Several students are making presentations for a science class. The chart describes the concept that each student will present to
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Answer:
The equation of the line is y = -4·x + 16
10 points on the line include;
(0, 16), (1, 12), (2, 8), (3, 4), (4, 0), (5, -4), (6, -8), (7, 12), (8, -16), (9, -20), and (10, -24)
Explanation:
The given points through which the line passes are;
(4, 0) and (3, 4)
The slope, 'm', of the line is given as follows;
Therefore, the slope of the line is (4 - 0)/(3 - 4) = -4
In point and slope form we can get;
The equation of the line in point and slope form is therefore;
y = -4·(x - 4) = -4·x + 16
The equation of the line in slope and intercept form is
y = -4·x + 16
10 points on the line are obtained using the equation of the line and the desired x-values input into cells on MS Excel and presented here as follows;
(0, 16), (1, 12), (2, 8), (3, 4), (4, 0), (5, -4), (6, -8), (7, 12), (8, -16), (9, -20), and (10, -24)
Following are the python program to the given question:
from collections import defaultdict #import package
import heapq as h#import package
def primsMST(gr, st_v): # defining a method primsMST that takes two values in parameters
primalMST = defaultdict(set)#defining primalMST as a variable that calls defaultdict method
v = set([st_v])# defining a variable v that calls the set method and hold its value
e_list = [(c, st_v, to)for to, c in gr[st_v].items()]#defining variable e_list that use loop to hold value in list
h.heapify(e_list)# use package that holds heapify and holds its value
while e_list:#defining while loop that checks e_list
c, s, e = h.heappop(e_list)#holding heapop method value in c,s,and e variable
if e not in v:#defining if block checks e value is not in v
v.add(e)# use add method to add value in v
primalMST[s].add(e)#use primalMST as list that adds value in mwthod
for nxt, c in gr[e].items():#defining for loop that uses nxt, and c variable that checks value in list
if nxt not in v:#defining nxt variable that checks value is not in v
h.heappush(e_list, (c, e, nxt))#add value into the heappush method
return primalMST#return method value
connects=[['A','B',1],['B','C',4],['B','D',6],['D','E',5],['C','E',1]]#defining a list connects
my_gr=dict()#defining a variable my_gr that holds method dict() value
for el in connects:#defining a for loop that uses el to count connects list value
my_gr[el[0]]=dict()#use my_gr as list hold value in dict method
my_gr[el[1]]=dict()#use my_gr as list hold value in dict method
for el in connects:#defining another for loop that uses el to count connects list
my_gr[el[0]].update({el[1]:el[2]}) # use update method that update value in my_gr
my_gr[el[1]].update({el[0]:el[2]})# use update method that update value in my_gr
x=dict(primsMST(my_gr, list(my_gr.keys())[0]))#defining x variable that calls dict method and hold its value
a=[]#defining an empty list
for k in x:#defining a for loop that uses k to hold dict method value
for no in x[k]:#defining a loop that checks list value
a.append([k,no,my_gr[k][no]])#use a that add value in list
print(a)#print list value.
Output:
Please find the attached file.
Program Explanation:
- Import package.
- defining a method primsMST that takes "gr and st_v" as parameters.
- Inside the method, a primalMST as a variable is declared that calls "defaultdict" method.
- Use the v variable that calls the set method and hold its value.
- Defining "e_list" that uses the loop to hold value in lists, and define the heapify and holds its value.
- In the next step, it defines a while loop checks e_list, and defines variable and hold value into the method and use another if to check value and return its value.
- A list "connects" is declared that holds a value and defines a "my_gr" that holds "dict" method value and uses multiple for loop to print the calculated list value.
Learn more:
dictionary: brainly.in/question/14673591
List: brainly.in/question/25140412
