If these are terms of a geometric sequence, they have a common ratio. That is, ...
... (k -1)/(2(1 -k)) = (k +8)/(k -1)
... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.
... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses
... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)
... 3(k +5)(k -1) = 0 . . . . . . . . . factor
Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)
The value of k is -5.
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The three terms are 12, -6, 3. The common ratio is -1/2.
Answer:
Step-by-step explanation: The answer for 7: is 7/2
8: 28/5.
9: 9/4
10: 24/5
Answer:
Yes
Step-by-step explanation:
Because its the square root of 12
<span>1259 units2 i hope this helps you</span>
Answer:
Step-by-step explanation:
a) The work done is equivalent to the change in potential energy of the block. The force due to gravity in the direction down the ramp does the work.
ΔPE = mg(Δh) = (1.25 kg)(9.8 m/s²)(1.81 m·sin(55.3°) ≈ 18.23 J
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b) The kinetic energy of the block can be used to estimate the speed:
KE = ΔPE = 1/2mv²
v = √(2KE/m) = √(2(18.23 J)/(1.25 kg)) ≈ 5.4 m/s
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c) Steven has added kinetic energy to the block. So, the final kinetic energy it has will be ...
initial KE + ΔPE = final KE
final KE = (1/2)mv² + 18.23 J = (1/2)(1.25 kg)(2.0 m/s)² + 18.23 J
= 2.5 J + 18.23 J = 20.73 J
So, the final velocity will be ...
v = √(2(20.73)/1.25) ≈ 5.76 m/s
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<em>Comment on the question</em>
For those of you seeking to copy the answer to "which forces do non-zero work?" we observe that there is no list of forces in this question to choose from. The best we can say is that the operative force is the component of gravity that is parallel to the ramp surface.