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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
Answer this equations x plus 42y equals 4?
Solving equations in two unknowns requires two independent equations. Since you have only one equation there is no solution.
What is the answer to 9x squared equal to 10x plus 2?
It depends on what precisely the question is.
One possible answer is that the quadratic expression has a value of 2 when x = 0.
Solve the following equation for A 2adivided by 3 equals 8 plus 4a?
2a/3=8+4a2a=3(8+4a)
2a=24+12a
-10a=24
a=-24/10
a=-12/5
What is the work for 2 sin squared x equals 2 plus cos x?
2sin2 x
2(1 - cos2 x) = 2 + cos x
2 - 2cos2 x = 2 + cos x
- 2cos2 x - cos x = 0
cos x(-cos x - 1) = 0
cos x = 0 or -cos x - 1 = 0
cos x = -1
Since the cosine has a period of 2pi, in the interval 0 ≤ x ≤ 2pi
when cos x = 0, x = pi/2 and x = 3pi/2, and
when cos x = -1, x = pi.
All values of x that satisfy the given equation are:
x = pi/2 + 2npi, x = pi +2npi, and x = 3pi/2+ 2npi where n is any integer.
3x + 15 = 60
3x = 60 - 15
3x = 45
x = 45/3
Therefore, x = 15.
If x-y equals -3 and 2x plus y equals 12 then what does x and y equal?
x - y = -3
2x + y = 12 (add both equations)
3x = 9 (divide by 3 to both sides)
x = 3
x - y = -3 (replace x with 3)
3 - y = -3 subtract 3 to both sides)
-y = -6 (multiply by -1 to both sides)
y = 6
The solution of the system of the equations is (3, 6).
What is the answer to 5x plus 7 plus 4x equals 79?
5x + 7 + 4x = 79
9x + 7 = 79 (Gather the x's)
9x = 72 (Take away 7 from each side)
x = 8 (Divide each side by 9 to get the answer)
How do you solve this linear system 8x-4y equals 3 and 5x plus 2y equals 3?
8x = 4y + 3 x = 0,5y + 3/8
We fill this out in the second formula:
5(0,5y + 3/8) +2y = 3
4,5y = 3 - 15/8
y = 2/3 - 15/36 = 24/36 - 15/36 = 9/36 = 1/4
X = 1/8 *1+3 = 1/2
What is the answer to 35 plus 2k equals 9k?
35 + 2k = 9k
subtract 2k from each side
35 + 2k - 2k = 9k - 2k
35 = 7k
divide both sides integers by 7
35/7 = (7/7)k
5 = k
check in original equation
35 + 2(5) = 9(5)
35 + 10 = 45
45 = 45
checks out
What is the y-intercept of y equals 2x plus 10?
The y-intercept means... When does the line cross through the y-axis?
This happens when the x-value is zero... so simply just plug in zero for "x"
y = 2 * (0) + 10
y = 10
y-intercept is equal to 10
For the x-intercept just make the y-value equal to zero.
This is kind of non-specific, but I'm assuming you're looking for the values of x that will make the following true:
x3-2x2-8x = 0
To find these values of x, you must factor the polynomial expression to the left of the equal sign.
x3-2x2-8x = x(x2-2x-8) = x(x-4)(x+2) = 0
By the zero identity, setting each individual factor equal to zero will yield a valid solution to the original equation:
x = 0
x-4 = 0, x = 4
x+2 = 0, x = -2
So the following values of x will solve the equation:
x = 0
x = 4
x = -2
What is x'2 plus 4.5x equals 0?
Simple factoring.
X^2 + 4.5X = 0
factor out X
X(X + 4.5) = 0
X = 0
X = -4.5
graph on TI-84 agrees
What does x in the problem x cubed equals 343?
There are three solutions to that equation.
The only one you care about is: x = 7 .
What is the slop of the function -6x-2y equal 8?
-6x-2y = 8
-2y = 6x+8
y = -3x-4
Therefore the slope is -3 and the y intercept is -4
What procedure would you use to solve the equation 3x plus 3 equals 24 for x?
3x+3 = 24
Subtract 3 from both sides:
3x = 21
Divide both sides by 3 to find the value of x:
x = 7
Many things.
Some of these are:
- movement of its point of suspension,
- precession caused by the earth's rotation,
- air resistance, wind,
- very massive objects brought nearby,
- thermal expansion or contraction,
- humidity or other factors altering the means of suspension.
What is the slope and y-intercept to 5x-8y plus 64 equals 0?
To determine slope and Y intercept, solve the equation for y...
5x - 8y + 64 = 0
-8y = -5x - 64
8y = 5x + 64
y = 5/8x + 8
... now that you have the equation in the form y = mx + b, you can easily see that the slope is 5/8, and the Y intercept is 8.
What is X plus 7y equals 33 and 3x 2y equals 7?
x + 7y = 33 (Eqn 1)
3x + 2y = 7 (Eqn 2)
Multiply Eqn 1 by 3, now the equations are
3x + 21y = 99 (Eqn 3)
3x + 2y = 7 (Eqn 2)
Subtract Eqn 2 from Eqn 4 and the result of subtraction is
19y = 92
Hence y = 92/19
Now substitute the value of y in Eqn 1
x + (7) x (92/19) = 33
x = 33 - 644/19 = -(17/19)
