Mathematics, 24.12.2019 09:31 alyssabond8325

For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. at a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?

Answers: 1

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Answer from: brebre63

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form y*x=k or y=k/x

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point (30,600)

$x=30\ psi\\y=600\ in^{3}$

Find the constant k

y*x=k

substitute the values of x and y

600*30=k

$k=18,000\ lb*in$

the equation is

y=18,000/x

therefore

the answer is

y=18,000/x

Answer from: jj1077348

$y=\frac{18000}{x}$

Step-by-step explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒ $y \propto \frac{1}{x}$

Let the proportionality be k

So, $y=\frac{k}{x}$ ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

$600=\frac{k}{30}$

$600 \times 30=k$

18000 =k

Substitute the value of k in A

So, $y=\frac{18000}{x}$

Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is $y=\frac{18000}{x}$

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

Answer from: Quest

$f(x) = (\sqrt[4]{162})^x = (162^{1/4})^x = 162^{x/4}.$

$162 = 2 \times 3^4$

then

$f(x) = (\sqrt[4]{162})^x = (\sqrt[4]{2\times 3^4})^x = (3\sqrt[4]{2} )^x = (3\times 2^{1/4})^x$

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