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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
What is the answer to 5 plus 4y y plus 8?
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There is no operator between 4y and y.
-2x - 10 + 4 = 2
-2x - 6 = 2
-2x = 2 + 6
-2x = 8
-x = 8 / 2
x = -4
Check:
-2(-4) - 10 + 4 = 2
8 - 10 + 4 = 2
8 - 6 = 2
2 = 2
Y equals negative five times x plus four swuared plus three?
That is a linear equation in two variables, x and y. The solution consists of all points on the line y = -5x + 19.
How do you solve 2sinsquared x 5sinx 3 0?
I presume that you are asking:
2 * sin^2(x) + 5*sin(x) + 3 = 0
This one is actually easy and you can avoid doing any tedious calculations by noticing that the range of sin(x) is [-1,1] while the range of sin^2(x) is [0,1]. Also note that every time sin(x) = -1, sin(x)^2 = (-1)^2 = 1.
Like good little Calculus students, we remember the unit circle which we memorized in high school trigonometry/advanced algebra/precalculus. The unit circle reminds us that sin(x) = -1 when x is (3/2) * pi. We also remember that sin(x) repeats itself for every 2*pi.
So our solution set is:
(3/2)*pi + 2*pi*n, where n is any integer.
Which of the points apply to the equation y equals x-2?
All of the infinitely many points whose ordinate is 2 less than its abscissa.
How do you factor 4xsquared plus 34x plus 42?
4x2 + 34x + 42
First, we can see that each term is divisible by two, so we'll factor that out:
= 2(2x2 + 18x + 21)
To further factor the remaining trinomial, we need to find two numbers whose product is equal to the product of our first and last terms' coefficent, and whose sum is equal to the end term's coefficient. In other words, we need two numbers that add up to 18, and multiply to make 42....
Factors of 42 are 2, 3 and 7. That means that our possible combinations of numbers are: 2 and 21, 6 and 7, or 3 and 14. Unfortunately, none of these can be added up to make 18, so the polynomial can not be factored any further.
How do you graph the equation for Y plus 4x equals 1?
Choose sensible scales for the X and Y axes.
Then plot two points for chosen values of x, say x = 0 and 5, the y values being calculated form the equation:
x = 0 → y = 4 x 0 + 1 = 1
x = 5 → y = 4 x 5 + 1 = 21
Finally, as y = 4x + 1 is a linear equation, draw a straight line through those two plotted points (0, 1) and (5, 21).
The amplitude of the Simple Harmonic Motion is 0.05.
Which number can be divide by 9?
Any number can be divided by 9.
If the original number happens to be a multiple of 9, then the division will end evenly, without fraction or remainder.
Add the digits of the number. If that total is divisible by nine, so is the original number. Example: 12,345,678 The digits total 36. 36 is divisible by 9. So is 12,345,678.
The number nearest to 60 which will divide by 9 without a remainder is 63.
How do you convert a 3 dimensional box listed in centimeters to cubic meters?
You can calculate the volume in cubic centimeters and then convert to cubic meters, or you can convert centimeters to meters and then calculate the volume. Let's say your box measures 100 cm by 150 cm by 200 cm. That's 100 x 150 x 200 cm = 3,000,000 (or 3E6) cubic centimeters (cc). Since there are one million (1E6) cc per cubic meter, you have 3E6/1E6 or 3 cubic meters. You could have converted to meters first: 100 cm = 1.00 m; 150 cm = 1.50 m; and 200 cm = 2.00 So, the volume is 1.00 x 1.50 x 2.00 m = 3 cubic meters.
To find rate of change.
Two common examples are:
rate of change in position = velocity and rate of change of velocity = acceleration.
If y equals a plus 12 times x plus 3 and y equals 4ax are parallel what is the value of a?
y = (a + 12)(x + 3) (line 1)
y = 4ax (line 2)
Since the equation of the second line is in a slope-intercept form, write the equation of the first line in the slope-intercept form, y = mx + b, where m is the slope of the line.
y = (a + 12)(x + 3)
y = a(x + 3) + 12(x + 3)
y = ax + 3a + 12x + 36
y = ax + 12x + 3a + 36
y = (a + 12)x + 3a + 36, where the slope is a + 12
y = 4ax, where slope is 4a
Since the lines are parallel they must have the same slope. So that,
a + 12 = 4a
3a = 12
a = 4
Thus, when a = 4, the parallel lines have a slope of 16.
How many solutions are in the set 16x plus 2 - 8 equals 16x plus 24?
16x + 2 - 8 = 16x + 24
implies 16x - 6 = 16x + 24
subtracting 16x from both sides, this implies: -6 = 24
So the equation has no soultions.
x2 - 19x + 60 = x2 - 15x - 4x + 60 = x(x - 15) - 4(x - 15) = (x - 15)(x - 4)
What is the anti-derivative of ex2?
You want e to the power x2, right?
The Wikipedia gives an answer, at http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions. I won't copy it here, too much trouble; and I don't know how to draw equations here.
This answer is quite complicated; it seems you basically use successive approximations to get the integral (antiderivative), instead of a simple expression as you might expect.
