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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
Why it takes several seconds for the odor of ammonia to travel a few feet?
Because the NH3 molecules have to travel through the nitrogen and oxygen molecules in the atmosphere.
How many roots does the equation 3 x plus 7 have?
That is not an equation, since it doesn't have an equal sign.
lets say x equals 9
(9+4)*4*4*4*4=
13*4*4*4*4=
52*4*4*4=
208*4*4=
832*4=
3328 there. Easy!
How come 1 cubic meter equals 1000 cubic centimeters isn't it 1 million cubic centimeters?
Whoever told you otherwise was wrong. One cubic meter equals 1,000,000 cubic comtimeters.
What is the square root of pie x 3 x 6.55444 plus 64.79 x 60.5465565?
3,957.66372 (as determined by google calculator)
It depends on the length. The surface area would be 4*length+8*length+16.
9 can get first. Then the remaining 8 can get second. 7 can get third. 6 can get fourth. 9*8*7*6=3,024.
How is Infinite used in real life applications?
There is really nothing infinite in real life. But there are several cases where for practical purposes, "infinity" is almost the same as "very large". One example is in optics, where it is not so much the distance from the lens to the object that matters, but the RECIPROCAL of the distance. In this distance, since the reciprocal of a very large number is close to zero, a far-away object (e.g., the Sun) can be approximated as "infinitely far away".
If y equals 3xsquare-2x.then what is the y-value for x equals 3?
When x = 3, y = 3*32 - 2*3 = 27 - 6 = 21
What is 4x y-3xy plus 15xy-12 plus 9xy -14xy plus 19 plus -13x y plus 7xy plus 16xy plus 21?
It is not clear whether the spaces that appear between some xy pairs are intentional or whether they should have had some other symbols.
Ignoring those spaces, 21xy + 28.
Assuming y = x(x - 10)
Either use the product rule:
u = x
v = (x - 10)
→ y = x(x - 10) = uv
d/dx (uv) = v du/dx + u dv/dx
→ dy/dx = d/dx x(x - 10)
= (x - 10)(d/dx x) + (x)(d/dx (x - 10))
= (x - 10)(1) + (x)(1)
= x - 10 + x
= 2x - 10
or expand the brackets and differentiate
dy/dx = d/dx x(x - 10)
= d/dx x² - 10x
= 2x - 10
How do you solve 6x-2y equals -16 4x plus 4y equals -32?
x = -4 and y = -4.
These are known as simultaneous equations. We have to manipulate the equations in order to remove one of the variables. Then we can solve for the remaining variable. Once we have done this, we can substitute this value back into one of the original equations to solve for the other variable. So:
1. 6x - 2y = -16
2. 4x + 4y = -32
If we multiply 1. by 2 then we will end up with a -4y in one equation and 4y in the other. We will then be able to add these together which will cancel out and remove the y variable altogether.
So, 1. multiplied by 2 gives:
3. 12x - 4y = -32
Adding 2. & 3. gives:
4. 16x = -64
x = -64/16
x = -4
Now we have worked out the value of x we can substitute this value back into one of the original equations.
Substituting x = -4 back into 1. gives:
(6 * -4) - 2y = -16
-24 - 2y = -16
2y = -24 + 16
2y = -8
y = -4
We can double check we have solved this correctly by substituting both values into the other original equation.
Substituting x = -4 & y = -4 into 2. gives:
(4 * -4) + (4 * -4) = -32
-16 + -16 = -32
-32 = -32 (Yes this works, we have found the correct values of x & y!)
What is 101' x 118' x 119' x 74' equal?
I assume the apostrophes represent feet; it really doesn't make sense to multiply four numbers together. Or at least, in most situations it wouldn't make sense. You would have feet to the fourth power; but we only live in a three-dimensional world. Anyway, if you want to know how much it is, just multiply the four numbers together. The answer will be in feet to the fourth power ... whatever that means.
One place where such measurements can be used is to specify the work done by a pump - if you multiply the volume of water pumped (say, in cubic feet) by the height (say, in feet), you get feet to the fourth power - which is actually (once you consider some implicit factors) a measurement of the work done by the pump.
Which sequence of fx equals 2x plus 2 has integer input values?
f(x)=2x+2. Put in 0, 1/2, 1, 3/2, 2... and you will get integer values. That is for the domain. The numbers you get when you put that in are the range integral values.
What are the order pairs for x plus y equals 6 and -x plus 3y equals -2?
The answer is - not are : (5, 1).
What is the solution to 2x squared minus 3x squared plus 5x minus 4 when x equals negative 1?
This is not calculus. Please post this in the correct forum.
However, 2x2 - 3x2 +5x - 4 = -1
therefore -x2+4x-3 = 0
therefore x2-4x+3 = 0
therefore (x-3)(x-1)=0
therefore x = 3 or x = 1.
Put your questions in the correct category. Makes then more likely to be answered correctly.
