Write the expression for 2 added to the product of a number p and 43
2 answers:
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In general, the volume
has total derivative
If the cylinder's height is kept constant, then
and we have
which is to say,
and 
are directly proportional by a factor equivalent to the lateral surface area of the cylinder (
).
Meanwhile, if the cylinder's radius is kept fixed, then
since
. In other words, and 
are directly proportional by a factor of the surface area of the cylinder's circular face (
).
Finally, the general case (
and 
not constant), you can see from the total derivative that is affected by both and in combination.
has total derivative
If the cylinder's height is kept constant, then
which is to say,
Meanwhile, if the cylinder's radius is kept fixed, then
since
Finally, the general case (
Answer:
(a)$13
(b) Loss of $4
Step-by-step explanation:
C(q) represents Cost of producing q units.
R(q) represents Revenue generated from q units.
P(q) represents Total Profit made from producing q units.
Marginal analysis is concerned with estimating the effect on quantities such as cost, revenue, and profit when the level of production is changed by a unit amount. For example, if C(q) is the cost of producing q units of a certain commodity, then the marginal cost, MC(q), is the additional cost of producing one more unit and is given by the difference
MC(q) = C(q + 1) − C(q).
Using the estimation
C'(q)≈=C(q+1)-C(q)
We find out that MC(q)=C'(q)
We can therefore compute the marginal cost by the derivative C'(q).
This also holds for Revenue, R(q) and Profit, P(q).
(a) If C'(50)=75 and R'(50)=88
51st item.
P'(50)=R'(50)-C'(50)
=88-75=$13
The profit earned from the 51st item will be approximately $13.
(b) If C'(90)=71 and R'(90)=67, approximately how much profit is earned by the 91st item.
P'(90)=R'(90)-C'(90)
=67-71= -$4
The profit earned from the 91 st item will be approximately -$4.
There was a loss of $4.