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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 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.
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.
Each angle may be used as a 'reference angle'. A 30 deg. angle in QI will have a sides, x = (sq rt 3)/2 , y= 1/2, r = 1. An angle of 150 deg (180 - 30) will create a triangle in Q2 with the same lengths except x is now negative. So if you know all trig values for 30, then change the signs for cos and tan because x is now negative and you know the values of all. Similarly for 210 deg (180+30) creates the same triangle in Q3 but both x and y values are neg. Sin and cos are neg, but tan (divide 2 neg's) is positive. In Q4 (360 - 30) creates a 330 deg angle for a triangle that is the same shape, but y is neg and x is pos so that sin and tan are neg but cos is pos.
ex: sin 30 = 1/2 (Q1), sin 150 = -1/2 (Q2), sin 210 = -1/2 (Q3), sin 330 = 1/2 (Q4)
notice only the sign (+/-) changes.
Most trig classes teach you that Q1 all trig functions are pos, Q2 sin is pos, Q3 tan is pos, Q4 cos is pos. Remember this and the 1st Quadrant values and then you can get all trig functions using the concept of a reference angle.
What property is x plus 3 equals 5 then 2 plus 3 equals 5?
Well, if x+3=5 and 2+3=5, I'm guessing x should equal 2
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
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).
What is x if x plus 10 percent of x equals 9705.22?
10 percent = 0.1
'x' plus 10 percent of 'x' = 1.1x
1.1x = 9,705.22
x = 9,705.22/1.1 = 8,822.927 (rounded)
How many gallons of water are contained in a volume of 22 acre-feet?
22 acre-feet equates to 7,169,000 gallons of water.
What is the answer to -2x plus y equals 5?
The answer is any pair of numbers, just as long as the 'y'-number is
5 more than double the 'x'-number. There are an infinite number of them.
You miight think that if there are that many, then it's pretty easy to stumble across
a pair of numbers that's an answer. Unfortunately, there's a bigger infinity of pairs
of numbers that are not answers.
Which method would you use to solve this equation5x plus 3y equals 10?
There are an infinite number of solutions to a single equation in two variables.
So, in order to save myself time, the first thing I would do is go out and look for
another equation to put along with the first one.
"Is it right to live only for pleasure?" belongs to study of ethics, which deals with right and wrong. The perception of pain and pleasure would probably fall under psychology or possibly biology. The question of matter belongs to physics or possibly chemistry. 2+2=4 is a question of math.
Why it is necessary for a function to be one-one for existing its inverse?
If it is not 1-1 then you will not know where the inverse value is to be mapped.
For example,
f(x) = x2 , being an even function, is not 1-to-1.
Thus, for example, (-3)2 =9 = 32
Suppose g(x) were the inverse of f(x). What would g(9) be? -3 or 3? There is no way of telling.
The only way around it is to define the domain of x to be non-negative numbers and then f would be 1-to-1 so that g was a well-defined function whose range was the non-negative numbers.
Incidentally, the domain of f could just as well be defined as the non-positive numbers.
Yes, because you can rewrite it as:
y = -x/10
Which is a line.
When you graph the above equation, the graph passes the vertical line test - meaning that the graph never intersects with any vertical line more than once.
