For a floating object, the buoyancy force is equal to the gravity force on the object. Hence, the buoyancy force doesn't change with a denser fluid. Instead the displaced volumedecreases to cancel out the effect of the increased fluid density.
Answer:
The ratio of energy of AA battery to the car battery is 0.0156.
Explanation:
An AA battery (remote control battery) supplies the circuit with 1.5V, while a car battery supplies 12V. What is the relationship between the energy supplied between these circuit elements?
Supply by AA battery = 1.5 V
Supply by car battery = 12 V
The resistance of the circuit is R.
The energy supplied = V^2/R
The energy supplied by the AA battery is
E = 1.5 x 1.5 / R = 2.25/R
The energy supplied by the car battery is
E' = 12 x 12/ R = 144 / R
So, the ratio of
E : E' = 2.25 : 144 = 0.0156
Distribute the product:
a×b = (8i + j - 2k) × (5i - 3j + k)
a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + k×j)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
Recall the definition of the cross product:
i×i = j×j = k×k = 0 (the zero vector)
i×j = k
j×k = i
k×i = j
and for any two vectors x and y, we have x×y = -(y×x).
So we have some cancellation and rewriting:
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + j×k)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)
a×b = -5i - 18j - 29k
Then
b×a = -(a×b) = 5i + 18j + 29k
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