Answer:
x= 4
Step-by-step explanation:
i dont think u need explanation but lmk if u do :)
-3x - 4y - 2z = 0
x + 3y + 2z = 1
-2x - y = 1
-4x - 4y - 2z = 10
3x + 4y +2z= 0
-x = 10. x = -10
-2(-10) - y = 1
20 - y = 1
-y = -19
y = 19
-10 + 3(19) + 2z = 1
-10 + 57 + 2z = 1
47 + 2z = 1
2z = -46
z= -23
check: 2(-10)+2(19)-23=-5
-20+38-23=-5
-43+38=-5
-5=-5
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).
The average rate of change in the monthly rate per year is -$0.056 i.e decreases by 0.056 every consecutive year.
Step-by-step explanation:
Step 1; The initial value is $7.69 in 1980 and the final value is $6.13 in 2008.
Difference in values = Final value - initial value = $6.13- $7.69 = -$1.56 (the negative symbol indicates that the cost has gone down with time)
Period between the values =Final year - initial year = 2008 - 1980 = 28 years.
Step 2; To find the rate of change per year, we divide the difference in values in that given period of time by the number of years in that period.
Rate of change per year = Difference in values in that period/ no of years.
= -$1.56 / 28 = -$0.056 (the negative symbol indicates that the cost has gone down with time)
So for every year between 1980 and 2008, the price of the monthly rate for basic able TV reduced by $0.056.
