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Colt1911 [192]
3 years ago
13

One half gallon is equivalent to 4 pints.how many gallons are the equivalent of 72 pints

Mathematics
1 answer:
malfutka [58]3 years ago
5 0

Answer: 9 gallons

<u>Step-by-step explanation:</u>

Set up the proportion, then multiply to solve for the variable.

\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=\dfrac{x}{72\ \text{pints}}

(72\ \text{pints})\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=(72\ \text{pints)}\dfrac{x}{72\ \text{pints}}

\dfrac{36\ \text{gallons}}{4}=x}

9 gallons = x

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Help I’ll mark brainlist if correct :)
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3 years ago
use green's theorem to evaluate the line integral along the given positively oriented curve. c 9y3 dx − 9x3 dy, c is the circle
Rina8888 [55]

The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.

<h3>What is green's theorem?</h3>

The theorem states that,

\int_CPdx+Qdy = \int\int_D(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y})dx dy

Where C is the curve.

<h3>Calculation:</h3>

The given line integral is

\int_C9y^3dx-9x^3dy

Where curve C is a circle x² + y² = 4;

Applying green's theorem,

P = 9y³; Q = -9x³

Then,

\frac{\partial P}{\partial y} = \frac{\partial 9y^3}{\partial y} = 27y^2

\frac{\partial Q}{\partial x} = \frac{\partial -9x^3}{\partial x} = 27x^2

\int_C9y^3dx-9x^3dy = \int\int_D(-27x^2 - 27y^2)dx dy

⇒ -27\int\int_D(x^2 + y^2)dx dy

Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as

0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π

Then the integral becomes

-27\int\limits^{2\pi}_0\int\limits^2_0r^2. r dr d\theta

⇒ -27\int\limits^{2\pi}_0\int\limits^2_0 r^3dr d\theta

⇒ -27\int\limits^{2\pi}_0 (r^4/4)|_0^2 d\theta

⇒ -27\int\limits^{2\pi}_0 (16/4) d\theta

⇒ -108\int\limits^{2\pi}_0 d\theta

⇒ -108[2\pi - 0]

⇒ -216π

Therefore, the required value is -216π.

Learn more about green's theorem here:

brainly.com/question/23265902

#SPJ4

3 0
1 year ago
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