
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:
The answer to your question is: d = 0.85 units
Step-by-step explanation:
Data
Line equation: 1.2 x − 0.5 y + 1.1 = 0 A = 1.2; B = -0.5; C = 1.1
Point (0, 0) x = 0; y = 0
Formula
d = | Ax + By + C | / √(A² + B²)
Process
d = |(1.2)(0) + (-0.5)(0) + 1.1 | / √ (1.2)² + (0.5)²
d = | 1.1 | / √ 1.44 + 0.25
d = 1.1 / √ 1.69
d = 1.1 / 1.3
d = 0.85 units
Let n = 30
We are actually looking for a_30.
a_30 = 4(30) + 1
a_30 = 120 + 1
a_30 = 121
Answer:
7%
11%
5%
14%
Step-by-step explanation:
To find a numbers percentage of another number you simply divide the smaller number by the bigger number then move the decimal point to the right 2 places.
Percentage of workers who prefer chicken soup who are part-time: 35÷500 = 0.07 move the decimal 2 to the right to get 7%.
Percentage of full-time workers who prefer mushroom soup: 55÷500 = 0.11 move the decimal 2 to the right to get 11%.
Percentage of workers who prefer lintel soup who are full-time: 25÷500 = 0.05 move the decimal 2 to the right to get 5%.
Percentage of part-time workers who prefer tomato soup: 70÷500 = 0.14 move the decimal 2 to the right to get 14%.
Hope this helps! :)