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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
A pendulum set in motion eventually stops because?
1). Air resistance
2). Friction in the pivot.
These two effects rob energy from the pendulum. Without air resistance or
friction in the pivot, a pendulum, once set in motion, would not stop.
2x + 5y = 11
4x - 3y = 9
Since this system of equations, determine a 2 x 2 matrix, it can have an inverse.
A = [a b], [c d] (imagine these as two rows of the matrix A)
A = [2 5],[4 -3]
Since the determinant of that matrix is different from zero (det A = [ad - bc] = [(2)(-3) - (5)(4)] = (-6 - 20) = -26), then it has an inverse (let call it A-1)
A-1 = (1/det A)([d -b], [-c a]) = [d/det A -b/det A], [-c/det A a/det A]
A-1 = [-3/-26 -5/-26], [-4/-26 2/-26] = [3/26 5/26], [4/26 -2/26]
By theorem, x = A-1b is the unique solution of Ax = b, where
x = [x1 x2 x3] , and b = [11 9] (imagine them as columns)
So we have:
x = A-1b = [3/26 5/26], [4/26 -2/26] x [11 9] = [(3/26 x 11 + 5/26 x 9) (4/26 x 11 + -2/26 x 9)] or
[x1 x2] = [(33/26 + 45/26) (44/26 - 18/26)] (imagine them as columns)
[x1 x2] = [(33 + 45)/26 (44 - 18)/26]
[x1 x2] = [78/26 26/26]
[x1 x2] = [3 1]
Thus, x1= 3 or x = 3, and x2 = 1 or y = 1
Check:
What is the inverse of mult ipacation?
The inverse of multiplication is division, such that:
8 x 9 = 72
72 / 9 = 8
72 / 8 = 9.
Yellow x with 2 is what hazard?
If an NFPA 704 Fire Diamond has a 2 in the yellow section it means the reactivity of the material is such that it can have violent chemical change at high temperature or pressure, it can react violently with water, or it can form explosive mixtures with water.
True
the average speed is 50 because 60+ 40= 100 divided by 2 = 50 and remember add them up and divide by the number of numbers you have
2X - 4 = - 10
add 4 to each side
2X - 4 + 4 = - 10 + 4
2X = - 6
divide each side by 2
X = - 3
check in original equation
2(-3) - 4 = - 10
- 6 - 4 = - 10
- 10 = - 10
checks
6by10 into x equals 1 then the percent by which x is greater than 6by10?
Zero percent.
(They're equal.)
What is the derivative of 3 to the power of 2 multiplied by f of x?
I think you mean;
f(x) = 3x^2
d/dx(3x^2)
= 6x
How can you find y equals x plus 4 graph?
Make a t-chart and choose your x values. There must me a negative, zero, and positive. Only three numbers. I like to choose -1, 0, 1. They are really easy to solve.
Then, plug it in!
y=-1+4; y=3
y=0+4; y=4
y=1+4; y=5
Your coordinate pairs would be: (-1, 3), (0, 4), (1, 5)
Then make your graph. The x values go on the x-axis (the horizontal line) and the y values go on the y-axis (the vertical line). So the first coordinate pair would go 1 to the left and three up from that point. Make a dot where the value is.
Connect your dots with a line. Tada! You're done!
If y equals one half x and x equals -14 find y?
common it's very easy !!
Y = 1/2 X and X = -14
and so :
Y = 1/2 * -14
Y = -7
When 9x-13 equals -31 what is the value of x-8?
9x - 13 = -31
Add 13 to each side:
9x = -18
Divide each side by 9:
x = -2
Subtract 8 from each side:
x - 8 = -10
If 2 plus 2 equals x and x2 equals y and y-x equals a and a plus y equals b what is b?
in order to solve this problem you have to solve for x first wich you are given the data to pre forme so x=4 and x.2=8 and 8=y and y-4=4=a=x so a+8=12 and 12=b
When solving a linear inequality do you always need to solve for y?
not always,sometimes you have to solve for x
Is x equals 3 y equals 6 a solution to y3x-3 and 3x-y3?
Neither y3x-3 nor 3x-y3 are equations, and so neither of them can have a solution.
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What is the integral of cos raised to 2 times x?
∫cos2(x).dx
Use the identity cos2(x) = (1/2)(1+cos(2x))
∫(1/2)(1+cos(2x))dx
Pull out constant:
(1/2)∫(1+cos(2x))dx
Integrate:
(1/2)(x + sin(2x)/2) + C
Simplify:
x/2 + sin(2x)/4 + C
The identity sin(2x) = 2sin(x)cos(x) can be used to rewrite it as
(x + sin(x)cos(x))/2 + C
