Answer:
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Answer:
The pressure is 
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form 
or 
In this problem we have
where
V is the volume of a gas at a constant temperature
P is the pressure
we have
For 
,
step 1
Find the value of k
substitute the values of V and P
The equation is equal to 
step 2
Find the pressure when the volume is 125 cubic inches
For 
substitute in the equation and solve for P
Answer: The box would have 99% of its volume taken up.
Step-by-step explanation: The box has dimensions as follows;
Length = 6 inches
Width = 5 inches
Height = 10 inches
Therefore the volume of the box shall become
Volume = L x W x H
Volume = 6 x 5 x 10
Volume = 300 cubic inches
Also a 3 inch cube would have its volume given as follows (
Volume = 3 x 3 x 3 (All sides of a cube has equal lengths)
Volume = 27 cubic inches
To find out how many of 3-inch cubes can fit in, divide 300 by 27 and that equals 11.11.
Hence you can have at most 11 cubes in the box. The total volume of 11 cubes is given as 11 x 27 which equals 297. Therefore, the percentage of the box taken up completely by the cubes is given as;
Percentage = (Volume of cubes/Volume of box) x 100
Percentage = (297/300) x 100
Percentage = 99
Therefore the box would have 99% of its volume taken up by the cubes.
f(x)=x3−5
Replace f(x)
with y
.
y=x3−5
Interchange the variables.
x=y3−5
Solve for y
.
Since y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
y3−5=x
Add 5
to both sides of the equation.
y3=5+x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=3√5+x
Solve for y
and replace with f−1(x)
.
Replace the y
with f−1(x)
to show the final answer.
f−1(x)=3√5+x
Set up the composite result function.
f(g(x))
Evaluate f(g(x))
by substituting in the value of g into f
.
(3√5+x)3−5
Simplify each term.
Remove parentheses around 3√5+x
.
f(3√5+x)=3√5+x3−5
Rewrite 3√5+x3
as 5+x
.
f(3√5+x)=5+x−5
Simplify by subtracting numbers.
.
Subtract 5
from 5
.
f(3√5+x)=x+0
Add x
and 0
.
f(3√5+x)=x
Since f(g(x))=x
, f−1(x)=3√5+x is the inverse of f(x)=x3−5
.
f−1(x)=3√5+x
(xy)=(9,4). Hope this helps
