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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 x2 equals cos x?
You can solve this to the accuracy of your liking by using Newton's method:
xn+1 = xn - f(xn) / f'(xn)
In this case, we'll say f(x) = x2 - cos(x)
f'(x) would then be 2x + sin(x)
Let's take a rough guess, and start with x0 = 0.5
x1 = 0.5 - (0.52 - cos(0.5)) / (2(0.5) + sin(0.5)) = 0.92420692729319751536
x2 = x1 - (x12 - cos(x1)) / (2x1 + sin(x1)) = 0.82910575599741780916
x3 = x2 - (x22 - cos(x2)) / (2x2 + sin(x2)) = 0.82414613172819520712
x4 = x3 - (x32 - cos(x3)) / (2x3 + sin(x3)) = 0.8241323124099124229
x5 = x4 - (x42 - cos(x4)) / (2x4 + sin(x4)) = 0.82413231230252242297
x6 = x5 - (x52 - cos(x5)) / (2x5 + sin(x5)) = 0.82413231230252242296
Now we can test our answer:
0.824132312302522422962 = 0.67919406818110235182
cos(0.82413231230252242296) = 0.67919406818110235183
So we're accurate to the nearest ten quintillionth.
What is the x in the problem x minus 12 over 2 equal 18?
You need to be careful in how you write such questions as it is important to know if you mean:
x - 12/2 = 18
or
(x-12)/2 = 18
If x - 12/2 = 18 then
x = 18 + 12/2
x = 18 + 6
x = 24
If (x-12)/2 = 18 then
x - 12 = 18 * 2
x - 12 = 36
x = 36 + 12
x = 48
What is the value of x if y is 5 more than 2 times the value of x if y equals 17?
y = 2x + 5
17 = 2x + 5
X = 6
What does x equal in the problem x divided by a equals y divided by b?
Sorry but i dont know te answer to this :(
x/a= y/b
therefore
x = ay/b
What is the range for y equals x plus 4?
It depends on the domain but, if the domain is the real numbers, so is the range.
How do you write a rational expression that is undefined when x equals 4 and x equals 0?
One possible expression is [ 1/(x - 4)+ 1/x ].
Does the length of pendulum affect the period of vibration?
Yes. Given a constant for gravity, the period of the pendulum is a function of it's length to the center of mass.
In a higher gravity, the period would be shorter for the same length of pendulum.
um I'm confused
A fresnel biprism is a triangular right prism with a highly obtuse angle in cross-section. The obtuse angle is near 180 degrees. The typical use of such a prism is to produce two coherent "virtual" light sources from one real point source. These virtual sources can be used to demonstrate interference.
Assuming that by sticking a question mark after that equation, you wish to solve it for x, it can be done this way:
x = x2 + 4x - 2
x2 + 3x = 2
x2 + 3x + 9/4 = 2 + 9/4
(x + 3/2)2 = (8 + 9)/4
x + 3/2 = ± √(17/4)
x = -3/2 ± √17/2
x = (-3 ± √17) / 2
Above
What is the answer to 3x plus y equals 9?
Solve for x:
3x + y = 9 is the same as -3x + 9 = y
Since you now know the equation for y you can plug it into the first equation:
3x + (-3x + 9) = 9
After solving, you will see that x cancels out and that 9 = 9.
Solve for y:
3x + y = 9 is the same as 3 - y/3 = x
Since you now know the equation for x you can plug it into the first equation:
3(3 - y/3) + y = 9
After solving, you will also see that y cancels out and that 9 = 9.
The Answer:
There are actually two posibble answers:
1.) y = 9 and x = 0
If you plug the numbers in then you will get 3(0) + (9) = 9
The answer is 9 = 9
2.) y = 0 and x = 3
If you plug the numbers in then you will get 3(3) + (0) = 9
This will also give you the answer 9 = 9
What is the derivative of 2square root of x?
First, the problem can be rewritten: 2(x^.5) From that step, take the derivative: 2(.5x^-.5) Finally simplify by distribution: x^-.5
What is the y-intercept and the slope of y plus 2 and a half equals 3 sevenths x?
To determine the answers to your question, we need to put the equation in the standard slope/intercept form of y = mx + c........where m is the slope and c is the y intercept.
y + 21/2 = 3/7x
Then y = 3/7x - 21/2
So, we have a slope of 3/7 and a y intercept of -21/2.
