Malcom is filling bags with rice . He starts with a 5 1/4 pound container of rice and fills each bag with 5/8 pounds of rice . H
1 answer:
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We want to find such that
. This means
Integrating both sides of the latter equation with respect to tells us
and differentiating with respect to gives
Integrating both sides with respect to gives
Then
and differentiating both sides with respect to gives
So the scalar potential function is
By the fundamental theorem of calculus, the work done by along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it
) in part (a) is
and does the same amount of work over both of the other paths.
In part (b), I don't know what is meant by "df/dt for F"...
In part (c), you're asked to find the work over the 2 parts (call them and
) of the given path. Using the fundamental theorem makes this trivial:
Answer:
slope =
Step-by-step explanation:
Calculate the slope m using the slope formula
m =
with (x₁, y₁ ) = (5, 3 ) and (x₂, y₂ ) = (9, 6 )
m = =
Answer:
Tamara's example is in fact an example that represents a linear functional relationship.
- This is because the cost of baby-sitting is linearly related to the amount of hours the nany spend with the child: the more hours the nany spends with the child, the higher the cost of baby-sitting, and this relation is constant: for every extra hour the cost increases at a constant rate of $6.5.
- If we want to represent the total cost of baby-sitting in a graph, taking the variable "y" as the total cost of baby-sitting and the variable "x" as the amount of hours the nany remains with the baby, y=5+6.5x (see the graph attached).
- The relation is linear because the cost increases proportionally with the amount of hours ($6.5 per hour).
- See table attached, were you can see the increses in total cost of baby sitting (y) when the amount of hours (x) increases.
