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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
9x+3y=-68
-2x+y=18
We are asked to solve with substitution so we first write y=18+2x.
Let us substitute this into the first equation.
9x+3(18+2x)=-68
9x+54+6x=-68
15x=-68-54=-122
so x=-122/15
and y =18+2(-122/15)==18+-244/15=270/15-244/15=26/15
So the solution is (-122/15,26/15) which is an ordered pair.
Why are factors in formulas squared eg gravity energy etc?
The simplest answer would be that it is simple the way it is. A linear change in distance and gravity just doesn't match up with reality. So a better answer is that this is way it must be. Nothing else really describes what is happening.
What is the factor of x to the power of 3-3x to the power of 2-9x plus 27?
x3 - 3x2 - 9x + 27
= x2(x - 3) - 9(x - 3)
= (x - 3)(x2 - 9)
= (x - 3)(x - 3)(x + 3)
What is the legality of D and X?
Several states have taken legal action to limit or ban D and X.March 2003,the United States Senate passed a bill banning partial birth abortions.but a federal judge declared the law unconstitutional,so that the government had not been able to enforce it.
How do you plug in cords in y equals mx plus b?
Y=m*x+b
Y = Y coordinate
M = slope
X = X coordinate
B = Y intercept
To get a coordinate just put a number into X and see what Y comes out as.
example:
Y = 2x - 1
coordinates:
(X,Y)
(-3,-7)
(-2,-5)
(-1,-3)
(0,-1)
(1,1)
(2,3)
(3,5)
What is the factorization of 2x2-6X plus 24?
There are no solutions to this quadratic equation because the discriminant is less than zero.
If x equals 1 3 when y equals 162 find x when y equals 3?
You need to know what is the relationship between x and y. Are they proportional? Inversely proportional? Several other options also exist.
What is the integral of one over the square root of forty-nine minus x squared?
Very sorry, I showed you how to take the derivative of the stated problem. I leave that below, however to take the integral you really just need your table of integrals.
The reference integral from my table (in my old calculus book) is:
integral of 1 / [ a2 - x^2]1/2 = sin-1|x / a| + c
a2 = 49 => a=7
x2 = x^2 => x = x
And your answer is:
sin
-1(x / 7) + c
If you are not allowed to use the table of integrals, the other alternative is trigonometric substitution.
Assume our integral is:
The integral of dx / sqrt ( a2 - x2)
Let x = a sin (θ)
dx = a cos (θ) d
θ
<-- this is just the derivative of x
θ = sin-1 (x/a) <-- solve the first equation for theta
So the integral transforms into:
the integral of ( a cos (θ)
d
θ
) / sqrt ( a2 -
a2sin2(θ) )
factor out an a2 in the root:
( a cos (θ)
d
θ
) / sqrt (
a
2 (1
-
sin2(θ) ) )
use the trig identity: sin2
(θ) + cos2
(θ) = 1
which can be rewritten:
1
-
sin2(θ) =
cos2
(θ)
and therefore:
( a cos (θ)
d
θ
) / sqrt (
a
2(
cos2
(θ)
) )
which simplifies to:
( a cos (θ)
d
θ
) /
( a cos (θ) )
which leaves us with the integral of
d
d
θ
it's now easy to solve and we get:
θ + C
plugin theta (from above):
sin
-1(x/a) + C
Plus in your a and x from the original equation, and you are good to go.
-----
Bonus: Here is how you find the derivative of this, since I already solved this on accident:
First, rewrite the expression to kill the fraction:1/(49-x2)1/2 =(49-x2)-1/2
Now, we can use u-substitution.
Let u = 49-x2
u` = -2x
Take thederivativeof u-1/2
(u-1/2)`= [ -u-3/2 ]/ 2
Now multiply by u`.
( [ -u-3/2]/ 2 ) ( -2x ) = (the 2's and negatives cancel)
x [ u-3/2] =
x / u3/2
Now plug u back in (remember: u = 49-x2)
x / u3/2 = x / (49-x2)3/2
The answer is:
x / (49-x2)3/2
Can you solve the equation 4x squared plus 7 equals 5?
Yes, but the solution is imaginary if you have learned that
4x^2 + 7 = 5
4x^2 = -2
x^2 = -1/2
x = +/-0.707i where i = square root of -1
How do you factor 4x2 plus 2x-6 equals 0?
If 4*2+2x-6=0 is what you meant, then I am going to say 2(2*1+1x-3) is your answer
Edit: if solving for x then -1 is your answer, sorry I'm used to solving for multiple possibilities for x so "factor" threw me off.
I don't see any description.
However, the exponential function is defined for any value of the argument; on the other hand, since you have 1/x, zero is excluded. The function is defined for any value other than zero.
How do you solve 8x plus 8 equals 32x?
Equation: 8x + 8 = 32x. x = 1/3
- Can start by dividing both sides by 8: x + 1 = 4x.
- Subtract x from both sides: 1 = 3x.
- divide both sides by 3: 1/3 = x, or x = 1/3.
Check answer in original equation: 8/3 + 8 = 32/3. Both sides equal 10 2/3, so our answer is correct.
