7. according to boyles law, the pressure of a...
7. according to boyles law, the pressure of a compressed gas is inversely proportional to its volume. if the pressure of a sample of gas is 30 pounds per square inch when the volume is 500 cubic inches, what is its pressure, in pounds per square inch, when expanded to 1,000 cubic inches? a. 7.5 psi b. 15 psi c. 30 psi d. 60 psi 8. solve the following equation 2g^(3/2)+10 = 64 9. solve the following equation 5(x - 2)^(2/3)=20
Answer
### 7.
# Explanation:
## Step1: Aplicar ley de Boyle
Según la ley de Boyle, $P_1V_1 = P_2V_2$, donde $P_1 = 30$ psi, $V_1=500$ pulgadas cúbicas y $V_2 = 1000$ pulgadas cúbicas.
## Step2: Despejar $P_2$
$P_2=\frac{P_1V_1}{V_2}=\frac{30\times500}{1000}$
$P_2 = 15$ psi
# Answer:
B. 15 psi
### 8.
# Explanation:
## Step1: Isolar el término con la variable
$2g^{\frac{3}{2}}+10 = 64$, entonces $2g^{\frac{3}{2}}=64 - 10=54$.
## Step2: Despejar $g^{\frac{3}{2}}$
$g^{\frac{3}{2}}=\frac{54}{2}=27$.
## Step3: Elevar ambos lados a $\frac{2}{3}$
$g = 27^{\frac{2}{3}}=(3^3)^{\frac{2}{3}}=3^2 = 9$.
# Answer:
$g = 9$
### 9.
# Explanation:
## Step1: Isolar el término con la variable
$5(x - 2)^{\frac{2}{3}}=20$, entonces $(x - 2)^{\frac{2}{3}}=\frac{20}{5}=4$.
## Step2: Elevar ambos lados a $\frac{3}{2}$
$x-2 = 4^{\frac{3}{2}}=(2^2)^{\frac{3}{2}}=2^3=8$.
## Step3: Despejar $x$
$x=8 + 2=10$.
# Answer:
$x = 10$