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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
How do you get all 6 numbers on the Powerball?
The only sure way to do that is to buy one ticket for every possible combination.
Then you're absolutely positively definitely guaranteed to hold a winning ticket. It
doesn't necessarily mean that you'll get the whole jackpot, however. There may be
other winning tickets besides yours, and if there are, you have to split the jackpot
with all the others.
What do you mean by time period of pendulum?
You know how when you pull a pendulum to the side and let it go, and then it swings
away from you to the other side, but then it stops and turns around and swings back
to you ?
The period of the pendulum is the length of time it takes, after you let it go, to go
away from you and then come back to your hand.
How do you graph 3x-y equals -2?
The easy way is to plot the x- and y-intercept points and draw the lines that passes through those two points.
If y = 0, then we have 3x = -2and x = -2/3. So the x-intercept point is (-2/3, 0).
If x = 0, then we have -y = -2and y = 2. So the y-intercept point is (0, 2).
Plot the points and draw the line.
How do you solve 3x plus 5 equals 23?
3x + 5 = 23
The object of solving this algebraic equation is to get x by itself, meaning to get everything that isn't x on x's side on the other side with 23.
So first let's deal with 5. 5 is easier to get rid of, so let's do that first and worry about the 3x after. To bring a number to the other side of the equation, the rule is to use the sign that is opposite of the sign used for the number on both sides of the equation. This might sound hard, but it's very simple- subtract 5 from 5 and from 23. (If the sign was minus, then you would have added 5 to both sides.) By subtracting 5 from both sides, the 5s cancel out because 5-5 is 0. 23-5 is 18. So now our equation looks like this:
3x = 18
Now for the 3x. Remember the rule for bringing the number to the other side- but first you need to know what operation is being used for 3x. Anytime you see a number attached to a variable, (x, y, z, etc.) they are being multiplied together. So 3x is using multiplication, meaning we need to use division to get rid of the 3 on it's originial side and bring it to 18's side. So divide by 3 on both sides- 3x divided by 3 leaves us with just x, because the threes cancel out. 18 divided by 3 is 6.
So now that x is by itself, we have solved the equation. The answer is x = 6.
Does a 40 sided polygon have 6840 diagonals?
The sum of the angles of a regular n-sided polygon is equal to (n - 2) x 180 degrees.
Therefore, the sum of the angles of a regular 40-sided polygon (tetradecagon) is equal to (40 - 2) x 180 = 6840 degrees. Therefore, 6840 refers to the sum of the degrees, not the number of diagonals.
The number of diagonals of an n-sided polygon is given by n(n-3)/2. So a 40-sided polygon has 40*37/2=740 diagonals.
What inequities did dams in Indonesia solve?
It solved NOTHING. My family is dEAD and now I must avenge their deaths! I have already bought the dynamite.
It's a simple linear equation in 'y'.
If you'd like to know the value of 'y' that makes it true,
you can find it as follows:
3y - 8 = 12
Add 8 to each side:
3y = 20
Divide each side by 3:
y = 20/3
What is sin squared x equals cos squared minus 2 sin x?
Since the word 'equals' appears in your questions it might be what is called a trigonometric identity, in other words a statement about a relationship between various trigonometric values.
How do you find the value of 2y-10 given that -11y-7 equals 4?
-11y - 7 = 4
Add 7 to both sides: -11y = 11
Divide both sides by -11: y = -1
Substitute y = -1 in the experession that you are trying to eveluate:
2*(-1) - 10 = -2 -10 = -12
How do you solve the equation of 5x 3 equals 12?
Assuming the sign of 3 is a minus:
Add 3 to each side: 5x = 15
Divide each side by 5: x = 3
QED
What is the domain of g of x is equal to negative 2 times x?
anything can be put into it so... (-infinity,infinity)
How many digits has Pi been calculated and is there a repeating pattern in these?
As of 17 October 2011, the answer is 10 trillion = 1013.
While there are repeats of short patterns from time to time, the decimal representation does not - and cannot - settle into a repeating pattern.
What is the derivative of pi raised to x?
y=x^pi
d/dx=pi*(x^pi-1)
This is true because of power rule.
d/dx (x^a)=a(x^(a-1))
3y-7 plus y plus 27 equals 6y plus 20-4y?
3y - 7 + y + 27 = 6y + 20 - 4y
Collect terms:
4y + 20 = 2y + 20
Subtract 20
4y = 2y
The only way that can happen is if
y = 0
Solve X squared-x-20 equals 0?
It is a quadratic equation and there are few ways to solve em
(Before we start note that the values of x in a quadratic equations are called roots or zeroes or solution)
- Mid term split method
- Quadratic formula
Lets try both:
- x^2 -x -20 = 0 can be split as x^2 -5x + 4x - 20 = 0
Taking terms common,
x(x-5) + 4(x-5) =0
(x-5)(x+4)=0
For this expression to be 0, either of the two numbers must be 0 since anything multiplied with 0 is 0.
So it can either be
(0)(x+4) = 0 Which is true or (x-5)(0) = 0 which is true too
When (x-5) = 0, x=5 and when (x+4) = 0 , x= -4
So we have two solutions 5,-4
- For the quadratic formula there's a long formula for roots which is
{-b ± √(b² - 4ac)}/2a
Where the quadratic equation is ax² + bx +c =0,
Here a= 1, b = -1 and c = -20,
Substituting the values in the formula :
[-(-1) ± √{(-1)² - 4(1)(-20)}]/2(1)
={1 ± √(1 +80)}/2
=(1 ± √81)/2
=(1 ± 9)/2
2 answers are possible from here on,
(1 + 9)/2 and (1 - 9)/2
which are 10/2 = 5 and -8/2=-4
Look we same answer from both methods.
Y equals 4x-18 y equals 4x Are they parallel or perpendicular?
Parallel. They both have a slope of 4.
How many inches are there in 0.3 centimeters?
There are 2.54 centimetres in one inch. Therefore, rounded to three significant figures, 0.3 centimetres is equal to 0.3/2.54 = 0.118 inches.
What is the purpose of differential calculus?
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
