A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each
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Answer:
Interval notation:
Step-by-step explanation:
<u>First inequality:</u>
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Therefore, this inequality restricts:
<u>Second inequality:</u>
Therefore, this inequality restricts:
Therefore, with both of these restrictions together, we have:
.
The partial fraction decomposition is
The fraction is given as:
Split the fraction as follows:
Take the LCM
Cancel the common factors
8x + 19 = Ax - A + Bx + 8B
By comparison, we have:
Ax + Bx = 8x
-A + 8B = 19
This gives
A + B = 8
-A + 8B = 19
Add both equations
9B = 27
Divide by 9
B = 3
Substitute B = 3 in A + B = 8
A + 3 = 8
Solve for A
A = 5
So, we have:
Hence, the partial fraction decomposition is
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