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Digiron [165]
2 years ago
11

A 20 inch long piece of rope is approximately 0.5 meters long. What is the length, in inches, of a rope that is 2.5 meters long,

rounded to the nearest tenth?
Mathematics
1 answer:
zlopas [31]2 years ago
3 0

Answer:

100 inches (using the given data)

98.43 (using exact numbers)

Step-by-step explanation:

1 inch = 2.54 centimeters

20 inches = 50.8 centimeters, but for the purpose of answering this question we will assume that 20 inches = 0.5 meters (instead of 0.58).

we must solve the following equation:

20 inches / 0.5 meters = X inches / 2.5 meters

(2.5  meters x 20 inches) / 0.5 meters = X inches

20 inches x 5 = X inches

100 inches = X inches

if we do the exact calculation, 2.5 meters in inches = 250 centimeters / 2.54 centimeters per inch = 98.43 inches

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Let φ(x, y) = arctan (y/x) .
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Answer:

a) \large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})

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Step-by-step explanation:

a)

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

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\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}

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