16.03.2021

Arthur plants 4 basil plants in a square frame like the one shown. The soil in this frame will be 2x in. deep. Given that each basil plant needs 1,300 in.3 of soil, will neighboring plants in the square frame be closer to each other or farther apart than neighboring plants in the rectangular frame?

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11.02.2023, solved by verified expert
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Answer:

The neighboring plants in the square frame will be farther apart than neighboring plants in the rectangular frame.

Step-by-step explanation:

Given that each plant requires 1300 in.^3 of soil and total plants are 4. 

Total soil required = 4(1300) = 5200 in.^3 

From the previous solution: 

Total required volume = 18x^3 +48x^2 +(32 -8π)x in.^3 

Therefore, 

18x^3 +48x^2 +(32 -8π)x = 5200

Solving this cubic equation for x. 

the value of x = 5.8 inches (approx.)

This means the distance between the plants = 5.8 inches. ......(1)

In case of the rectangular frame, 

Arthur plants 4 basil plants in a square frame, №15256789, 16.03.2021 07:46

36x^3 +102x^2 +(72 -18π)x = 1300*6 = 7800

36x^3 +102x^2 +(72 -18π)x = 7800

solving for x

x = 5.17 inches  (approx.) .......(2)

Form (1) and (2), the neighboring plants in the square frame will be farther apart than neighboring plants in the rectangular frame.

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