10 pounds of soil are needed to

Mathematics

1 answer:

Wewaii [24]3 years ago

3 0

Answer:

40/3

Step-by-step explanation:

w = weight of soil needed

f = number of flower beds

a = constant value

w = a * f

substitute

10 = 6a

simplify

5/3 = a

w = (5/3)f

plug in 8

w = (5/3)(8)

simplify

w = 40/3

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SUppose the total cost C(x) to manufacture a quantity x of insecticide (in hundreds of liters) is given by

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Answer:

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b) $C(x)$ decreases in $(8\,s, 10\,s)$ .

Step-by-step explanation:

Let $C(x) = x^{3}-27\cdot x^{2}+240\cdot x +850$ , where $x$ is the quantity of insecticide, measured in hundreds of liters, and $C(x)$ is the total manufacturing cost as a function of the quantity of the insecticide, measured in US dollars. A possible approach to determine which regions of $C(x)$ are decreasing and increasing by means of the first derivative and graphing tools. The first derivative of the function is:

$C'(x) = 3\cdot x^{2}-54\cdot x+240$ (1)

Please notice that regions where C(x) is increasing has $C'(x) > 0$ , whereas $C'(x) < 0$ when $C(x) < 0$ .

We notice that $C(x)$ is increasing in two regions: (i) $(+\infty, 8\,s)$ and (ii) $(10\,s,+\infty)$ . Besides, $C(x)$ decreases in $(8\,s, 10\,s)$ .