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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
The maximum distance an object in simple harmonic motion moves from equilibrium is called the?
amplitude
What is X to the second power minus 25 simplified?
x2 - 25
This expression is the difference of squares. Thus:
x2 - 52
(x + 5)(x - 5).
variation
How do you solve 7r equals 3r-52?
7r (- 3r) = 3r - 52 (- 3r)
4r = - 52
4r / 4 = -52 / 4
r = -13
Is x2 equals y2 plus 7 a function?
Possibly. It is not standard to but a number after a letter (e.g X or Y), so I'm not sure if you mean
2x = 2y + 7, or
x^2 = y^2 +7 (Say, "X squared equals y squared plus 7).
Both of those are functions. But it is mathematically "bad grammar" to put the number after the letter, as it makes it unclear if you have missed off the ^ sign to indicate that it should be a power. If the question box does not let you enter a ^ symbol, write "squared", or "cubed", or whatever the power happens to be . :)
How do you solve for 8x-y equals 4 and 5x plus 3y equals 17?
A system? Try elimination
3(8X - Y = 4)
5X + 3Y = 17
24X - 3Y = 12
5X + 3Y = 17
-------------------------+
29X = 29
X = 1
-----------find Y
8(1) - Y = 4
- Y = - 4
Y = - 1
-----------check
By inspection one can see this is inconsitent
How do you solve the square root of 25?
There is no simple way to do it except to look for a number which, when multiplied by itself, gives 25.
So (-5)*(-5) = 25 and 5*5 = 25 mean that -5 and 5 are two possible answers.
What are the coordinates for y equals x-2 to the power of two minus 1?
There are infinitely many points on the curve defined by the equation so it is not possible to list them.
How many galons of water are in an-6 x 4 x 1 fish pond?
If the pond is perfectly rectangular all the way to the bottom,
then the volume of the pond is:
6' x 4' x 1' = 24 cubic feet = 179.53 gallons.
We have no way to know how much water there may be in it.
What is x when 5 raised to the x-2 equals 70?
5x-2 = 70
⇒ (x-2) log 5 = log 70
⇒ x = log 70/log 5 + 2
≈ 4.640
(You can use any base you like for the logs, as long as you use the same base for both of them.)
What function is most likely to have the smallest value for y if x is large?
1/x (not a function though, since it's not defined for x=0). e^(-x) converges close to zero as x increases, would be a good choice.
How do you factor x to the 2nd power plus x plus 3?
In order to factor a quadratic formula with no coefficient on the first term, you'll need to find a pair of numbers whose product is your last term, and whose sum is the coefficient of your middle term. In the case of the given equation:
x2 + x + 3
This means we'll need a pair of numbers that add up to 1, and multiply to make 3. There are no numbers that meet this condition, which means that the given polynomial can not be factored.
What is the answer to 5x-5 equals 2x plus 13. What is x?
5x - 5 = 2x + 13
Subtract 2x from each side of the equation:
3x - 5 = 13
Add 5 to each side:
3x = 18
Divide each side by 3:
x = 6
16x2 + 8x + 1 = 0 : This factorises to (4x + 1)(4x + 1) = 0
When 4x + 1 = 0 then 4x = -1 : x = -1/4.
