Which is the solution to the inequality?
1 answer:
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Answer:
We need to find the lowest common divisor which is the smallest possible number that is dividable by ALL numbers.
We have the following numbers:
For the denominators (3, 3, 5, 5) the least common multiple (LCM) is 15.
LCM(3, 3, 5, 5) . Therefore, the least common denominator (LCD) is 15.
Rewriting the original inputs as equivalent fractions with the LCD:
125/15, 300/15, 75/15, 180/15
Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;
b) S''(1) = -38; S''(2) = -26; S''(4) = -2
Step-by-step explanation:
a) S' means first derivative;
(6t³ - 45t² +180t +130) = 6t² - 50t + 180
S'(1) = 6.1² - 50.1 + 180
S'(1) = 136
S'(2) = 6.2² - 50.2 + 180
S'(2) = 104
S'(4) = 6.4² - 50.4 + 180
S'(4) = 76
b) S'' is the second derivative of S:
(6t² - 50t + 180) = 12t - 50
S''(1) = 12.1 - 50
S''(1) = -38
S''(2) = 12.2 - 50
S"(2) = -26
S"(4) = 12.6 - 50
S"(4) = -2
c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.
Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.