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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 factor-x2 plus 7x plus 18?
Factorising -x2 + 7x + 18:
(a - x)(x + b) = -x2 + (b - a)x + ab
so ab = 18, b - a = 7 giving a = 2, b = 9:
(2 - x)(x + 9)
What are the exact solutions of x2 equals 4 - 7x?
x2 = 4 - 7x
x2 + 7x - 4 = 0
Using the quadratic formula, x = 1/2*{-7 ± sqrt[72 - 4*1*(-4)]}
= 1/2*{-7 ± sqrt[49 + 16]}
= 1/2*{-7 ± sqrt[65]}
2x plus 5y equals 10 find slop and y-intercept?
2x + 5y = 10
Subtract 2x from each side:
5y = -2x + 10
Divide each side by 5:
y = - (2/5)x + 2
Slop = - (2/5)
Y-intercept = 2
Solution set for 4x2-6 equals 2x2?
Reading this as:
4x2-6=2x2
This implies that:
-6=-2x2
3=x2
x=sqrt(3) and x=-sqrt(3)
So x can equal plus or minus the square root of 3
How do you solve y plus y equals 10?
You have to recognize that " y plus y " is the same as " 2y ".
This wouldn't be any problem if it was "house plus house" or "dog plus dog" ... you'd know
right away that it was "two houses" or "two dogs". But for some reason, a lot of people get
scared when they see " y plus y ", and totally freeze up.
y + y = 10
2y = 10
Divide each side by 2:
y = 5
0.25 * 5 = 1.25
It would have been quicker to use a calculator and you cannot be sure that I have got the correct answer!
What is the rational zeros for x3 plus x2-17x plus 15?
x3 + x2 - 17x + 15 = (x - 1)(x - 3)(x + 5).
Thus, the zeros are 1, 3, and -5.
All three zeros are rational.
How do you rewrite and solve for y 2x less than y plus 7?
your equation is this...
2x < y + 7
Now solve for y...
2x - 7 < y
Since you have two variable the most you can get out of (y) is the graph and the y-intercept.
the y-intercept is y > -7
6 + 7x = -36
first, subtract 6 from both sides
7x = -42
then, divide both sides by 7
7x/7 = -42/7
x = -6
to check, put -6 back into the original equation:
6 + (7 x -6) = -36
6 - 42 = -36
How do you solve the problem x-5 equals 2x?
First, you have to know what 'solve' means, so you know what you're looking for.
'Solve' means find a number for 'x' that will make the problem a true statement
when you plug that number in wherever 'x' appears.
Here's how to find it. First, write the problem down and look at it:
x - 5 = 2x
Now subtract 'x' from each side:
-5 = x
And there you are.
What is 16x squared minus 12x plus 9?
It's a second degree trinomial in 'x'. Its numerical value depends on the value of 'x'.
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The first contributor observed:
Very nice exercise with the quadratic formula. But it doesn't apply here.
The formula is used to solve a quadratic equation, but there's no equation
here ... the question doesn't say that the trinomial is equal to anything.
If the trinomial were equal to zero, then your application of the formula
is the way to solve it; but as it stands, there's nothing to solve.
Also BTW: (B2 - 4AC) < 0 doesn't mean no roots. It means a pair of imaginary
or complex conjugate roots. A quadratic equation alwayshas two roots, even
though they may be equal or imaginary.
How do you graph the equation y equals -x?
First, you look at the equation long enough to recognize that it's the equation
of a straight line with [ slope = 1 ] and [ y-intercept = 0 ].
Then you draw that line. It passes through the origin, and slopes up toward the
right at 45 degrees.
As another technique, you could use the equation to calculate two points on the line,
then mark the points on the graph, and draw a line between them.
To calculate two points, choose two values for 'x', and then calculate the value
of 'y' for each one.
Let's just pick two numbers out of the blue for 'x':
x = 2 and x = 9 .
Can you use the equation [ y = x ] to calculate the value of 'y' that goes with each one ?
That's right. Good work. When x=2, 'y' is also 2. And when x=9, 'y' is also 9.
So now you have two points on the graph ... (2, 2) and (9, 9).
Using a soft pencil, mark each of those two points on your graph with a small dot.
Then, using the same pencil along with a ruler, draw a line that connects the two
dots. You can extend the line as far as you want to, past either point, in either direction.
X2 - 5X - 6 = 0
What two factor of - 6 add up to - 5 ??
(X + 1)(X - 6)
So,
X = - 1
===
How do you accurately graph y -x2 8x 5 as a parabola?
There are two (main) ways to graph this parabola.
The first is to simply substitute in values of x, find the corresponding y values and then plot those points and connect the points with a curve.
The second way is to 'complete the square' so that we can find where the maximum or minimum occurs and the y-intercept and graph from those two points. This is the process described below.
y = -x2 + 8x + 5
y = -(x2 - 8x) + 5
y = -(x2 - 8x + 16 - 16) + 5
y = -(x2 - 8x + 16) + 16 + 5
y = -(x-4)2 + 21
From this we can see that a maximum occurs at (4,21). To find the y-intercept, substitute in x=0, giving y=5.
From these two points, we get a pretty good idea of what the graph looks like. If you want more accuracy, substitute in more values of x.
