Answer:
10%
Step-by-step explanation:
Answer:
Solution:
According to the Pythagorean Theorem, is that the square of the hypotenuse is equal to the sums of squares of the two legs in which if you take the square root of the sum you are going to get the actual length of the hypotenuse but the two legs are already squared so all you have to do now is sum them and take the square root of it.
It takes value from a user and then user the operation of (+,-,*/).
i used c++ programming language to solve this program:
#include<iostream>
using namespace std;
int main() {
int var1, var2;
char operation;
cout << "Enter the first number : ";
cin >> var1;
cout << endl;
cout <<"Enter the operation to be perfomed : ";
cin >> operation;
cout << endl;
cout << "Enter the second nuber : ";
cin >> var2;
cout << endl;
bool right_input = false;
if (operation == '+') {
cout << var1 << " " << operation << " " << var2 << " = " << (var1 + var2);
right_input = true;
}
if (operation == '-') {
cout << var1 << " " << operation << " " << var2 << " = " << (var1 - var2);
right_input = true;
}
if (operation == '*') {
cout << var1 << " " << operation << " " << var2 << " = " << (var1 * var2);
right_input = true;
}
if (operation == '/' && var2 != 0) {
cout << var1 << " " << operation << " " << var2 << " = " << (var1 - var2);
right_input = true;
}
if (operation == '/' && var2 == 0) {
cout << "Error. Division by zero.";
right_input = true;
}
if (!right_input) {
cout << var1 << " " << operation << " " << var2 << " = " << "Error;";
cout << "Invalid Operation!";
}
cout << endl;
system("pause");
return 0;
}
- Force=0.02N=F
- Acceleration=a=8m/s^2
- Mass=m
According to Newton's second law
Done
The dimensions of a box that have the minium surface area for a given Volume is such that it is a cube. This is the three dimensions are equal:
V = x*y*z , x=y=z => V = x^3, that will let you solve for x,
x = ∛(V) = ∛(250cm^3) = 6.30 cm.
Answer: 6.30 cm * 6.30cm * 6.30cm. This is a cube of side 6.30cm.
The demonstration of that the shape the minimize the volume of a box is cubic (all the dimensions equal) corresponds to a higher level (multivariable calculus).
I guess it is not the intention of the problem that you prove or even know how to prove it (unless you are taking an advanced course).
Nevertheless, the way to do it is starting by stating the equations for surface and apply two variable derivation to optimize (minimize) the surface.
You do not need to follow with next part if you do not need to understand how to show that the cube is the shape that minimize the surface.
If you call x, y, z the three dimensions, the surface is:
S = 2xy + 2xz + 2yz (two faces xy, two faces xz and two faces yz).
Now use the Volumen formula to eliminate one variable, let's say z:
V = x*y*z => z = V /(x*y)
=> S = 2xy + 2x [V/(xy)[ + 2y[V/(xy)] = 2xy + 2V/y + 2V/x
Now find dS, which needs the use of partial derivatives. It drives to:
dS = [2y - 2V/(x^2)] dx + [2x - 2V/(y^2) ] dy = 0
By the properties of the total diferentiation you have that:
2y - 2V/(x^2) = 0 and 2x - 2V/(y^2) = 0
2y - 2V/(x^2) = 0 => V = y*x^2
2x - 2V/(y^2) = 0 => V = x*y^2
=> y*x^2 = x*y^2 => y*x^2 - x*y^2 = xy (x - y) = 0 => x = y
Now that you have shown that x = y.
You can rewrite the equation for S and derive it again:
S = 2xy + 2V/y + 2V/x, x = y => S = 2x^2 + 2V/x + 2V/x = 2x^2 + 4V/x
Now find S'
S' = 4x - 4V/(x^2) = 0 => V/(x^2) = x => V =x^3.
Which is the proof that the box is cubic.
