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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
Is 10 a solution to x plus 12 equals 38?
x + 12 = 38.
Subtract 12 from 38, getting 26.
The 12 goes away because you subtracted it.
x = 26, it cannot equal ten.
What does x equal if X power 4 plus x power 2 equal 1?
x4 + x2 = 1
x4 + x2 - 1 = 0 (a quartic equation: 4 roots).
Let x2 = t
t2 + t - 1 = 0 (use the quadratic formula)
t = [-1 ± √[12 - 4(1)(-1)]]/2(1) = [-1 ± √(1 + 4)]/2 = (-1 ± √5)/2
t = (-1 + √5)/2 ≈ 0.62 or
t = (-1 - √5)/2 ≈ -1.62
Since x = ± √t we have:
x = ± √0.62 = ± 0.79
x = ± √-1.62 = ± i√1.62 = ± 1.27i
Or you can find real roots of the equation by graphing y = x4 + x2 - 1 (in a standard window), and find real zeros of the function, which are ± 0.79. But you have to work more in order two find the other two imaginary roots such as:
Let the other roots be a + bi and a - bi.
Since there is not a third power term, the sum of the roots is 0. So that
0.79 + -0.79 + a + bi + a - bi = 0
2a = 0
a = 0 (the imaginary roots are bi and -bi)
The product of the roots equals to -1/1 = -1 (the constant/the coefficient of x4). So that
(0.79(-0.79)(bi)(-bi) = -1
-b2i2 = -1/-0.6241 (substitute -1 for i2)
b2 = 1.61
b = ± √1.61 = ± 1.27 .
the imaginary roots are ± 1.27i.
How do you graph equations on x and y axes?
Make sure the linear equation is in the form y = mx + b. This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. The values in the equation do not need to be whole numbers. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b.
m is called the "slope," or sometimes "gradient." Slope is defined as rise over run, or the change in y over the change in x.
b is defined as the "y-intercept." The y-intercept is the point at which the line crosses the Y-axis.
x and y are both variables. You can solve for a specific value of x, for example, if you have a y point and know the m and b values. x, however, is never merely one value: its value changes as you go up or down the line.
Plot the b number on the Y-axis. Your b is always going to be a rational number. Just whatever number b is, find its equivalent on the Y-axis, and put the number on that spot on the vertical axis.
For example, let's take the equation y = 1/4x + 5. Since the last number is b, we know that b equals 5. Go 5 points up on the Y-axis and mark the point. This is where your straight line will pass through the Y-axis.
Convert m into a fraction. Often, the number in front of x is already a fraction, so you won't have to convert it. But if it isn't, convert it by simply placing the value of m over 1.
The first number (numerator) is the rise in rise over run. It's how far the line travels up, or vertically.
The second number (denominator) is the run in rise over run. It's how far the line travels to the side, or horizontally.
For example:
A 4/1 slope travels 4 points up for every 1 point over.
A -2/1 slope travels 2 points down for every 1 point over.
A 1/5 slope travels 1 points up for every 5 points over.
Start extending the line from b using slope, or rise over run. Start at your bvalue: we know that the equation passes through this point. Extend the line by taking your slope and using its values to get points on the equation.
Continue extending the line, using a ruler and being sure to use the slope, m, as a guide. Extend the line indefinitely and you're done graphing your linear equation.
What is the answer to -2x - 2 4?
- 2X - 2 = 4 ?
If so.....,
- 2X - 2 = 4
add 2 to each side
- 2X = 6
divide each sides integers by - 2
X = - 3
==========check
- 2(- 3) - 2 = 4
6 - 2 = 4
4 = 4
-------------checks
Why is the period of a pendulum independent of its mass?
As we derive the expression for period using dimensional analysis,
we get T = 1/2pi ./(l/g)
In this no mass is present. Hence the conclusion
What is the lateral area of a rectangular solid with length 10 width 6 and height 4?
The formula for getting the Rectangular prism/solid is (Perimeter of the base)(Height)
* Get the Perimeter of the rectangular prism first (2L + 2W) P = (2)(10) + (2)(6) = 20 + 12 = 22
* Now lets solve for the Lateral Area LA = (22) (4)
LA = 88
4 SINS of Speech; 1. Lying, 2. Slander, 3. Abuse, 4. Idle Talk.
3 SINS of the Mind; 1.Covetousness, 2. Hatred, 3.Ignorance..
Answer DA sin is a transgression of the religion commands or the religion laws. The sin is an act or saying of disobedience, intentionally or ignorantly, to God commands and God will. Muslims believe that God, the All-Merciful and the All-Forgiving, allowed his followers to repent when committing a sin. To repent you should admit that you committed a sin, then you should intend not to commit it again, return the rights or the apology to whom is affected by the sin (if any), then you ask God (Allah) for forgiveness. The biggest sin in Islam is setting partners in worship with God (Allah).Quran says (meaning English translation):
{Verily, Allah forgives not that partners should be set up with him in worship, but He forgives except that (anything else) to whom He pleases, and whoever sets up partners with Allah in worship, he has indeed invented a tremendous sin. (48) }
[Quran, chapter 4, verse 48]
Quran says also:
{ Surely, they have disbelieved who say: "Allah is the Messiah ['Iesa (Jesus)], son of Maryam (Mary)." But the Messiah ['Iesa (Jesus)] said: "O Children of Israel! Worship Allah, my Lord and your Lord." Verily, whosoever sets up partners in worship with Allah, then Allah has forbidden Paradise for him, and the Fire will be his abode. And for the Zalimun (polytheists and wrong-doers) there are no helpers. (72)} [Quran, chapter 4, verse 72]
Answer:
"Whosoever committeth sin transgresseth also the law: for SIN IS the transgression of the law." (I John 3:4)
Sin is the breaking of the Ten Commandments. As Paul says:
"...I had not known sin, but BY the law: for I had not known LUST, except the law had said, THOU SHALT NOT COVET." (Rom.7:7)
SIN is NOT OBEYING THE TEN COMMANDMENTS. SIN is LAWLESSNESS... disobedience to God's laws.
What are the domains of sine cosine and tangent?
The domain of a function is the set of values of the independent variable for which the function is valid. In practice, this is the allowable values of X or, in this case, theta. The sine and cosine functions have a domain of all numbers from negative infinity to positive infinity. The tangent function, however, is sine(theta) / cosine(theta). Cosine(theta) has value of zero at theta equal to pi / 2, 3pi/2, 5pi/2, ... in the positive direction, and -pi/2, -3pi/2, -5pi/2, ... As a result, tangent(theta) is undefined at these values, so the domain of tangent is all numbers from negative infinity to positive infinity except all numbers n pi/2 where n is odd.
AC = 1.5
BC = 2.0
AB = ? (hypotenuse)
We can use the basic Pythagorean theorem for this instance:
c2 = a2 + b2
C will always be the hypotenuse, while a and b will be the two legs.
c2 = (1.5)2 + (2.0)2 (plug in the values for the two legs)
c2 = 2.25 + 4 (square the numbers)
c2 = 6.25 (add)
c = 2.5 (find the square root of 6.25)
Side AB will be equal to 2.5. Remember, the hypotenuse will ALWAYS be larger than either of the two legs.
What is the value of y 6y plus 22 equals 4y-42?
y = -32
6y + 22 = 4y - 42 subtract -4y from both sides
2y + 22 = -42 subtract 22 from both sides
2y = -64 Divide both sides by 2 to get y by itself
y= -32
That completely depends on what 'x' is. Whenever 'x' changes,
[x + 1,525] also changes immediately.
Factoring this expression Check by multiplying factors xy plus ay plus ab plus bx?
xy + ay + ab + bx = y(x + a) + b(a + x)
= y(x + a) + b(x + a) = y(x + a) + b(x + a) = (y + b)(x + a)
To check, multiply out the two brackets making sure that each pair is evaluated.
What is the ordered pair is a solution of 2x-2y8?
2x - 2y8 is an expression. It is not an equation and so cannot have a solution.
A concave polygon.
