Let be "f" the amount of money (in dollars) that the first person contributed to the purchase, "s" the amount of money (in dollars) that the second person contributed to the purchase and "t" the amount of money (in dollars) that the third person contributed to the purchase.

With the information given in the exercise, you can set up the following equations:

Equation 1 → f+s+t=298

Equation 2 → s=f-9

Equation 3 → t=f-14

Substitute the Equations 2 and 3 into the Equation 1 and then solve for "f":

f+(f-9)+(f-14)=298\\\\3f-23=298\\\\f=\frac{321}{3}\\\\f=107

Finally, substitute the value of "f" into the Equation 2 and then into the Equation 3, in order to find the values of "s" and "t".

Therefore, you get:

s=107-9\\\\s=98\\\\\\t=107-14\\\\t=93

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C

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Multiply the 1.5 hours per pound by 2.75 pounds and we get 4.125 hours or    4 1/8

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Flannery used 30 lilies and 78 roses to create six identical flower arrangements. Write an equation to describe the relationship
Volgvan

Number of lilies used= 30 lilies

Number of roses used= 78 roses

To make the six identical arrangements:

We need to divide lilies into six equal parts, as well as number of roses in six equal parts.

I=Number of lilies in each arrangement = \frac{30}{6}=5

r=Number of roses in each arrangement = \frac{78}{6}=13

Total number of flowers in arrangement (I + r)= 5 Lilies + 13 Roses=18 (Flowers)

The relationship between l, the number of lilies, and r, the number of roses:

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Answer: 2\ minutes

Step-by-step explanation:

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Solved for the time "t":

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Knowing that:

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