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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 many solutions 4x2 plus 8x plus 3 equals 0?
Start with the equation 4x2 + 8x + 3 = 0.
Invoke the quadratic equation:
x = [-b ± √(b2 - 4ac)]/2a, where a = 4, b = 8, and c = 3.
Plug in the values for a, b, and c and solve:
x = [-8 ± √(82 - 4*4*3)]/2*4,
x = [-8 ± √(64 - 48)]/8,
x = -1 ± √(16)/8,
x = -1 ± 1/2,
x = {-1/2, -3/2}.
What is x in the equation 12 to the 2x power equals 28?
(12)2x = 28
(2x) log(12) = log(28)
2x = log(28) / log(12) = 1.34098 (rounded)
x = 0.67049 (rounded)
The lines are perpendicular.
What is 2X plus 3 equals 6 plus 4X?
First, let's put that information into an equation. 2x + 3 = 6 + 4x
Subtract 2x from both sides.
3 = 6 + 2x
Subtract 6 from both sides.
-3 = 2x
Divide each side by 2.
x = -3/2
How do you solve 3y-4j equals 9?
Express one variable in terms of the other.
3Y - 4J = 9
3Y = 4J + 9
Y = (4J + 9)/3
------------------------
insert back into original equation
3(4J + 9)/3 = 9
you see the 3 factors cancel
4J + 9 = 9
4J = 0
J = 0
-------------you have J
3Y - 4(0) = 9
3Y = 9
Y = 3
----------------one set of solutions to this problem
A Greek queen of Mycenae, wife of Perseus and mother of seven sons: Perses, Alcaeus, Heleus, Mestor, Sthenelus, Electryon, and Cynurus as well as two daughters, Autochthe and Gorgophone.
Cameron Escalante is 19 years old (born September 19, 1997).
What is the differentiation of y with respect to x for x equals y exponent y?
x = yy differentiate both sides with respect to x
dx = (y * yy-1) dy
dy/dx = y * yy-1
dy/dx = yy = x
hence differentiate of y wrt x is x only
2x+4=8
2x=8-4 (you subtract 4 on both sides)
2x=4 (you then divide by 2 on both sides)
x=2
How do you derive the formula for the simple EOQ model?
The simple, or basic, economic order quantity (EOQ) is a special case of the continuous rate EOQ, which can be derived from the equation of total cost as follows.
Here is the equation for total cost (TC) as a function of run size (q):
TC(q) = K*D/q + P*D + q*H(r - D)/(2r), where:
K = Fixed cost per order
D = Annual Demand of product
q = run size
P = Purchasing cost per unit
H = Annual holding cost per unit
r = Production rate
K*D/q = Setup cost
P*D = Purchasing cost
H(r - D)/(2r) = holding cost.
To find the maximum value of q, you take the derivative, d[TC(q)]/dq, set it equal to zero, and solve for q.
First, take the derivative:
d[TC(q)]/dq = -K*D/q2 + H(r - D)/(2r).
Then, to maximize, set this equal to zero, and solve for q:
H(r - D)/(2r) - K*D/q2 = 0,
q2 = (2*r*K*D)/[H(r - D)],
q = √((2*r*K*D)/[H(r - D)]).
That's the formula for the continuous rate EOQ.
Basic EOQ is the special case of r >> D, which means r - D pretty much equals r, which allows you to cancel the r's in the above equation, giving you the formula:
q = √((2*K*D)/H).
This is the formula for basic EOQ.
What is x to the problem 68 plus 28x-28 equals 236?
68 + 28x - 28 = 236
28x + 68 - 68 -28 + 28 = 236 - 68 + 28
28x = 196
x = 7
Why do you need to find the inflection point on a graph?
To find the inflection points on a graph, you need to take the second derivative. Then, set that equal to zero to find the x value(s) of the inflection point(s).
