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barxatty [35]
3 years ago
5

A flat circular plate has the shape of the region x 2 + y 2 ≤ 1. points on the plate have temperature t(x, y) = x 2 + 2y 2 − x.

find the temperatures of the hottest and coldest points of the plate
Mathematics
1 answer:
Rudik [331]3 years ago
5 0

A flat circular plate has the shape of the region x 2 + y 2 ≤ 1. points on the plate have temperature t(x, y) = x 2 + 2y 2 − x. find the temperatures of the hottest and coldest points of the plate

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Step-by-step explanation:

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What is the following sum? 2 (RootIndex 3 StartRoot 16 x cubed y EndRoot) 4 (RootIndex 3 StartRoot 54 x Superscript 6 Baseline y
san4es73 [151]

Equivalent expressions are expressions that have the same value, and can be used interchangeably.

The result of the sum 2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5}) is 4x\sqrt[3]{2y}  + 8x^2y\sqrt[3]{2y^2})

The expression is given as:

2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5})

Rewrite the expression as:

2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y})  + 4 (\sqrt[3]{3^3 \times 2x^6y^5})

Evaluate the roots

2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y})  + 4 (3x^2y\sqrt[3]{2y^2})

Open the brackets

2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y}  + 12x^2y\sqrt[3]{2y^2})

The above expression cannot be further simplified.

Hence, the result of the sum 2 (\sqrt[3]{16x^3y})  + 4 (\sqrt[3]{54x^6y^5}) is 4x\sqrt[3]{2y}  + 8x^2y\sqrt[3]{2y^2})

Read more about equivalent expressions at:

brainly.com/question/2972832

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