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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
If y is proportional to the square of x fully explain what happens when x is doubled?
Example with numbers:
Y = X2
Y = (2)2
Y = 4
====
So if Y is ( directly ) proportional to X2 when X is doubled Y is increased four times.
What is a method to solve a system of equations by substituting for the variables?
Given the two equaitons
Ax + By = C
Dx + Ey = F
The values for x and y that satisfy both equations is
x = CE -BF y = CD-AF
AE -BD , -AE+BD
A full explanation can be found here
http://math-journal.blogspot.com/p/algebra.html
How do you make the area of a shape to one decimal?
One decimal = 435.6 square feet, so you could have a circle with radius 11.775 ft, approx.
How do you solve 14y minus 6y equals 48 Alegebra 1?
14y minus 6y means "14 times a number, minus 6 times the same number". If you have 14 things and you take away 6 things, you are left with 8 things.
So, 8 times a number equals 48.
8 times what number gets you 48?
Since you are already in Algebra I, you know 8 times 6 gets you 48, so the number (y) is 6.
The formal Algebra I approach is to combine like terms, then divide.
14y - 6y = 48 (Subtract 6y from 14 y. (14y - 6y = 8y, and the y does not go away)
8y = 48 (Now divide both sides by 8 to get the y all by itself)
8/8y = 48/8 (8/8 is 1, and 48/8 is 6, so 1y = 6. You can lose the 1 because one thing is the thing itself.)
y = 6
Does that help? There are many ways to solve this problem, but Algebra I is teaching the proper steps for solving one, two and three step equations. Stick with it.
How do you determine if the graph of a function is concave down without looking at the graph?
If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.
What responsibilities did the women have on the wagon train?
The last arrival of emigrants came down the street with about twenty waggons.... What is remarkable, this body, as well as a very large portion of the emigrants were from the extreme western states - N. England send but a small proportion, but they are better furnished than the rest. ...one remarkably pretty little girl was seated on horseback, holding a parasol over her head to keep off the rain ... as I passed their waggons I observed three old men, with their whips in their hands, discussing some point of theology - which is hardly the disposition of the mess of the emigrants."
How do you type the infinity sign?
Switch on the 'Num lock' and press and HOLD the 'Alt' key,
now type 236 on the num-lock keypad.
Release 'Alt' key = Infinity symbol '∞'
4y20 equals 500 and x plus y equals 500?
4y20 = 500 => y20 = 25 => y = 20√25 = 1.1746 approx
Then x = 500 - y = 489.8254 (approx).
How do you solve the inequality of 4X plus 5 is greater then or equle to 11?
4x + 5 >= 11.... subtract 5 from both sides and divide by 4.
How do you change x plus y-5 equals 0 into a y equals mx plus b format?
x + (y - 5) = 0
x + y - 5 = 0
Subtract x from each side:
y - 5 = -x
Add 5 to each side:
y = -x + 5
m = -1
b = 5
What is -0.5x2 plus 2x plus 10?
Doesn't factor evenly, use quadratic
-.5xx+2x+10
-.5(xx-4x-20)
No factors of -20 add up to -4
Y varies directly as x find the constant of variation k if y equals negative 5 x?
Y=kx+m
Y=-5x+m
K=-5
The point you desire, is (1, 0).
The explanation follows:
b0 = 1, for all b; thus,
logb(1) = 0, for all b.
On the other hand, logb(0) = -∞,
which explains the vertical asymptote at the y-axis.
Where is the x -acsies on a graph?
The x axis is the one that lies horizontal. It can be denoted by the equation y=0. A good way to remember this is to think "x is a cross" as in "x is across."
What is the smallest two-digit number that can be written as the sum of two different cubic numbers?
The difference between cubic numbers gets larger as you go up the scale, so we know that we are looking for the small end of the range. Let's take a small set of perfect cubes and play with it:
- 125, -64, -27, -8, -1, 0, 1, 8, 27, 64, 125
27 + -8 would give us 0 would give us 16. And that would be our best option. Note of course that -27 + 8 would also fit the bill, giving us -16.
What is a polynomial function as a graph?
A polynomial function have a polynomial graph.
... That's not very helpful is it, but the most common formal definition of a function is that it is its graph.
So, I can only describe it. A polynomial graph consists of "bumps", formally called local maxima and minima, and "inflection points", where concavity changes. What's more? They numbers and shape varies a lot for different polynomials. Usually, the poly with higher power will have more "bumps" and inflection points, but it is not a absolute trend.
The best way to analyze the graph of a polynomial is through Calculus.
What is the pH of a solution with H plus equals 2.3 10 12?
2.3 X 10 -12 ? ( signs are not showing up on this site lately )
- log(2.3 X 10 -12 )
= 11.6 pH
=============not much H +
What are the zeros of the graph of the function y equals 2x plus 5x-12?
y = 2x + 5x - 12 = 7x - 12
So the zero is 12/7 = 1.7143 (approx)
I think you mean to solve:
(-2 cos23x) - (3 sin 3x) = 0
cos2 x + sin2 x = 1
⇒ cos2x = 1 - sin2 x
⇒ -2 cos2 3x - 3 sin 3x = -2(1 - sin2 3x) - 3 sin 3x = 0
⇒ 2 sin2 3x - 3 sin 3x - 2 = 0
⇒ (2 sin 3x + 1)(sin 3x - 2) = 0
⇒ sin 3x = -1/2 or 2
sin 3x = 2 is impossible as the range of sine is -1 ≤ sine ≤ 1
Thus:
sin 3x = -1/2
⇒ 3x = 2nπ - π/6 or 2nπ - 5π/6
⇒ x = 2/3nπ -π/18 or 2/3nπ -5π/18
