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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
Formula for solving X2 plus -2x -5.25 equals 0?
x2-2x-5.25 = 0
When factored:
(x-7/2)(x+3/2) = 0
Therefore: x = 7/2 and also x = -3/2
To solve a quadratic equation use the formula:
x = -b/2a + and also - the square root of b2-4ac over 2a
Whereas in this particular equation: a = 1, b = -2 and c = -5.25
How do you solve sinx divided by 1 plus cosx plus cosx divided by sinx?
sin x/(1+cos x) + cos x / sin x
Multiply by sin x (1+cos x)
=[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x)
= [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x)
sin^2 x + cos^2 x = 1
= (1+cos x) / sin x (1+cos x)
= 1/sin x
X squared plus 10x plus 21 divided by x plus 3?
Factorising, we obtain,
x2 + 10x + 21 = (x + 7)(x + 3).
Thus,
x2 + 10x + 21 / (x + 3) = x + 7.
That's usually easier than dividing it out!
Add 4x to each side: 68 = 13x + 16
Subtract 16 from each side: 52 = 13x
Divide each side by 13: 4 = x
What is 5x-7 equals 2x plus 5?
X=4
1. Subtract 2x from each side
2. Add 7 to each side
3. Divide each side by 3
Definition of netted venation?
Venation is the arrangement of veins in an insect's wing or the leaf of a plant. Such venation is said to be netted if the smaller vessels branch from the larger ones either as in a feather or like the fingers of a hand. Please see the link.
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.
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 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
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.
