Answer:
Explanation:
The detailed steps and appropriate calculation with analysis is as shown in the attachment.
For the data points (1,1),(2,1/2),(3,1/3),(4,1/4), finde the natural cubic spline.
1 answer:
Answer:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12
Explanation:
A cubic has the form:
y = ax³ + bx² + cx + d
Given four points, we can write a system of equations:
1 = a + b + c + d
1/2 = 8a + 4b + 2c + d
1/3 = 27a + 9b + 3c + d
1/4 = 64a + 16b + 4c + d
Solving this algebraically would be time-consuming, but we can use matrices to make it easy.
First, we find the inverse of the coefficient matrix. This is messy to do by hand, so let's use a calculator:
Now we multiply by the solution matrix (again using a calculator):
So the cubic is:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12
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Answer:
Check the explanation
Explanation:
Points to consider:
We need to take the input from the user
We need to find the manhatan distance and euclidian using the formula
(x1, y1) and (x2, y2) are the two points
Manhattan:
Euclidian Distance:
Code
#include<stdio.h>
#include<math.h>
struct Point{
int x, y;
};
int manhattan(Point A, Point B){
return abs(A.x - B.x) + abs(A.y- B.y);
}
float euclidean(Point A, Point B){
return sqrt(pow(A.x - B.x, 2) + pow(A.y - B.y, 2));
}
int main(){
struct Point A, B;
printf("Enter x and Y for first point: ");
int x, y;
scanf("%d%d", &x, &y);
A.x = x;
A.y = y;
printf("Enter x and Y for second point: ");
scanf("%d%d", &x, &y);
B.x = x;
B.y = y;
printf("Manhattan Distance: %d\n", manhattan(A, B));
printf("Euclidian Distance: %f\n", euclidean(A, B));
}
Sample output
