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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 graph y equals x2 plus 6x plus 7?
y = x2 + 6x + 7
a = 1, b = 6, c = 7
Since a is positive, the graph opens upward. You can find the vertex coordinates (-b/2a, f(-b/2a)) = (-3, f(-3)) = (-3, -2), so the equation of the axis of symmetry is x = -b/2a = -3, plot the y-intercept point (0, 7), plot the point (-b/a, 7) = (-6, 7), and draw the graph that passes through these points.
Or complete the square.
y = x2 + 6x + 7
y = x2 + 6x + 9 - 9 + 7
y = (x2 + 6x + 9) - 2
y = (x + 3)2 - 2
So start with the graph of y = x2 whose vertex is at the origin. Move it 3 units to the left, and 2 units do
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals". It would appear that some symbols are missing from the question.
How do you solve the following equation using identities 2sin2x sinx plus 1 equals 0?
Unfortunately, the browser used by Answers.com for posting questions is incapable of accepting mathematical symbols. This means that we cannot see the mathematically critical parts of the question. We are, therefore unable to determine what exactly the question is about and so cannot give a proper answer to your question. Please edit your question to include words for symbols and resubmit.
It is not clear whether there should be a symbol (operator) between sin2x and sinx and, if so, what it is.
How do you solve 3ysquared equals x?
It is generally not possible to solve a single equation in two variables: this is one such.
How do you solve this system algebracally 9x plus 2y equals 5 and y-2x plus 3 equals 0?
9x + 2y = 5
y - 2x + 3 = 0
Put both equations into the same format. It is often easiest to have just one unknown on (say) the left-hand side of the equation. Let's pick y for this purpose.
2y = -9x + 5
y = 2x - 3
Now make the coeficients of y the same. This can be done by multiplying the 2nd equation by 2.
2y = -9x + 5
2y = 4x - 6
Then, -9x + 5 = 4x - 6
13x = 11 : x = 11/13
And substitue for x in any equation - take the very first original equation.
9x + 2y = 5
99/13 + 2y = 5 : 2y = 5 - 78/13 = - 28/13
y = - 14/13
Formula for instantaneous speed?
lim as h->0 of (f(x+h) - f(x))/h
or
lim as x->a of (f(x) - f(a))/(x - a)
What is the derivative of cosx divided by sinx?
When dealing with a right angled triangle trigonometric functions can be defined by :-
cos x = adjacent/hypotenuse
sin x = opposite/hypotenuse
Therefore cos x/sin x = adj/hyp ÷ opp/hyp = adj/hyp x hyp/opp = adj/opp
The tangent of an angle is given by the formula : opposite/adjacent
The tangent of the complementary angle is therefore : adjacent/opposite
Then cos x/sin x = tan(90-x)
The area of a square whose sides are 6 inches is how many square inches?
Area = side x side = 6 x 6 = 36 inches2
7x + 2 = -4 7x + 2 - 2 = -4 - 2 7x = -6 7x/7 = -6/7 x = -6/7
What is the answer for 3x plus 5y equals 2z?
"3x + 5y = 2z" doesn't ask any question.
If you're looking for numbers for 'x', 'y', and 'z' that make the statement true, there are
an infinite number of sets that do it.
A few of them are:
x=1, y=3, z=9
x=2, y=4, z=13
x=3, y=5, z=17
If you want to set up a puzzle where there's only one correct answer ... only one secret set of
values for 'x', 'y', and 'z' that solves the puzzle, then you need two more equations.
The one equation you gave us is the equation of a line in 3 dimensions. Every point on the line
has the coordinates (x, y, z), and every point satisfies the equation.
Does y equals 3x2-5x plus 1 cross the x-axis?
This can be easily answered using the well-known formulae for solving quadratic equations:
y = 3x2 - 5x + 1
then
x = (5 +- sqrt(25 - 4*3*1))/6
since 25-4*3*1 = 25-12 = 13, which is > 0, this parabola has two intersections with the x-axis (as the quadratic equation has two real roots).
What is the x-value when y equals 8?
Since the relationship between x and y is not defined, x can have any value whatsoever.
2 - 8y + 6 = 4y - 70
2 + 6 + 70 = 4y + 8y
78 = 12y
y = 78/12
y = 6.5
Describe what it means for a function to be one to one?
It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.
