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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 would i Solve the system x plus y equals 9comma -3 equals 2x - y?
Rearrange the second equation to read 2x - y = -3
Add the two equations: 3x = 6:
Divide by 3: x = 2 so y = 7
It has no asymptote. 3x is a straight line and therefore is a tangent to itself.
Simplify 3X plus 2Y plus 6Z equals 24?
You can't simplify it any further than
3x+2y+6z=24, unless you have been given values of x,y and z or other equations to find x,y and z.
Find the value of x in the equation x plus 5 equals x plus 45?
There is no numerical value for 'x' that can make this a true statement.
Factor the expression 6x3y 6x2y2 plus 2x2y?
I'm guessing its written like this---> 6x3y - 6x2y2 + 2x2y?
Well, I'm guessing the answer is2x2y(3x - 3y + 1)
This problem could not be solved if it was prime..
Prime: If the letters and numbers don't match. (This is simply talking about the exponents)
How Find the produnct of 2x-3 4x plus 9 and 2x plus 3?
(2x - 3)(4x + 9)(2x + 3)
= (2x - 3)(2x + 3)(4x + 9)
= [(2x)^2 - (3^2)](4x + 9)
= (4x^2 - 9)(4x + 9)
= (4x^2)(4x) + (4x^2)(9) - (9)(4x) - (9)(9)
= 16x^3 + 36 x^2 - 36x - 81
Solving for any variable in an equation differs from equation to equation. You can use various methods such as the quadratic formula, factoring, brute force algebra etc.
Example
Solve x in the the equation logx8=3/2 Answer(5(root(10)))/4
What are the steps for 7x plus 8 equals 36?
7x + 8 = 36
- 8 = - 8
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7x = 28
7x/7 = 28/7
x = 4
What is y in x equals 4y2 plus 6 when x equals 42?
In the equation x = 4y2 + 6 where x = 42, we need to substitute 42 for x and solve for y.
x = 4y2 + 6
42 = 4y2 + 6
42 - 6 = 4y2 + 6 - 6
36 = 4y2
36 / 2 = 4y2 / 2
18 = 4y
18 / 4 = 4y / 4
9 / 2 = y
4 1/2 = y (or 4.5 = y)
the quantity 1 less 2/3 multiplied by 1/2 is 1/6
You really should consider trying this yourself before reading the answer, and you should understand the answer, otherwise you will not learn the lesson. Read each step, and do not proceed unless you understand it.
To maximize the volume of an open box made from a sheet of material 8 x 3, by cutting equal squares of side x from the corners and folding up the sides, first draw the box...
The box is 8-2x by 3-2x by x. Try again to draw it...
The volume of the box is (8-2x)(3-2x)x. Can you see the solution?
Simplify the volume. It is 4x3 - 22x2 + 24x. Can you see the solution?
Differentiate. This is a simple polynomial. Can you see the solution?
The deriviative is dy/dx = 12x2 - 44x + 24. Can you see the solution?
The maximum volume occurs when the deriviative is zero. Can you see the solution?
Solve for 12x2 - 44x + 24 = 0. How about the quadratic equation? Last chance to solve it yourself.
There are two roots of x: 3, and 2/3. 3, however, is not valid because you can not cut a square larger than 1.5 out of the original side of 3, so the answer is 2/3.
(4x - 8) + 2x = 6 + x
4x - 8 + 2x = 6 + x
6x - 8 = 6 + x
Subtract x from each side:
5x - 8 = 6
Add 8 to each side:
5x = 14
Divide each side by 5:
x = 14/5 = 2-4/5 = 2.8
Think of it in reverse - trying to get it in the form of (x + a)2
This equals x2 + 2ax + a2
Compare the coefficients&constants to those of the original equation:
x2 + 8x + c = x2 + 2ax + a2
2a = 8 and c = a2
a = 4, so c = 16
How do you solve for x in the equation of 20 over x squared minus 1 over x equals 1?
20/x2 -1/x = 1
Multiply all terms by x2:
20 -x = x2
Subtract x2 from both sides:
20 -x -x2 = 0
Divide all terms by -1 and form a quadratic equation:
x2+x-20 = 0
Factor the equation:
(x+5)(x-4) = 0
Solution: x = -5 or x = 4
Can you answer this 5 divided by x plus 5 equals 25 divided by x plus 9?
5/x+5=25/x+9
5/x=25/x+4
5=x*(25/x+4)
5=25+4x
-20=4x
-5=x
We'll check this:
5/(-5)+5=25/(-5)+9
-1+5=-5+9
4=4
Yep, it's right.
This check isn't entirely optional, since we divided by x, so if x was calculated to be zero we would have to report that there are no solutions (you can't divide by 0).
an easy way to think of knots is a little less than one and a half mph. this will give you a decent estimate and idea
