In: Electrical Engineering

We wish to install a residential solar array at location Lat 400 N; Long 900W with (a) fixed tilt angle (θ) or (b) adjustable θ. (a) Define and evaluate θ. (b) Specify the range on θ and the time interval (∆t) between θMAX and θMIN

On a circular array with n positions, we wish to place the
integers 1, 2, ... r in order, clockwise, such that consecutive
integers, including the pair (r,1) are not in adjacent positions on
the array. Arrangements obtained by rotation are considered the
same. In how many ways can this be done? Give a combinatorial
proof.

We have an array A of size n. There are only positive integers
in this array. Note that the array may have integers that are not
distinct, and it could be any array of positive integers in
creation (I like the numbers found the decimal expansion of π for
instance). When possible provide the exact complexity of the
algorithm. If it’s not possible explain the O/Ω/Θ complexity. a.
Design an efficient algorithm to find the maximum difference
between any two...

We have an array A of size n. There are only positive integers
in this array. Note that the array may have integers that are not
distinct, and it could be any array of positive integers in
creation (I like the numbers found the decimal expansion of π for
instance). When possible provide the exact
complexity of the algorithm. If it’s not possible explain the O/Ω/Θ
complexity. a. Design an efficient algorithm to find the maximum
difference between any two...

In this problem, we consider replacing an existing electrical
water heater with an array of solar panels. The net installed
investment cost of the panels is $1,365 ($2,100 less a 35% tax
credit from the government). Based on an energy audit, the
existing water heater uses 220 kilowatt hours (kWh) of electricity
per month, so at $0.12 per kWh, the cost of operating the water
heater is $26.4 per month. Assuming the solar panels can save the
entire cost of...

We wish to coat flat glass (n = 1.50) with a
transparent material (n = 1.31) so that reflection of
light at wavelength 500 nm is eliminated by interference.
(a) What minimum thickness can the coating have to do
this?
(b) What is the next thickness for which destructive interference
would occur?

Given an array A[1..n], with distinct values and k with 1 ≤ k ≤
n. We want to return the k smallest element of A[1.....n], in
non-decreasing order. For example: A = [5, 4, 6, 2, 10] and k = 4,
the algorithm returns [2, 4, 5, 6]. There are at least the
following four approaches:
a. heapify A and then extract k elements one by one
b. sort the array (e.g. using MergeSort or HeapSort) and then
read the...

Consider the problem of sorting an array A[1, ..., n] of
integers. We presented an O(n log n)-time algorithm in class and,
also, proved a lower bound of Ω(n log n) for any comparison-based
algorithm.
2. Give an efficient sorting algorithm for an array C[1, ..., n]
whose elements are taken from the set {1, 2, 3, 4, 5}.

We have a random sample of size n (which is large), and we wish
to test - Ho: X~UNIF(0,1) vs Ha: X~exp(1). How would you conduct
hypothesis testing? Describe procedure.

1. We have an array A of size n. There are only positive
integers in this array. Note that the array may have integers that
are not distinct, and it could be any array of positive integers in
creation (I like the numbers found the decimal expansion of π for
instance). When possible provide the exact complexity of the
algorithm. If it’s not possible explain the O/Ω/Θ complexity.
Design an efficient algorithm to find the maximum difference
between any two...

1. We have an array A of size n. There are only positive
integers in this array. Note that the array may have integers that
are not distinct, and it could be any array of positive integers in
creation (I like the numbers found the decimal expansion of π for
instance). When possible provide the exact complexity of the
algorithm. If it’s not possible explain the O/Ω/Θ complexity.
Design an efficient algorithm to find the maximum difference
between any two...

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