Let x1, . . . , xn be real numbers representing positions on a number line. Let w1, . . . , wn be positive real numbers representing the importance of each of these positions. Consider the quadratic function: f(θ) = 1 2 Pn i=1 wi(θ − xi) 2 . What value of θ minimizes f(θ)? Show that the optimum you find is indeed a minimum. What problematic issues could arise if some of the wi 's are negative? [NOTE: You can think about this problem as trying to find the point θ that's not too far away from the xi 's. Over time, hopefully you'll appreciate how nice quadratic functions are to minimize.] [HINT: View f(θ) as a quadratic function in θ, i. E. F(θ) = αθ2 +βθ +γ, where α, β, γ are real numbers depending on wi 's and xi 's.]

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step-by-step explanation:

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.

step-by-step explanation:

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answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92