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:
110 + 10x ; 40x
4
Step-by-step explanation:
Given that:
For every visit to Arts museum:
Scenario 1:
Parking fee = $15
Admission fee = $25
Total amount for scenario 1:
If number of visits = x
Total cost = $(15 + 25) × number of visits
Total cost : $40x
With membership :
Price of membership = $110 (one time payment)
Parking fee = $10
Admission fee = $0
Let number of visits = x
Total cost :
Membership fee + (parking fee × number of visits)
$110 + ($10 * x)
= 110 + 10x
B) number of visits for which member cost is less than non-member cost :
Member cost = 110 + 10x
Non member cost = 40x
110 + 10x < 40x
10x - 40x < 110
-30x < 110
x > 3.67
Hence x = 4
Number of visits for which member cost is greater than non member cost is 4
Answer:
Choice A is the correct answer
Step-by-step explanation:
To evaluate the limits, we simply perform direct substitution; substitute -infinity into each expression in the alternatives and then simplify the expression. Notice that only the expressions in alternative A will fit this criteria since they will be tending to -infinity as x approaches -infinity.
The amount of substance left of a radioactive element of half life,
after a time, t, is given by:
Given that <span>potassium-40 has a half life of approximately 1.25 billion
years.
The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:
Therefore, </span><span>the maximum age of a fossil that we could date using 40k is
12.5 billion years.</span>
