Answer:
Following are the answer to this question:
Explanation:
In option 1:
The value of n is= 7, which is (base case)
when n=k for the true condition:
when n=k+1 it tests the value:
since k>6 hence the value is KH>3 hence proved.
In option 2:
when:
for n=1:(base case)
0<=0 \\ condition is true
when the above statement holds value n=1
when n=k
when n=k+1
![[\therefore KH>K \Rightarrow \log(KH>\loK)]](https://tex.z-dn.net/?f=%5B%5Ctherefore%20KH%3EK%20%5CRightarrow%20%20%5Clog%28KH%3E%5CloK%29%5D)
In option 3:
when n=1:
when n=k
![\to (A_1\cap A_2 \cap.....A_k) \cup B\\=(A_1\cup B) \cap(A_2\cup B_2)....(A_k \capB).....(a)\\\to n= k+1\\ \to (A_1\cap A_2 \cap.....A_{kH}) \cup B= (A_1\cup B)\\\\\to [(A_1\cap A_2 \cap.....A_{k}) \cup B]\cap (A_{KH}\cup B)\\\\\to [(A_1\cup B) \cap (A_2 \cup B) \cap (A_3\cup B).....(A_k\cup B)\cap (A_{k+1} \cup B)\\\\ \ \ \ \ \ \ substituting \ equation \ a \\\\](https://tex.z-dn.net/?f=%5Cto%20%28A_1%5Ccap%20A_2%20%5Ccap.....A_k%29%20%5Ccup%20B%5C%5C%3D%28A_1%5Ccup%20B%29%20%5Ccap%28A_2%5Ccup%20B_2%29....%28A_k%20%5CcapB%29.....%28a%29%5C%5C%5Cto%20n%3D%20k%2B1%5C%5C%20%5Cto%20%28A_1%5Ccap%20A_2%20%5Ccap.....A_%7BkH%7D%29%20%5Ccup%20B%3D%20%28A_1%5Ccup%20B%29%5C%5C%5C%5C%5Cto%20%20%5B%28A_1%5Ccap%20A_2%20%5Ccap.....A_%7Bk%7D%29%20%5Ccup%20B%5D%5Ccap%20%28A_%7BKH%7D%5Ccup%20B%29%5C%5C%5C%5C%5Cto%20%20%5B%28A_1%5Ccup%20B%29%20%5Ccap%20%28A_2%20%5Ccup%20B%29%20%5Ccap%20%28A_3%5Ccup%20B%29.....%28A_k%5Ccup%20B%29%5Ccap%20%28A_%7Bk%2B1%7D%20%5Ccup%20B%29%5C%5C%5C%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20substituting%20%5C%20equation%20%5C%20a%20%5C%5C%5C%5C)
hence n=k+1 is true.
Answer:
Given,
P = (22, 1, 42, 10)
Q = (20, 0, 36, 8)
a. Formula for Euclidean Distance :
distance = ((p1-q1)^2 + (p2-q2)^2 + ... + (pn-qn)^2)^(1/2)
Now,
distance = ( (22-20)^2 + (1-0)^2 + (42 - 36)^2 + (10-8)^2) ) ^(1/2)
=( (2)^2 + (1)^2 + (6)^2 + (2)^2 ) ) ^(1/2)
=(4+1+36+4)^(1/2)
=45^(1/2)
Distance = 6.7082
b.Manhattan distance :
d = |x1 - x2| + |y1 - y2|
d = |22- 20| + |1 - 0|
d = |2| + |1|
Explanation:
$ 75000 is the maximum amount that he can spend per month paying off credit cards and loans and not be in danger of credit overload.
More than this amount will exceed his income.
D is the answer cause coding
