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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 solve 2 sin squared x is equal to sin x?
There will be 4 possible solutions if all you are looking for is the angles, so you will need to find out which quadrant your angle is in.
2sin²x = sin x **Subtract sin x from both sides.
2sin²x - sin x = 0 **Then factor out sin x.
sin x(2sin x - 1) = 0 **Set each equal to zero. (AB=0 is the same as A=0 OR B=0).
sin x = 0 or 2sin x - 1 = 0 to 2sin x = 1 to sin x = 1/2
At this point all that is left to do is find out where sin x = 0 or 1/2, which is 0, 180 for sin x = 0 or 30, 150 for sin x = 1/2.
What does the gallon capacity on trash cans mean?
The capacity in gallons of water to completely fill the container.
Solve quadratic equation by using formulae?
with the quadratic equation being ax2+bx+c and the formula being
x=[-b±(b2-4ac)1/2]/2a just plug in the values for a b and c
the quantity raised to the one half denotes a square root of that quantity.
16+2x can not be simplified any further.
16+2x would normally be written as 2x+16 to keep the degrees of the terms in order from highest to lowest.
How do you solve X2 plus 24X plus 144 equals 0?
X^2 + 24x + 144 = 0. Dontcha just luv algebra?
You are looking for a polynomial: (X+somenumber) * (X+somenumber) = X^2 + 24x + 144.
Then just solve for (X+somenumber) * (X+somenumber) = 0.
The trick is to find the pair of factors of 144 that add up to 24.
These are the pairs of factors of 144:
1 x 144
2 x 72
3 x 48
4 x 36
6 x 24
8 x 18
12 x 12
You want the pair of factors that add up to 24:
1 + 144 = more than 144 and is too large
2 + 72 = more than 72 and is too large
3 + 48 = more than 48 and is too large
4 + 36 = more than 36 and is too large
6 + 24 = 30
8 + 18 = 26
12 + 12 = 24!
so,
(X +12) * (x + 12) = X^2 + 24 +144 = 0
So either (X +12) or the other (X +12) is going to be zero because you can only get zero from multiplying something by 0.
If X+12 =0, then put -12 on both sides of the equation:
X+12 -12 = 0 -12
x + 12-12 = -12
x + 0 = -12
x = -12.
Normally you would then solve for the other (X+12) = 0, but that's the same thing as what we just did. So this time, there is only one answer x = -12.
Why is it important to know various techniques for solving systems of equations and inequalities?
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
When graphed are the lines y equals 8x plus 4 and y equals 8x parallel perpendicular or neither?
The slope of both lines is 8. So they're parallel.
What is the integral of e x 2?
http://www.wolframalpha.com/input/?i=integrate+exp(x^2)
The solution lists an "imaginary error function". This means that the integral can NOT be expressed as a finite number of the so-called elementary functions (that is, as any combination of addition, subtraction, multiplication, division, trigonometric functions, inverse trigonometric functions, exponential function, natural logarithm).
The site mentioned also shows a series expansion.
Is it rate x time x people equals cost or rate x time x cost equals people?
The first: rate*time*people = cost.
Eqn (A): => 2x + 5y = 16
Eqn (B): => 5x + 2y = -2
5*Eqn (A) - 2*Eqn (B): 21y = 84 => y = 4
Substituting for y in Eqn (a): x = -2
Is x squared plus 5y minus x equals 7 a function?
No. It is an equation.
A function would link the variable x to another variable - possibly denoted by y. It is a relationship between two (or more) variables.
What does C stand for in E equals mc squared?
Lower case c is speed of light, capital C is for specific heat in thermodynamics.
Given that 3x-ax-2x-73x3-32x2 87x-70 determine the value of a?
3x-ax-2x-73x3-32x2=87x-70 First change to addition so it is easier to simplify 3x+(-ax)+(-2x)+(-73x3)+(-32x2)=87x-70 Combine all of the like terms x+(-ax)+(-73x3)+(-32x2)=87x-70 get rid of the x on the left side -ax+(-73x3)+(-32x2)=86x-70 Now you can move the 73x3 and the 32x2 to the other side by adding it to both sides to get rid of the first because they are negative. -ax=86x-70+73x3+32x2 now divide both sides by -x to get a by itself and positive. a=(86x-70+73x3+32x2)
.... -------------------------
...................-x
(Ignore the dots, they wont let me space without getting rid of the spaces after I post it) Then you can use distributive property on the fraction. a=-86-(70/-x)+(73x3/-x)+(32x2/-x)
Now I'm stuck, sorry, but can somebody else take over please?
Difference between laplace transform and z transform?
the difference is the "S" and "Z" parameters.
S used for analog computation while Z for digital processing.
basically Z is the digital approximation of the analog frequency domain signal.
Z=exp(sT)
where T is the sampling time.
