When the temperature stays the same, the volume of gas is inversely proportional to the pressure of the gas. If a balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 38 cubic inches.

84 pounds per square inch

Step-by-step explanation:

 Extracting the key information from the question:

*** Volume of a gas is inversely proportional to pressure of the gas.

*** A balloon is filled with  228 cubic inches of a gas at a pressure of 14 pounds per square inch.

*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.

    Since volume is inversely proportional to pressure, then:

     V = k × (1/p)

      V = k/p

V = volume, p= pressure, k = mathematical constant

Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?

 Substituting appropriately, we have:

     228/1 = k/14

  cross multiply

K = 228 × 14 = 3192

 Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.

  V = k/p

Here, volume = 38, k = 3192

 We now have:

   38/1 = 3192/p

 Cross multiply

 38 × p = 3192

   p = 3192/38

   p = 84 pounds per square inch.

 The new pressure of the gas after decrement of the volume= 84 pounds per square inch

where's the diagrams?

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.