Answer:
-1/2
Step-by-step explanation:
The answer is 4 + 3i
It is the only one there with a 
or i
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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).
Answer:
Variance = 5
Standard deviation = 2.236
0.2650257
Step-by-step explanation:
For a Poisson distribution is σ² = μ.
Given that:
Mean , μ of bankruptcies files per hour = 5
μ = 5
For a Poisson distribution :
P(x = x) = (μ^x * e^-μ) / x!
The Variance and standard deviation :
Variance : σ² = μ = 5
Standard deviation = sqrt(variance) = sqrt(5) = 2.236
B.) Find the probability that at most three businesses will file bankruptcy in any given hour.
P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)
P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379
P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897
P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243
P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738
0.0067379 + 0.0336897 + 0.0842243 + 0.1403738
= 0.2650257
Answer:
Volume of the cylinder = 
Step-by-step explanation:
Height of the Cylinder(h)=5 units
Radius(r)=2 units
Volume of a cylinder=
Putting the values in the formula;
Volume of the cylinder 
As, 
Volume of the cylinder= 
The Volume of the cylinder is
