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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 volume for 120ft X 240ft x 9ins?
Well firstly, you need to change everything into 1 type of unit. Either you can have everything in feet or everything in inches.
In this example, since 2 of the 3 units are already in feet, I'll change the 3rd one into feet as well.
In 1 foot, there are 12 inches.
So to find out how many feet there are in 9 inches, just do 9 divided by 12 which equals 0.75ft
Now, to finish it off just simply do 120ft x 240ft x 0.75ft and you get an answer of 21600ft3
NOTE: Remember that the units will be ft3 as this is a measurement for volume.
Hope that helps.
Jamz159
What is the derivative of cosx divided by sinx?
When dealing with a right angled triangle trigonometric functions can be defined by :-
cos x = adjacent/hypotenuse
sin x = opposite/hypotenuse
Therefore cos x/sin x = adj/hyp ÷ opp/hyp = adj/hyp x hyp/opp = adj/opp
The tangent of an angle is given by the formula : opposite/adjacent
The tangent of the complementary angle is therefore : adjacent/opposite
Then cos x/sin x = tan(90-x)
7x + 2 = -4 7x + 2 - 2 = -4 - 2 7x = -6 7x/7 = -6/7 x = -6/7
The area of a square whose sides are 6 inches is how many square inches?
Area = side x side = 6 x 6 = 36 inches2
Does y equals 3x2-5x plus 1 cross the x-axis?
This can be easily answered using the well-known formulae for solving quadratic equations:
y = 3x2 - 5x + 1
then
x = (5 +- sqrt(25 - 4*3*1))/6
since 25-4*3*1 = 25-12 = 13, which is > 0, this parabola has two intersections with the x-axis (as the quadratic equation has two real roots).
What is xx plus 2x plus 3x plus 6 equal to?
X can't be solved, you don't have anything on the right side of the equal.
What is the x-value when y equals 8?
Since the relationship between x and y is not defined, x can have any value whatsoever.
What is the answer for 3x plus 5y equals 2z?
"3x + 5y = 2z" doesn't ask any question.
If you're looking for numbers for 'x', 'y', and 'z' that make the statement true, there are
an infinite number of sets that do it.
A few of them are:
x=1, y=3, z=9
x=2, y=4, z=13
x=3, y=5, z=17
If you want to set up a puzzle where there's only one correct answer ... only one secret set of
values for 'x', 'y', and 'z' that solves the puzzle, then you need two more equations.
The one equation you gave us is the equation of a line in 3 dimensions. Every point on the line
has the coordinates (x, y, z), and every point satisfies the equation.
2 - 8y + 6 = 4y - 70
2 + 6 + 70 = 4y + 8y
78 = 12y
y = 78/12
y = 6.5
Why are milliter and cubic centimeters the same?
Every unit in the International Standards of Units ("SI units") has a universal standardized definition. By universal, it is used everywhere. For instance, a meter is defined as "Length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second (17th CGPM)" Yes. The definitions are usually pretty weird, but they stay consistent, which is important.
Now, the reason why the milliliter and the cubic centimeter are the same is much simpler. The liter was originally created as another word for a cubic decimeter. Because there are 1000 milliliters in a liter, and 1000 cubic decimeters in a cubic centimeter[see note], a milliliter and a cubic centimeter and therefore, the same.
Note: millimeter, centimeter, decimeter. While the centimeter is 10 times smaller than the decimeter, we are also dealing with cubic terms, so a cubic centimeter is therefore, 103 or 1000 times smaller than a cubic decimeter.
Describe what it means for a function to be one to one?
It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.
How do you solve x squared plus x squared plus x?
Add the x's squared together to get 2x^2+x. You cannot add anymore so the answer is 2x^2+x
What is the history of limits in calculus?
newton and Leibniz were first introduced the concept of limit independently
4x+5 = 8x+10
But you are saying
4x+5 = 8x+4
If this were the case, 8x+10 = 8x+4, and so 10=4
Thus there is no possible solution for X.
====================================
Honk! Go to your room.
8x + 4 = 4x + 5
Subtract 4x from each side:
4x + 4 = 5
Subtract 4 from each side:
4x = 1
Divide each side by 4:
x =1/4
Check:
Left side: 8x + 4 = 8/4 + 4 = 2 + 4 = 6
Right side: 4x + 5 = 4/4 + 5 = 1 + 5 = 6
6 = 6 yay!
What is the solution for x plus y equals 1 and -4x plus 2y equals -2?
OK, there's two ways to solve systems of linear equations. The first way is substitution and the second way is called elimination/addition, but we're only going to solve it this way (because it's hard to show the other way just with text).
Let's do the simplest first, the substitution. You have:
x+y=1 and -4x+2y=-2
Solve for one of the variables (x or y) on the first equation. For example, solve for y in x+y=1:
x+y=1
y=1-x ;Subtract x on both sides
Now substitute 1-x into every y on the other equation:
-4x+2y=-2
-4x+2(1-x)=-2 ;Plug in 1-x into all the y's
-4x+2-2x=-2 ;Distribute the 2
-6x+2=-2 ;Combine the x's
-6x=-4 ;Subtract 2 to both sides
x=(-4/-6) ;Divide both sides by -6
x=2/3 ;Simplify the fraction
Now that you have what x is equal to, plug that back into y=1-x:
y=1-(2/3) ;Plug in 2/3 for x
y=1/3
Your solution for both equations is ( 2/3 , 1/3 ).
Why is natural log given the initials ln instead of nl?
Euler came up with the log, and being Swiss, would've spoken french. In French the natural log would be le logarithme naturel, and his notation would've just caught on. I might be wrong, I've not really looked this up, just seems like a logical assumption...
