Answer:
B.
Step-by-step explanation:
Given: expressions
To find: the expression whose value is closest to e
Solution:
Value of e is 2.718

Therefore, value 2.659 is closest to the value of e.
So, option B. is correct.
It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is
<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)
The cosine of the angle between the vectors can be obtained from the dot product identity,
<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>) ==> cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)
so that
<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)
For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is
<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> <em>W</em> ≈ 5.12 J
(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).
Once we find what x and y is, that's where they intercept and we can write that as an ordered pair as (x,y)
Now we need to find what y is. So let's put x into the original first equation
3x+4y=16
3(4)+4y=16
12+4y=16 ---Subtract 12 from both sides
4y=4 ---Divide both sides by 4
y=1
Alright, so our ordered pair is (4,1)
<span>The answer would be yes, the locus of points idea allows you to
define a circle without giving a numerical value for the radius.
A locus of points</span> is the set of <span>points<span>, and only those </span>points</span>, that satisfies given conditions. The locus of points at a given distance from a given point is a circle whose center
is the given point<span> and whose radius is the given distance.</span>
Because there are 2 pints in a quart, 712 quarts would equal 1,424 pints.