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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 x plus 5y equals 55?
Massage the equation into the standard form [ y = f(x) ] so that you can read off the slope and y-intercept.
x + 5y = 55
Subtract x from each side:
5y = -x + 55
Divide each side by 5:
y = -(1/5)x + 11
Now you know that the slope of the graph is -(1/5), and the y-intercept is 11.
That should help a lot.
What is the answer to x plus 5y equals negative12?
x + 5y = -12 is not a question, and thus has no answer. This is equivalent to asking "What is the answer to yellow?"
- If you want to know the nature of the equation, it describes a line with a slope of -1/5, an x-intercept of -12/5, and a y-intercept of -12
- If you wish to solve that equation for x, the answer is x = -12 - 5y
- If you wish to solve that equation for y, the answer is y = (12 + x) / -5
- If you wish to find the rate of change of y with respect to x, the answer is -1/5
- If you wish to find the rate of change of x with respect to y, the answer is -5
- If you wish to find the indefinite integral of the function for y, the answer is -12x/5 - x2/10 + C
- If you wish to find the indefinite integral of the function for x, the answer is -12x -5y2/2 + C
How do you prove that sinθ plus cosθ2 plus sinθ-cosθ2 equals 2?
Sinθ plus cosθ2 plus sinθ-cosθ2 equals 2 does not equal 2. It equals 2sinθ. The cosθ2 terms cancel out and you are left with sinθ + sinθ which is 2sinθ.
What are the X and Y intercept forms for 2X plus 3Y equals A?
Set y = 0: So 2x =a ie x = a/2. So the x-intercept is (a/2, 0)
Set x = 0: So 3y = a ie y = a/3. So the y intercept is (0, a/3)
8x to the 6th plus 24x to the 5th plus 16x to the 4th?
8x6 + 24x5 + 16x4 = 8x4 ( x2 + 3x + 2) = 8x4 (x + 2) ( x + 1)
3/10. If you multiply by 10 yo divide by 10 to maintain the consistency.
What is the answer to x plus 3 equals 10?
X+3=10
X= 7
But I'm sure I understood your question incorrectly, since I don't expect someone to ask such an easy question. (No offense!)
What is the nature of the solutions of the equation x2 plus 11 equals 0?
The two solutions are the conjugate complex numbers, +i*sqrt(11) and -i*sqrt(11), where i is the imaginary square root of -1.
How do you make a fraction into the simplest form?
Any fraction can be written in many different ways.
For example, 1/2 of a cake is the same amount of cake as 4/8ths, or 8/16ths. 3/4 of 100 dollars is the same as 75/100ths of 100 dollars.
We say that 1/2, and 4/8 and 8/16 are equivalent fractions. 3/4 and 75/100 are equivalent too.
If you take any fraction and multiply both the top number and the bottom number by the same amount, the fraction means the same as before. It doesn't matter what that amount is, as long as it's the same.
This also means that you can divide the top and bottom numbers by the same amount too. 12/18 = 6/9. We divided the top and bottom numbers by 2. But we can divide by 3 as well. 6/9 = 2/3. This is the simplest form we can write the fraction in.
So to turn a fraction into its simplest form, you go on dividing the top and bottom numbers by whatever whole number you can until you can't divide any more.
90/150 = 9/15 (dividing by 10)
9/15 = 3/5 (dividing by 3)
So 90/150 in its simplest form is 3/5
How would you factor x2-2x plus 3 when trying to find the zeros of a function?
That doesn't factor neatly. Applying the quadratic equation, we find two imaginary solutions: 1 plus or minus i times the square root of 2
x = 2.4142135623730951i
x = 0.4142135623730951i
where i is the square root of -1
The gradient of the line y equals 4 plus 3 is?
Zero, the line is parallel to the x-axis at a distance 4+3 = 7
Solve this equation using subtitution x plus 2y equals 7 and 2x plus y equals 8?
x + 2y = 7
So x = 7 - 2y
Substitute this value for x in the second equation
which then is: 2(7 - 2y) + y = 8
Simplify: 14 - 4y + y = 8
-3y = -6
y = 2
Put this value of y back into the first equation:
x + 2*2 = 7
ie x + 4 = 7
x = 3
x + 7 + y82, and without more information it is not possible to give a better answer than that.
What does 14x-2y plus 7x-3y plus -3x equal to?
(14x-2y)+(7x-3y)+(-3x) = 14x-2y+7x-3y-3x
=(14+7-3)x-(2+3)y
=18x-5y
