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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 do you solve the equation of 5x-3 equals 12?
We're about to give you the complete solution. It may get complicated,
and we hope you can stay with us as we slog through it.
Before we begin to attempt a solution,
we first write down the equation:
5x - 3 = 12
Add 3 to each side:
5x = 15
Divide each side by 5:
x = 3
Were you able to follow all of that ?
10 miles per hour
100 feet per second
$25 per hour
etc...
How do you solve the equation x plus 6 equals x plus 8?
X + 6 = X + 8
This is a nice example of an equation that has no solution.
If you subtract 'X' from both sides of the "equation", it says: " 6 = 8 " .
This should immediately lead us to suspect that something here is not kosher, (that is to say, unorthodox).
What is highest common multiple of 15 and 18?
The highest common multiple of any set of numbers is infinite.
What is the five x plus y equal one?
To figure that out, you'll need at least one of the pronumeral's values.
The other thing you could be asking for is a graph. If you go to http://www.calc5.com/ and type in "graph(5x+y=1)", you can see a graph of that equation on a number plane.
How would you distinguish exponents and logarithms using a graph and a sequence?
Exponential graphs of the form y = bx (if the b >1) have the neg. x axis as an asymptote, pass thru (0,1) and (1,b) and increase toward infinity rapidly. Log graphs of the form y = logb x (if the b >1) have the neg. y axis as an asymptote, pass thru (1,0) and (b,1) and increase slowly toward infinity.
When looking at a sequence, if you divide 2 terms (a2 / a1), (a3 / a2), (an / an-1), you sill get the same answer (b) if it represents an exponential system.
What is the answer to 3x2-6x-7 equals 0 in quadratic form?
I would not even attempt to factor this, so the quadratic formula.
X = - b (+/-) sqrt(b2 - 4ac)/2a
a = 3
b = - 6
c = - 7
X = - (- 6 ) (+/-) sqrt[(- 6)2 - 4(3)(- 7)]/2(3)
X = 6 (+/-) sqrt(36 + 84)/6
X = 6 (+/-) sqrt(120)/6
X = 6 (+/-) sqrt( 22 * 30)/6
X = [6 (+/-) 2sqrt(30)]/6
----------------------------------------exact answer less clean up
Write 8x2 plus 6x - 35 as a polynomial in descending order?
Type your answer here... (2x + 5)(4x - 7)
Fifteen x squared - seventeen x plus 4 equals 0?
15x2 - 17x + 4 = 15x2 - 5x - 12x + 4
= 5x(3x - 1) - 4(3x - 1).
= (5x - 4)(3x - 1).
Thus the solution,
when 15x2 - 17x + 4 = (5x - 4)(3x - 1) = 0,
is: x = 4/5 or 1/3.
* * * * *
The technique, in case it is not familiar, is quite simple:
Step 1: Note that the three co-efficients of the given quadratic are 15, -17, and 4.
Step 2: We seek two numbers whose sum and product are -17 and 60.
(Note that 60 is, itself the product of 15 and 4.)
The two numbers we seek are -5 and -12.
Step 3: Replace the middle term, '-17x' with two terms, '-5x' and '-12x'.
Step 4: Continue factorisation easily, as shown. Then, combine like terms.
Step 5: To find solution, apply the following principle: The product of two factors is equal to zero if, and only if, one or other of the two factors is equal to zero.
How do you solve 4y-2x equals 0?
Add 2x to each side: 4y = 2x
Divide each side by 2: 2y = x
So any two numbers where one is twice the other will be a solution.
When do you say that the graph is a function?
A function takes one input and assigns to it exactly one output, so a graph qualifies as a function if it passes the vertical line test (run a vertical line across the entire plane; the function should only cross your line once no matter where you are testing).
