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Calculus

The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.

25,068 Questions

Ignoring wind resistance how long will it take a rock to hit the ground if it is released from the top of a 36 foot tall building?

Just over 1 second. Gravity moves objects here on Earth at 32 ft per second squared. At the end of the first second it will fall 32 of the 36 ft.

What is the minimum of y equals X2-2X plus 10?

y = x2 - 2x + 10

This is a minimum when dy/dx = 0

dy/dx = 2x - 2 :

When 2x - 2 = 0 then 2x = 2 : x = 1

Substituting in the equation gives y = 12 - (2 x 1) + 10 = 1 - 2 + 10 = 9.

Why is pi known as an irrational?

it can't be expressed as a fraction. the numbers after the decimal go on and on without end. No fraction can be divided to equal pi, therefore, it's irrational.

Area bound by the straight line y equals x and the parabola y equals x2?

1st we find the intersection point of the straight line y=x & y=x^2, which are (0,0) & (1,1).

after that we can use multiple integral with the 1st limit of y co-ordinate 0 to 1 & x limits x=y to x=square root(x).

or simply we 1st calculate the area between the parabola & x-axis & the area between the straight line & x-axis in the interval 0 to 1. & after that we subtract the area of parabola by area of straight line.

If x equals 2 and y equals 9 then 7x plus 3y equals?

7x+3y where x=2 and y=9 can be written as (7*2)+(3*9) which can be simplified to (14)+(27), from there it's basic addition.

Factor 20y2 plus 3y - 2?

You just have to use trial and error on this one to find the two factors. Use the FOIL method of multiplying to check and see if the factors add up to the original statement.

(4y - 1)(5y + 2)

Write a java program to find out the sum of a number of n digits?

class Sum_Of_Digits

{

public static void printSumandnoofdigits(int n)

{

int temp = n;

int count = 0;

int sum = 0;

while ( n > 0 )

{

sum = sum + n % 10;

n = n / 10;

count ++;

}

System.out.println("The number is..." + temp );

System.out.println("The sum of digits is..." + sum);

System.out.println("The number of digits is..." + count);

}

}

Examples of simple harmonic motion?

  • Clock Pendulums
  • weights on springs
  • A yardstick hung from the rafters from a cord and twisted slightly
  • A Rubidium ion in a lithium chloride crystal

How do you solve 5-4mdivided by 3 equals -7?

To solve for m, we must isolate m:

(5-4m)/3 = -7

Multiply both sides by 3:

5-4m = -21

Subtract 5 from both sides:

-4m = -26

Divide by -4:

m = 13/2 = 6.5

2x plus 2 equals x plus 6?

2x+2=x+6 first subtract 2x. -2x -2x
2=-1x+6 then subtract 6
-6 -6
-4=-1x finally divide by -1
x=4 X equals four.

What is the relationship between the length of the string of a pendulum and the number of swings?

There's no relationship between the length of the pendulum and the number of swings.

However, a shorter pendulum has a shorter period, i.e. the swings come more often.

So a short pendulum has more swings than a long pendulum has in the same amount

of time.

What are the exponents for fx equals x 1 3 on a graph?

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