Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180. Subtract 180-118, which gives you 62. Then you have 2x=62. Divide both sides by 2 to get a final answer of x=31.
One function you would be trying to minimize is
<span>f(x, y, z) = d² = (x - 4)² + y² + (z + 5)² </span>
<span>Your values for x, y, z, and λ would be correct, but </span>
<span>d² = (20/3 - 4)² + (8/3)² + (-7/3 + 5)² </span>
<span>d² = (8/3)² + (8/3)² + (8/3)² </span>
<span>d² = 64/3 </span>
<span>d = 8/sqrt(3) = 8sqrt(3)/3</span>
9514 1404 393
Answer:
KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP
Step-by-step explanation:
Instead of starting with adjacent letters in the list, we start with the same letter. There are 15 possible pairs.
KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP
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<em>Additional comment</em>
We leave out pairs with letters previous, because you've said KL is the same as LK, and KL has already been listed. The problem with this list is that it misstates the probabilities of randomly obtaining a given pair. It is not 1/15, but is 2/25 for all but letter duplicates. For duplicates (KK), the probability is 1/25, not 1/15.
(a)36 = 6
(b)81 = 9
(c)256 = 16
(d)196 = 14
