0
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
What number is x in equation x squared plus 3x equals 7?
x^2 + 3x = 7
There is no integer value that can answer this question x=1 yields the inequality 5= 7 and x=2 yields the inequality 10 = 7.
This can be rewritten as x^2 + 3x - 7 = 0.
Using the quadratic equation and substitution we get
X -3 + (3^2 -4*1*(-7))^(1/2)
x= -----------------------------------
X 2*1
x=(-3 +/- (9-28)^(1/2))/2
X -3 +/- (-19)^(1/2)
x=-----------------------
X 2
Since we are taking the square root of a negative number we change the sign and put a -i in front.
X -3 +/- -i(~4.35)
x= ---------------------
X 2
X -3 -/+ 4.35i
x=---------------
X 2
x can be either -1.5 - 2.175i or -1.5 + 2.175i
What does a rapid change of a magnetic field induce?
It does not have to be positive or negative either one will produce reversal of the voltage applied by a factor
Slope of period squared vs pendulum length?
Using some basic properties from physics and some small angle approximations, one can quickly arrive at the formula
T=2π√(L/g)
Where T is the period of a pendulum in seconds, L is its length in meters, and g is the acceleration due to gravity (9.81m/s²). If you square both sides of this equation, you can quickly derive that
T²=4π²*L/g
Then, if you rearrange this so that L is alone on the left hand side, you will find that
L=g*T²/(4π²)
The slope of this line is everything that is multiplying the T² term, or just g/(4π²).
What is the derivative of y equals aex plus be2x plus ce3x with respect to x?
if y=aex+be2x+ce3x then its derivative dy/dx or y' is:
y'=aex+2be2x+3ce3x
How do you solve -0.7x equals 14?
Multiply both sides by -10 (to make it a positive whole number instead of a decimal ) and then divide by 7 to make left hand side of the equation just x
-0.7*-10/7 x = 14*-10/7
x = -20
Solve this system of equations using the addition methodx plus y equals 3?
Answer by Hilmarz for a very similar question:
When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations.
Pricen2: given that there is no second equation with which to solve the original equation the values of x and y could be any of great number of values.
If you knew the value of x then you would use y=3-x to find the value of y
If you knew the vlaue of y then you would use x=3-y to find the value of x
What is the square footage if a room is 12'1 x 12'3?
12'1" * 12'3" = 12.0833.. * 12.25 = 148.0208 sq feet (to 4 dp).
What is piecewise smooth function?
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
Where do you put the horizontal or vertical line for this to be true 10 10 11 equals 10.50?
A vertical line through the equals sign so that it reads:
10 10 11 ≠10.50
What are the methods in describing or writing a set?
In general, in mathematics, we write sets to indicate a collection of objects or elements.
For instance, we referring to the variable x, we may state {x ∈ ℤ}. That is, x is an element of integers.
We can also state conditions within the set notation. For instance, within a given domain of mathematics, such as discussing convergence of series, we can state
{x ∈ ℝ | the series ∑an converges}. That is, x is an element of real numbers, such that the series converges.
What is the x-intercept to the following linear equation 5x-2y equals 20?
Put in function form.
5X - 2Y = 20
- 2Y = - 5X + 20
Y = 5/2X - 10
-------------------------zero out the Y
5/2X - 10 = 0
5/2X = 10
X = 20/5
X = 4
---------------or, just zero out the Y in original equation
5X - 2(0) = 20
5X = 20
X = 4
-----------either way if only X intercept is wanted.
