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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 -5 a solution to x-6 equals 1?
X - 6 = 1
add 6 to each side
X = 7
====
So, - 5 is not a solution here.
What is Four to the third power minus three to the second power?
4 cubed is 64, 3 squared is 9, so 55.
How does 1 plus x divided by 2 equal 2?
It has to equal 3 because if you plug it in to the equation you get:
(1+3)/2 = 2
4/2 = 2
2=2 check.
To SOLVE for the equation you have to set the whole thing equal to X.
(1+X)/2 = 2
1. Multiply both sides by 2. (2)(1+X)/2 = 2 (2)
2. subtract 1 from both sides. 1+X = 4 X-1 = 4 -1
3. This will give you your answer of 3. X = 3
What are the 3 methods in writing sets?
1. For finite sets, and some sets with no pattern you can write down the elements.
{a1, a2, a3, a4, ....., an} or {a1, a2, a3, ....} for infinite sets
e.g. {1, 3, 5, pi/sqrt(2)}
{1, 2, pi, 56, 4, i, sqrt(pi), ...}
You can do this with all sets, there is no order required.
2. If there is a generic way of describing the set, as in there is one universal pattern for all of them then you can write:
{x | x satisfies P(x)} where P is a condition
2'. For sets have a name and a symbol, for instance the natural numbers, just write the symbol.
bolded N for natural numbers
3. If a set is countable, meaning its elements can be written in a sequence an (a sequence is an infinite order of "numbers" with respect to the natural numbers) then you can write:
{an} to represent the set.
e.g. (an) = ((-1)^n) = (-1, 1, -1, 1, -1, 1, -1, ...).
Then we can say {an} = {(-1)^n} but there are only two distinct elements, so it's also {1, -1}
A better one. (bn) = (1/2^n) = (1/2, 1/4, 1/8, 1/16, ....)
Write {1/2^n} suffices.
Note: You have to specify that n is a natural number beforehand so both the sequence and set notation makes sense
Can't think of a fourth way yet.
What number do you have at the beginning when you multiply by 308 and point ten then divide by 3?
Any number at all.
Does 3y equals 6x-3 and y equals 2x-1 have a concident graph?
You might need to elaborate more i am not sure what you mean by concident, but if you mean consistent as in is the graph consistent or inconsistent and dependant or independant . then I can help
we have 3y=6x-3
which equals y=2x-1
so m= 2 and b=-1
and we have
y=2x-1
so m=2 and b=-1
soo they are the same line which means they have infinite solutions and they are consistent( the system) and dependant( the equations)
Hope this is what you were looking for if not repost and I will try and help!
What is the slope 2x plus 3x plus 6 equals 0?
There is no slope, because the equation as provided was in one variable only, x, no y. Sorry. Please restate the question.
Which operation should be performed x plus 9 equals 20?
Subtract 9 from each side. ( subtraction; both sides )
X + 9 = 20
X + 9 - 9 = 20 - 9
X = 11
-----------------check in original equation
11 + 9 = 20
20 = 20
checks
Where can i find Proof square root of 5 is irrational?
The proof that the square root of 5 is irrational is exactly the same as the well-known proof that the square root of 2 is irrational - except using 5 in place of 2. We can prove a more general result: the square root of any prime is irrational.
First of all, we require the lemma:
for any prime p, and integer x,
p|x2 ⇒ p|x
That is, if x2 is divisible by p, then so is x.
Proof:
The prime factorization of x2 necessarily contains p at least once, since it is divisible by p. But it also has to contain an even power of every prime, since it is the prime factorization of a square. Therefore, it contains p at least twice, and its square root, x, contains p at least once: that is, x is divisible by p.
Now, given a prime p, assume that its square root is rational. Then, it may be written in the form a/b, where a and b have no common factors (that is, the fraction a/b is in lowest terms). This is always possible for any nonzero rational number. Since this quantity is the square root of p, its square equals p, that is
(a/b)2 = p
a2/b2 = p
a2 = pb2
Now, pb2 is a multiple of p, so a2 must be too. And, using the result above, this means that a must be a multiple of p also. Thus, there exists an integer c such that
a = PC
Then,
(PC)2 = pb2
p2c2 = pb2.
Since p is not zero, we may divide both sides by p to obtain
PC2 = b2
That is, b2 is divisible by p also, and thus b is divisible by p.
Since a and b were both divisible by p, the fraction a/b could not have been in lowest terms, which contradicts our initial assumption. Therefore, the square root of p cannot possibly be a rational number. Since 5 is prime, the proof is complete.
Your best bet is to make the equation as simple as possible. You have
X+4X+5=40
subtract 5 from both sides
X+4x=35
simplify the terms on the left side
5x=35
then just divide both sides of the equation by five to find X.
it is 7yx978
= inegrate (e-2x) / derivate -2x = (e-2x)/-2
-> integral esomething = esomething , that's why (e-2x) don't change
-> (-2x)' = -2
How can you break down numbers?
The best way to break down a number (from the perspective of arithmetic!) is to write it as a product of its prime factors. For instance,
24 = 2 x 3 x 4
where x is the multiplication operator and of course 2, 3, and 4 are all prime numbers.
X2 plus 12x minus 13 equals 0?
x2+12x-13=0
The factor of x2+12x-13 is: (x+13)(x-1)
So: x+13 = 0 or x-1 = 0
The answer is: x=-13 or x=1
What are the values of x and y if 7x plus 6y plus 20 equals 180?
7x + 6y + 20 = 180
We're just going to re-arrange it a bit, without changing anything:
Subtract (7x+20) from each side of the equation:
6y = -7x + 160
Divide each side by 6:
y = - 7/6 x + 80/3
This is exactly the same equation that you gave us in the question. But when we
write it in this form, we can see that it's the equation of a straight line that has a
slope of (- 7/6) and cuts the y-axis of the graph at (y = 80/3).
Every point on that line has a pair of coordinates ... one 'x' and one 'y' ... that are
a solution of the equation. And you know how many points there are on a line . . .
5x = 1
To find the answer to this question, x needs to be isolated by itself on one side of the "=" sign. Divide both sides by 5 and you get
(5x)/5 = 1/5
5/5 is one, so the equation becomes
1x = 1/5
And the answer is:
x = 1/5
What is the derivative of sin x?
f'[x] = lim(h->0) (f[x+h]-f[x])/h
lim(h->0) (sin[x+h]-sin[x])/h
By angle-addition formula, we have:
lim(h->0) (sin[x]cos[h]+sin[h]cos[x]-sin[x])/h
lim(h->0) (sin[x]cos[h]-sin[x])/h + lim(h->0) (sin[h]cos[x])/h
sin[x]*lim(h->0) (cos[h]-1)/h + cos[x]*lim(h->0) sin[h]/h
In a calculus class, it is shown that:
lim(h->0) (cos[h]-1)/h = 0 and that lim(h->0) sin[h]/h is 1. So,
sin[x]*lim(h->0) (cos[h]-1)/h + cos[x]*lim(h->0) sin[h]/h becomes
sin[x]*0 + cos[x]*1
cos[x]
So, if f[x] = sin[x], f'[x] = cos[x]
