A glass ball is packed in the box shown. Which expression represents the volume of foam padding needed to fill the space in the
box around the sphere in terms of Pi
1 answer:
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Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to simplify:
First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:
Now, create a common denominator. To do this, we can multiply the first term by (<em>a</em> + 1) and the second term by (<em>a</em> + 2). Hence:
Add the fractions:
Factor:
Simplify:
We can expand. Therefore:
Problem 2)
We want to simplify:
Again, let's create a common denominator. First, let's factor out a negative from the second term:
Now to create a common denominator, we can multiply the first term by (<em>a</em> - <em>c</em>) and the second term by (<em>a</em> - <em>b</em>). Hence:
Subtract the fractions:
Distribute and simplify:
Cancel. Hence: