How to calculate the volume of glass juice? - c

The radius of the upper part r1 and lower part r2 is given. If the height of the glass is h and height of the juice is p what is the volume of the juice in the glass? For some input-output is wrong:
#include <stdio.h>
#include <math.h>
int main() {
int r1, r2, h, p;
scanf("%d %d %d %d", &r1, &r2, &h, &p);
//for juice height p we will find out the radius r3
float r3 = ((r1 * p) / h); //calculating r3 by percentage formula
float v = ((M_PI / 3) * 3 * ((r3 * r3) + (r2 * r2) + (r3 + r2)));
printf("Volume : %f\n", v);
return 0;
}
EDIT: After I changed the all int to double still for some input output is wrong for an example for input 5 2 3 2 the answer should be 58.64.

Integer division yields an integer result - 1/2 == 0, 5/2 == 2, etc., so ((r1*p)/h) is not giving you the right value.
You should declare your inputs as double instead of int and use %lf instead of %d to read them:
double r1,r2,h,p;
scanf("%lf %lf %lf %lf",&r1,&r2,&h,&p);
You'll also want to declare r3 and v as double instead of float.

Besides the errors shown in John Bode's answer, the posted code is using the wrong formulas to calculate the volume.
#include <stdio.h>
#include <math.h>
// M_PI is not a standard macro
#if !defined(M_PI)
#define M_PI 3.14159265358979323846
#endif
int main(void)
{
// Given the following calculations, I'd use a floating-point type
// to store the values.
double r1, r2, h, p;
// The format specifiers need to be changed accordingly.
scanf("%lf%lf%lf%lf", &r1, &r2, &h, &p);
// To extimate the radius of top surface of the juice, we can't forget
// the radius at the bottom of the glass (it's not zero!).
double r3 = r2 + ((r1 - r2) * p) / h;
// The volume of the conical frustum can be calculated with a formula different
// from the posted one and we need to consider the height of the juice.
double v = M_PI * p * (r3 * r3 + r3 * r2 + r2 * r2) / 3.0;
printf("Volume : %f\n", v);
return 0;
}

Related

Roots of equation in C

I am relatively new to C, and am trying to improve myself in it. I made a calculator and added the quadratic equation solver to it, cause i know the formula of finding the roots. But i am faced with two problems.
Code:
#include <stdio.h>
#include <maths.h>
#include <stdlib.h>
#include <windows.h>
main(){
float A1, A2, A, B, C, ans, Z;
printf("Welcome to Quadratic Equation solver. Enter the coefficient of X^2, followed by\nthe coefficient of X, followed by the integer value.\n\nEnter values: ");
scanf("%f%f%f", &A, &B, &C);
CheckF = (B * B - 4 * A * C);
if (CheckF < 0) {
system("COLOR B4");
printf("This calculator HeX, currently cannot handle complex numbers.\nPlease pardon my developer. I will now redirect you to the main menu.\n");
system("pause");
system("cls");
system("COLOR F1");
goto Start;
} else if (CheckF >= 0) {
Z = pow(CheckF, 1/2);
A1 = (-B + Z)/(A+A);
A2 = (-B - Z)/(A+A);
if (A1 == A2) {
ans = A1;
printf("\nRoot of equation is %f (Repeated root)\n", ans);
Sleep(250);
} else if (A1 != A2) {
printf("Roots of equation are %f and %f \n", A1, A2);
Sleep(250);
}
}
}
Problem 1:
When i run the code and input 3 32 2, mathematically the output should be Roots of equation are -0.06287 and -10.6038, that i double checked with my sharp calculator. However, the output that i got was was off: Roots of equation are -5.166667 and -5.500000 i am totally unsure why is it not computing the correct roots of the equation.
Problem 2:
Some roots do not have the coefficient of X^2, for example (2X + 2), which can be solved to get repeated roots of -2, (6X - 3), which gives us that x is 0.5 repeated. However, according to the quadratic equation, which is divided by 2A, will never work, as it is divided by 0. What is the possible way out of this situation? Is it to check if A = 0 then do something else? Any help will be appreciable.
integer division
pow(CheckF, 1/2) is 1.0 as 1/2 is integer division with a quotient of 0.
// Z = pow(CheckF, 1/2);
Z = pow(CheckF, 1.0/2.0);
// or better
Z = sqrt(CheckF);
// Even better when working with `float`.
// Use `float sqrtf(float)` instead of `double sqrt(double)`.
Z = sqrtf(CheckF);
Best - re-write using double instead of float. Scant reason for using float here. double is the C goto floating point type.
Other issue
//#include <maths.h>
#include <math.h>
// main() {
int main(void) {
// CheckF = (B * B - 4 * A * C);
float CheckF = (B * B - 4 * A * C);
// goto Start;
Use an auto formater
I see some problems with the code. First, I suggest you to use double instead of float. They offer much better precision and an ideal calculator needs precision. Secondly, you do:
Z = pow(CheckF, 1/2);
You should use sqrt(CheckF) since there is a dedicated function in C for square roots! The following works for me so if you fix the above two problems, your code will probably work.
int main() {
double A1, A2, A, B, C, ans, Z;
printf("Welcome to Quadratic Equation solver. Enter the coefficient of X^2, followed by\nthe coefficient of X, followed by the integer value.\n\nEnter values: ");
A = 3;
B = 32;
C = 2;
double CheckF = (B * B - 4 * A * C);
if (CheckF >= 0) {
Z = sqrt(CheckF);
A1 = (-B + Z) / (A + A);
A2 = (-B - Z) / (A + A);
if (A1 == A2) {
ans = A1;
printf("\nRoot of equation is %f (Repeated root)\n", ans);
} else if (A1 != A2) {
printf("Roots of equation are %f and %f \n", A1, A2);
}
}
}

Task is to calculate the straight line distance between the two objects moving in a circle

We have two point objects B and C at rest on a straight line at a distance r1 and r2 units from a point A. At time t=0 seconds, the objects start moving in a circular path with A at the center with angular velocity v1 and v2 degrees per second.
Given inputs v1, v2, r1 and r2, calculate the distance between the B and C after N seconds.
I've done it but it's giving the wrong answer can anyone suggest me a better solution.
#include"stdio.h"
#include"math.h"
int main()
{
float v1,v2,r1,r2,t;
scanf("%f%f%f%f%f", &v1, &r1, &v2, &r2, &t);
int diff = v1 > v2 ? (v1 - v2) : (v2 - v1);
int total_diff = diff * t;
if(total_diff % 360 == 0)
printf("%.2f", r2 - r1);
else if(total_diff % 180 == 0)
printf("%.2f", r1 + r2);
else if(total_diff % 90 == 0)
printf("%.2f", sqrt(pow(r2, 2) - pow(r1, 2)));
else
printf("%.2f", sqrt(pow(total_diff, 2) - pow(r2-r1, 2)));
}
I've taken else part from:https://math.stackexchange.com/questions/1727504/calculate-distance-between-two-points-on-concentric-circles
Better method as requested
I would use polar coordinates for this. It fits the problem much better.
#include <stdio.h>
#include <math.h>
float distance(float v1, float r1, float v2, float r2, float dt) {
// Calculate new positions and convert to radians
float fi1 = v1*dt*M_PI/180, fi2 = v2*dt*M_PI/180;
// Polar distance formula
return sqrt(pow(r1, 2) + pow(r2, 2) - 2*r1*r2*cos(fi1-fi2));
}
int main()
{
float v1,v2,r1,r2,t;
scanf("%f%f%f%f%f",&v1,&r1,&v2,&r2,&t);
printf("%.2f\n", distance(v1,r1,v2,r2,t));
}

Rotation program in C

I'm basically trying to make a math rotation program in C. But the output is always wrong. P(x,y) is rotated about Q(r,s); clockwise (direction=1) or anticlockwise (direction=0). The a,b,c are angles in triple ,I guess question meant c is in hundred's then b is in ten's and a is unit's.
Input:
0
7 3
0 1 1
0 0
Output: -3 7
Whereas I'm getting -5 5.
Thanks for your time if you help me.
Original question link: https://www.codechef.com/problems/DSPC305
i found another question by the same uploader which uses TRIPLE too. He further added a note :Triple is defined by a,b,c where a is base, b is height and c is hypotenuse of a triangle. Each triple corresponds to an angle given by cosA= a/c
#include<stdio.h>
#include<math.h>
int main() {
int x,y,a,b,direction,c,r,s,xnew,ynew;
scanf("%i", &direction);
scanf("%i %i", &x, &y);
scanf("%i %i %i" , &a, &b, &c);
scanf("%i %i", &r, &s);
float PI = 3.1415926535897932384626;
float theta = ((c*100+b*10+a)*PI)/180;
if (direction==1)
{
xnew= (x-r) * cos(theta) + (y-s) * sin(theta);
ynew= -(x-r) * sin(theta) + (y-s) * cos(theta);
printf("%i %i", xnew+r, ynew+s);
}
if (direction==0)
{
xnew =( (x-r) * ((cos(theta))) - (y-s) * sin(theta));
ynew =( (x-r) * ((sin(theta))) + (y-s) * cos(theta));
printf("%i %i", (xnew+r), (ynew+s));
}
return 0;
}
This
float theta = ((c*100+b*10+a)*PI)/180;
has nothing to do with the definition of a triple.
You can use this code:
#include<stdio.h>
#include<math.h>
int main()
{
double xp,yp,xq,yq,a,b,c;
double t,xn,yn;
int z;
scanf("%d",&z);
scanf("%lf%lf",&xp,&yp);
scanf("%lf%lf%lf",&a,&b,&c);
scanf("%lf%lf",&xq,&yq);
t=asin(b/c);
if(z==0)
{
xn=xp*cos(t)-yp*sin(t)-xq*cos(t)+yq*sin(t)+xq;
yn=xp*sin(t)+yp*cos(t)-xq*sin(t)-yq*cos(t)+yq;
}
else
{
xn=xp*cos(t)+yp*sin(t)-xq*cos(t)-yq*sin(t)+xq;
yn=-xp*sin(t)+yp*cos(t)+xq*sin(t)-yq*cos(t)+yq;
}
printf("%0.lf %0.lf",xn,yn);
return 0;
}
This code gave correct output for both of the test cases provided in the question.
Do tell if it worked :)

Calculating Maxwell-Boltzmann Distribution

I am trying to calculate Maxwell-Boltzmann Distribution but this code gives 0.00000, what is the problem?
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
int main()
{
float e=2.718228183, pi=3.14159265, m=2.66*pow(10,-23), t, k=1.38*pow(10,-23), v, result;
scanf("%f %f", &t, &v);
result = sqrt(pow( m / (2*pi*k*t), 3)) * 4 * pi * pow(v,2) * pow(e, -(m * pow(v,2)) / (2*k*t));
printf("%f", result);
}
As described in the comments, the use of float together with the reduced precision of the constants give a result that is not representable anymore as a float. Changing the data type to double alone gives two decimal digits of accuracy. If we use exp, more digits for pi and do a bit of recombination of the computations we get 12 digits of accuracy. E.g.:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main()
{
double pi = 3.1415926535897932384626433832795028842, m = 2.66e-23, k =
1.38e-23;
double t, v, v2, dkt, result;
// check omitted
scanf("%lf %lf", &t, &v);
v2 = v * v;
dkt = 2 * k * t;
result = pow(m / (pi * dkt), 3 / 2.0) * 4 * pi * v2 * exp(-(m * v2) / (dkt));
printf("%.20g\n", result);
return 0;
}
The result from Pari/GP is 8.1246636077915008261803395870165527173e-9 and the result we get with the code above is 8.1246636077914841125e-09. Without the intermediate results v2, dkt and the replacement of sqrt we got 8.1246636077914824582e-09, not much of a difference, especially with accuracy where it gained nothing.
If you want the full 16 decimal digits of accuracy you need to take the whole thing apart and take a different approach.
replace
double pi=acos(-1.);
instead of
double pi=3.1415926535897932384626433832795028842;

Numerical Differentiation

How can I calculate the numerical second derivative of a function involving an exponential and a singularity at infinity. Unfortunately, the numerical derivative by Ridder's methods provided in "Numerical Recipes in C" can only calculate the first derivative (It requires analytical expression of the function beforehand.) Furthermore I have tried Chebyshev approximation and differentiating the function afterwards but the values given were way off the actual values. I have also tried some finite difference algorithms provided in a mathematical paper yet they were error prone too. The function is e^(x/2) / x^2. I would appreciate any help on the matter.
Thanks in advance
Latest Edit: The issue was solved the FADBAD libraries available in C++ did an extremely good job. They are available via http://www.fadbad.com/fadbad.html
EDIT:
// The compilation command used is given below
// gcc Q3.c nrutil.c DFRIDR.c -lm -o Q3
#include <stdio.h>
#include <math.h>
#include "nr.h"
#define LIM1 20.0
#define a -5.0
#define b 5.0
#define pre 100.0 // This defines the pre
/* This file calculates the func at given points, makes a
* plot. It also calculates the maximum and minimum of the func
* at given points and its first and second numerical derivative.
*/
float func(float x)
{
return exp(x / 2) / pow(x, 2);
}
int main(void)
{
FILE *fp = fopen("Q3data.dat", "w+"), *fp2 = fopen("Q3results.dat", "w+");
int i; // Declaring our loop variable
float x, y, min, max, err, nd1, nd2;
// Define the initial value of the func to be the minimum
min = func(0);
for(i = 0; x < LIM1 ; i++)
{
x = i / pre; // There is a singularity at x = 0
y = func(x);
if(y < min)
min = y;
fprintf(fp, "%f \t %f \n", x, y);
}
fprintf(fp, "\n\n");
max = 0;
for(i = 0, x = a; x < b; i++)
{
x = a + i / pre;
y = func(x);
nd1 = dfridr(func, x, 0.1, &err);
//nd2 = dfridr((*func), x, 0.1, &err);
fprintf(fp, "%f \t %f \t %f \t %f \n", x, y, nd1);
if(y > max)
max = y;
}
fprintf(fp2, "The minimum value of f(x) is %f when x is between 0 and 20. \n", min);
fprintf(fp2, "The maximum value of f(x) is %f when x is between -5 and 5. \n", max);
fclose(fp);
fclose(fp2);
return 0;
}
EDIT: Chebyshev
// The compilation command used is given below
//gcc Q3.c nrutil.c CHEBEV.c CHEBFT.c CHDER.c -lm -o Q3
#include <stdio.h>
#include <math.h>
#include "nr.h"
#define NVAL 150 // Degree of Chebyshev polynomial
#define LIM1 20.0
#define a -5.0
#define b 5.0
#define pre 100.0 // This defines the pre
/* This file calculates the func at given points, makes a
* plot. It also calculates the maximum and minimum of the func
* at given points and its first and second numerical derivative.
*/
float func(float x)
{
return exp(x / 2) / pow(x, 2);
}
int main(void)
{
FILE *fp = fopen("Q3data.dat", "w+"), *fp2 = fopen("Q3results.dat", "w+");
int i; // Declaring our loop variable
float x, y, min, max;
float nd1, nd2, c[NVAL], cder[NVAL], cder2[NVAL];
// Define the initial value of the func to be the minimum
min = func(0);
for(i = 0; x < LIM1 ; i++)
{
x = i / pre; // There is a singularity at x = 0
y = func(x);
if(y < min)
min = y;
fprintf(fp, "%f \t %f \n", x, y);
}
fprintf(fp, "\n\n");
max = 0;
// We make a Chebyshev approximation to our function our interval of interest
// The purpose is to calculate the derivatives easily
chebft(a,b,c,NVAL,func);
//Evaluate the derivatives
chder(a,b,c,cder,NVAL); // First order derivative
chder(a,b,cder,cder2,NVAL); // Second order derivative
for(i = 0, x = a; x < b; i++)
{
x = a + i / pre;
y = func(x);
nd1 = chebev(a,b,cder,NVAL,x);
nd2 = chebev(a,b,cder2,NVAL,x);
fprintf(fp, "%f \t %f \t %f \t %f \n", x, y, nd1, nd2);
if(y > max)
max = y;
}
fprintf(fp2, "The minimum value of f(x) is %f when x is between 0 and 20. \n", min);
fprintf(fp2, "The maximum value of f(x) is %f when x is between -5 and 5. \n", max);
fclose(fp);
fclose(fp2);
return 0;
}
That function is differentiable so using a numeric method is likely not the best. The second derivative is:
6*exp(x/2)/(x^4)-2*exp(x/2)/x^3 + exp(x/2)/(4*x^2)
The above can be simplified of course to speed up computation. Edit: had original formula wrong the first time.
If you want a 100% numeric approach then look at the numerical recipes for a cublic spline interpolation (Charter 3.3). It will give you the 2rd derivative at any location.
call spline() with x and y values to return the 2nd derivatives in y2. The second derivative varies linearly within each interval. So if for example you have
x y y2
0 10 -30
2 5 -15
4 -5 -10
then the 2nd derivative at x=1 is y2=-22.5 which is in-between -30 and -15.
you can also make a new splint() function to return the 2nd derivative a*y2a[i]+b*y2a[i+1]

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