Changing Volume If each edge of a cube is increasing at the constant rate of 3 centimeters per second, how fast is the volume in
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Answer:
<u>Create a function representing number of published articles per month:</u>
Where:
- a = total number of articles published
- m = number of months
- 12 = slope = number of articles published per month
- 60 = y-intercept = number of published articles at the start (month 0)
<u>Now substitute in the values of m to get the a-value:</u>
- m = 1 → a = 12(1) + 60 = 72
- m = 3 → a = 12(3) + 60 = 36 + 60 = 96
- m = 4 → a = 12(4) + 60 = 48 + 60 = 108
- m = 9 → a = 12(9) + 60 = 108 + 60 = 168
We factor the denominators
Factor x^2 - 16
x^2 - 4^2
We use a^2 - b^2 = (a+b)(a-b)
so x^2 - 4^2 = (x+4)(x-4)
Replace it in the given equation
Excluded values are the values that makes the denominator 0
we have (x-4) and (x+4) in the denominator
We set the denominator =0 and solve for x
x-4 =0
Add 4 on both sides
x= 4
x+4=0
subtract 4 onboth side
so x= -4
Excluded values are x=-4 and x=4