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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
Find the radius of x2 plus y2-2x-18y equals -78?
x2 + y2 - 2x - 18y = -78
x2 - 2x + 1 + y2 - 18y + 81 = 81 + 1 - 78
(x - 1)2 + (y - 9)2 = 4
(x - 1)2 + (y - 9)2 = 22
So the radius of the circle is 2, and it's center is located at the point (1, 9).
How do you solve this equation -3x plus y equals 1 5x plus 2y equals 4?
If you mean:
-3x + y = 1
5x + 2y = 4
You must replace one letter, for example y, so it gives you an equation only using x.
If you bring everything to one side on the bottom equatin, it would read:
y = (4 - 5x)/2
Now use this equation to replace the y on the first equation:
-3x + (4-5x)/2 = 1 and solve for x
Find a common denominator, which is 2...
(-6x)/2 + (4-5x)/2 = 1
Combine...
(-6x + 4 - 5x) / 2 =1 which is:
(-11x + 4) / 2 = 1 Bring the 2 to the other side...
-11x + 4 = 2 Bring the 4 to the other side...
-11x = -2 Bring the -11 to the other side...
x = -2 / -11 or 2/11
Now plug in this number for x to solve for y:
5x + 2y = 4
5(2/11) + 2y = 4
10/11 + 2y = 4
2y = 4 - (10/11) common denominator is 11 so,
2y = 44/11 - 10/11
2y = 34/11 divide by 2
y = 34/11 * 1/2
y = 34/22 simplify
y = 17/11
x = 2/11 y = 17/11
If you replace both letters in the top equations with these answers, both sides should equal each other.
-4x + 3y + 3z = -209
-6x - y - 8z = -209
-9x + 4y - 7z = -418
Make a simple equation from elimination.
-4x + 3y + 3z = -6x- y - 8z
2x + 4y + 11z = 0
-4x + 3y + 3z = -209
4x + 8y + 22z = 0
11y + 25z = -209
Make another simple equation.
-36x - 6y - 48z = -1254
-36x + 16y - 28z = -1672
-22y - 20z = 418
Solve for "z" with the 2 simple equations and then subsitute in simple equations for the solution of "y".
22y + 50z = -418
-22y - 20z = 418
30z = 0
z = 0
11y + 25(0) = -209
y = -19
Subsitute "y" and "z" and solve for "x".
-6x + 19 = -209
-6x = -228
x = 38
(38, -19, 0).
No. x2+5x is a polynomial, an algebraic expression or a formula, but it is not a function. It could be used to help define a function.
{(x,y) | y = x2 + 5x , x any real number} is a function
What has the same answer as 17 plus x equal?
x + 17, perhaps.
x + 17, perhaps.
x + 17, perhaps.
x + 17, perhaps.
How do you solve 6x plus 7 equals -14y?
It is not possible to solve a single linear equation in two variables.
If in 360 seconds I travel 157 feet how many feet would I travel per second?
157/360 ft/sec = 0.436 ft/sec
Tell whether the fraction is in the simplest form 3 Fourths 6 eighths?
You have to figure out all the multiples of the numerator and denominator. So for 6/8 or six eights, we need to figure all the numbers that go evenly into them, excluding 1 and the number itself. 6 has two: 2 and 3. 8 has only one: 2, since 2x2x2 is 8. We can eliminate one of the twos in each of the numbers. This leaves us with 3 and 2x2 which is 4. So it becomes 3/4.
