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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
What is the rate of change of the function y equals 1?
0 because y=1 can be written as y = (0)x +1 and its gradient is 0.
Solve for y in x euqals 4 plus y?
So you have x=4+y.
Simply subtract 4 from both sides, and you're left with x-4=y. Written in a slightly more familiar way, y=x-4.
4 (x+3)2 - 5(x+3)
First of all, there's no equation here, so it's not possible to solve it and find
a value for 'x'. Therefore, our next question has to be: What exactly do you
need to "do" with it ? We're suspecting that it's an exercise in elementary
algebra, and the assignment is to re-write this expression in a simpler form,
just to give you some practice in handling algebraic expressions. Understand
that if we do this, the result will not be an "answer" or a "solution" to anything
except the teacher's assignment, which was to write the same thing in a
different way.
We can see two different ways to go about this exercise. They should both
lead to the same thing. Since the purpose of the whole thing is to practice
these manipulations, we'll demonstrate both ways. That will give us the practice,
and we hope that you'll then try and go through it so that you also get the practice.
4 (x+3)2 - 5(x+3)
Before we begin the first method, let's make the expression a bit simpler to
handle. Notice that (x+3) appears in two different places. To cut down slightly
on the amount if writing required, let's call that quantity 'Q' for only a few seconds.
Now we have
4 Q2 - 5Q. This can be factored: Q (4Q - 5), and we can now replace (x+3)
wherever we see 'Q':
(x+3) [ 4(x+3) - 5 ]
Inside the brackets, eliminate the parentheses: (x+3) [ 4x + 12 - 5 ] = (x+3) [ 4x + 7 ].
Now multiply the (x+3) on the left by the [4x+7] on the right:
4x2 + 7x + 12x + 21 = 4x2 + 19x + 21 and that's the result of our first method.
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Now here's our second method:
4 (x+3)2 - 5(x+3)
Square the first (x+3) as indicated, and put its square inside the first parentheses:
4 (x2+ 6x + 9) - 5(x+3)
Eliminate the first parentheses:
4x2+ 24x + 36 - 5(x+3)
Eliminate the second parentheses:
4x2 + 24x + 36 - 5x - 15
Combine the 'x' terms:
4x2 + 19x + 36 - 15
Combine the numerical terms:
4x2 + 19x + 21 and notice that this is the same as the result of the other method.
What is 6 x 6 plus 5678194834 - 76735 x 793?
(6 x 6) + 5 678 194 834 - (76 735 x 793) = 5 617 344 015
What is the solution of 5 plus 2x greater than or equal to 13?
5 + 2x ≥ 13
Subtract 5 from both sides: 2x ≥ 8
Divide both sides by 2: x ≥ 4
Is y2-5y plus 2x-x2-120 equals 0 a circle or something else?
y2 - 5y + 2x - x2 - 120 is not a circle. It is a hyperbola rotated through 90 degrees.
How many roots does y equals x2 - 4x plus 6 have?
No real roots. Imaginary roots as this function does not intersect the X axis.
What is x in this equation 2x-1 equals -5x plus 34 What is x worth?
Add 5 to each side. You'll be left with 7x minus 1 equals 34. Next, you subtract one from each side and you'll be left with 7x equals 35. Finally, you divide each side by 7 and you get x equals 5
How would you answer this 15-3 open brackets 1-2x close brackets equals 2-3x x equals?
Unfortunately, limitations of the browser used by WA means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. While you HAVE tried to do so, the end of the question is missing some symbols. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc.
What is the constant of xy plus 3y plus 27?
xy+3y+27
x and y are variables, so the only term that doesn't change with x or y is 27
y must be the same. so x being 6 and y being 3, 18+9 is 27.
What is x plus 7 times x plus 7 times 4 times x squared?
Error: There cant be two x's in a equation either one to be y and other x or some other variable.
Sure there can be two x's. There is no '=' in this question anyway, so it is not an equation. You cannot solve for x with the information given, but you can simplify it as follows.
Performing the operations in proper order (exponents, then multiplication (and division, if any), and lastly the addition/subtraction operations, gives you:
x +(7x) + (7)(4) (x2)
Which is 8x + [28 (x2)] or 8x + 28x2 .
How do you take the integral from negative infinity to 4 of 1 over1 plus x2?
Recall that the antiderivative of 1/(1+x2) is arctan(x).
arctan(negative infinity) = -pi/2.
arctan(4) = approximately 1.325818.
The answer then is arctan(4) - (pi/2) = approximately -0.244979
7-2 is equivalent to 5, although you would get peculiar looks if you asked for 7-2 apples in a shop. 5 is the answer to the question "what is 7-2?". An equation like x-3=4 means there is a value for x that makes this equality true. There are 2 ways of looking at it. You might say "x-3=4 is true (or not true)". Or you could say "given that x-3=4, I can say x must be 7". The first approach is the logician's, the second approach is a mathematician's. Sometimes both are combined, if there is some doubt about the truth of x-3=4. "Equals" commonly means "the same as".
