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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
Six x squared plus twenty one x - forty five?
Assume the question refers to solving the quadratic equation 6x2 +21x - 45 = 0, then :-
This equation can be factored 6x2 + 21x - 45 = (6x - 9)(x + 5) = 0
This holds true when either 6x - 9 or x + 5 = 0
When 6x - 9 = 0 then x = 9/6 = 1.5 : When x + 5 = 0 then x = -5
How do you factor 12x2 plus 28x-17?
The trick with this kind of question is to find two terms that add up to the middle one (28x), and whose coefficients are equal multiples of the first and last term:
12x2 + 28x - 17
= 12x2 - 6x + 34x - 17
= 6x(2x - 1) + 17(2x - 1)
= (6x + 17)(2x - 1)
The only trick with this technique is that sometimes it's difficult to find those two middle terms (-6x and 34x in this case). If it takes too long to figure this out, you can actually break it down into ~another~ quadratic equation, which will usually be easier to factor, and give you those two values. Consider:
Let "a" and "b" be the unknown coefficients. We know:
b = 28 - a <-- we know this because they must add up to the middle term
12/a = b/17 <-- this must be true in order for us to end up with a common multiple.
∴ 12/a = (28 - a)/17
∴ 28a - a2 = 204
∴ a2 - 28a + 204 = 0
We can then solve for "a" by factoring this equation:
(a - 34)(a + 6) = 0
So our coefficients are the two possible values for "a", 34 and -6. We can then simply plug them in to the original equation and factor it out as shown above.
How do you foil 1 plus 2sinx plus sin2 x?
sin2(x) + 2 sin(x) + 1
It might be easier for you if you use 'S' temporarily to represent 'sin(x)', just long enough to look at it.
Then you have
S2 + 2S + 1
Can you 'foil' that ?
It's just the square of (S + 1). The factors are (S+1) and (S+1).
The original expression is the square of [sin(x) + 1].
What should be added to both sides of this equation to solve for the variableA plus 39 equals -60?
-21
How do you graph 3y plus x plus 6 equals 0?
Plug in numbers. If you don't know which numbers to plug in, solve the equation for y to give you a better idea. It ends up being y=(-x/3) - 2
What is 20x plus 80y equals 0 in y equals mx plus b?
20x + 80y = 0
Subtract 20x from each side of the equation:
80y = -20x
Divide each side by 80:
y = -1/4 x
m = -1/4
b = 0
Which line lies completely between y equals 4x-5 and y equals 4x plus 1?
y = 4x -2.5
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The slope has to be the same as the two original equations, in this case 4. This way the lines are parallel. And the y-intercept has to lie between the two original equations (0,1) & (0,-5) on the y-axis.
Some of these points include:
(0,0) y=4x
(0,-1) y=4x-1
(0,-2) y=4x-2
(0,-3) y=4x-3
(0,-4) y=4x-4
...and so on for any point in between, including (0, -2.5) as the previous poster listed.
What is an equation composed of?
An equation is composed of mathematical statements, which can be arranged to result in a series of equations/inequalities which can be solved for each unknown.
2x^2+2x-14
(-2 +- sqrt(2^2 -4(2)(-14))/2(2)
simplifies to
+- sqrt 29
So your answers would be, sqrt(29), and, -sqrt(29)
What does x equal if 3 equals 2x plus 5?
3 = 2x + 5
Subtract 5 from each side:
-2 = 2x
Divide each side by 2:
-1 = x
What is the answer to x plus 2 equals 7?
X is a variable. So you subtract 7 minus 2 to find the variable answer.So your answer is 5
How do you solve -5x2 plus 5x plus 60 equals 0?
-5x2 + 5x + 60 = 0
Remove the common factor of 5
-x2 + x + 12 = 0
Where the coefficient of x2 is negative, it is best to make it positive by multiplying throughout by -1
x2 - x - 12 = 0
The above equation will factorise.
(x - 4)(x + 3) = 0 ; therefore x - 4 = 0 when x = 4, or x + 3 = 0 when x = -3
The solutions (roots) of this equation are x = 4 and x = -3.
by 4. You do this because you want to find out what x equals. If you divide by 16, you find out what 1/4X equals, and that isn't much good to you. x=4 is the answer.
How do you solve x plus y equal 79 and xy equals 1288?
If: x+y = 79 Then: y = 79-x
If: xy = 1288 Then: x(79-x) = 1288 and it follows that: 79x-x2-1288 = 0
Solving the above quadtratic equation gives x a value of 23 or 56
So the values are x = 23 and y = 56
Check: 23+56 = 79 and 23*56 = 1288
