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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 point inside a production possibilities frontier is?
A point inside the PPF means that resources are not being used efficiently. One or more resources (Land, labor, or capital) is being waisted or not used to its potential. More of both goods could be produced than are currently being produced.
What number is the solution to the equation 22 equals 7x plus 1?
22=7x+1 (take 1 of each side of the equals)
21=7x (divide each side by seven)
3=x (BAM! answer)
What is this type of function called y equals mx to the power of -b?
Assuming that b > 0, it is an inverse power function or an inverse exponential function.
-7 (negative 7) transpose the 9x then transpose the 6. divide both sides by 3x and your answer will be -7 =]
A = b.
15x2-24x plus 9 divided by 3x-3?
15x2 - 24x + 9 = 3*(5x2 - 8x + 3) = 3*(5x2 - 5x - 3x + 3)= 3*[5x(x - 1) -3*(x - 1)]
= 3*(5x - 3)*(x - 1) . . . . . (A)
3x - 3 = 3*(x - 1) . . . . . . . (B)
So, (A) and (B) have 3*(x - 1) as common factors and cancelling these gives
(A)/(B) = 5x - 3
Log zero is not defined, and if it were defined, it would be more likely to be minus infinity than infinity.
Show that [(2x-3)/(x-3)] - [(2x-1)/(2x+1)] = (2x^2+3x-6)/(x-3)(2x+1)
First, you want to get a common denominator. The easiest way to find a common denominator for these two terms is to multiply the denominators together.
(x-3)*(2x-1) You do not need to multiply them out because it is not done so in the answer.
So, in the first term the denominator was multiplied by 2x+1. Since the denominator was multiplied by 2x+1, the numerator must also be multiplied by 2x+1 to ensure that the value has not changed. Its much like multiplying by 1/1, but instead its (2x+1)/(2x+1)
The numerator will be (2x-3)*(2x+1). Multiplying these together will result in 4x2-6x+2x-3. Adding like terms give us 4x2-4x-3
So the first term becomes (4x2-4x-3)/(x-3)(2x+1)
For the second term we multiply the numerator by x-3 instead
(x-3)*(2x-1) The result is (2x2-6x-x+3). Add like terms to give (2x2-7x+3)
The second term becomes (2x2-7x+3)/(x-3)(2x+1)
Since the two terms have the same denominator we only have to subtract the numerators from each other to find the answer.
(4x2-4x-3)-(2x2-7x+3) Now subtract like terms from each other, but pay attention to the sign of each term.
4x2 - 2x2 = 2x2
(-4x) - (-7x) = 3x
(-3) - 3 = (-6)
Combine those terms and the result is 2x2+3x-6
This the numerator, so bringing back the denominator will give us the final answer.
(2x2+3x-6)/(x-3)(2x+1)
How do you solve 2 t squared - 98 equals 0?
2t^2 - 98 = 0
add 98 to each side
2t^2 = 98
divide both sides by 2
t^2 = 49
take square root of both sides
t = +/- sqrt(49)
t = +/- 7
you should see that this checks
What is the name of a vertical line on a graph?
The name of a vertical line is simply named by the number on the x axis it is on.
What are the values of x and y in the equation 3x plus 2y equals 5x plus 2y equals 7 show work?
If: 3x+2y = 5x+2y = 7 which is the same as 7 = 7 = 7
Then: 3x+2y = 7 and 5x+2y = 7
Subtracting equations: x = 0
Therefore by substitution: x = 0 and y = 3.5
What is the answer for 5x plus 7 equals -4x plus 25?
The "answer" is the number that 'x' must be in order to make the equation
a true statement.
Here's how to find it:
5x + 7 = -4x + 25
Add 4x to each side of the equation:
9x + 7 = 25
Subtract 7 from each side:
9x = 18
Divide each side by 9:
x = 2
x2/242-y2/62=1
The right column changes by the same amount for each change of one in x.
So Ux is linear. That is, Ux = a + bx
That "same amount" is 3 so b = 3. That gives Ux = a + 3x
There are now two ways to find the value of a.
You can either take any row of the function table and solve the equation. Suppose you take row 3 - which is 4 and 8.
8 = a + 3*4 = a + 12
and that gives a = -4
OR
Take the sequence back two steps to what it would have been when x = 0. The sequence increases by 3 as you move up the xs. So it decreases by 3 for each step back. Then starting from x = 2 and y = 2 and moving back one step gives x = 1 and y = -1. A second step gives x = 0 and y = -4 (as before).
So, the final answer is Ux = -4 + 3x
How do you solve 2 sin squared x is equal to sin x?
There will be 4 possible solutions if all you are looking for is the angles, so you will need to find out which quadrant your angle is in.
2sin²x = sin x **Subtract sin x from both sides.
2sin²x - sin x = 0 **Then factor out sin x.
sin x(2sin x - 1) = 0 **Set each equal to zero. (AB=0 is the same as A=0 OR B=0).
sin x = 0 or 2sin x - 1 = 0 to 2sin x = 1 to sin x = 1/2
At this point all that is left to do is find out where sin x = 0 or 1/2, which is 0, 180 for sin x = 0 or 30, 150 for sin x = 1/2.
What does the gallon capacity on trash cans mean?
The capacity in gallons of water to completely fill the container.
Solve quadratic equation by using formulae?
with the quadratic equation being ax2+bx+c and the formula being
x=[-b±(b2-4ac)1/2]/2a just plug in the values for a b and c
the quantity raised to the one half denotes a square root of that quantity.
16+2x can not be simplified any further.
16+2x would normally be written as 2x+16 to keep the degrees of the terms in order from highest to lowest.
How do you solve X2 plus 24X plus 144 equals 0?
X^2 + 24x + 144 = 0. Dontcha just luv algebra?
You are looking for a polynomial: (X+somenumber) * (X+somenumber) = X^2 + 24x + 144.
Then just solve for (X+somenumber) * (X+somenumber) = 0.
The trick is to find the pair of factors of 144 that add up to 24.
These are the pairs of factors of 144:
1 x 144
2 x 72
3 x 48
4 x 36
6 x 24
8 x 18
12 x 12
You want the pair of factors that add up to 24:
1 + 144 = more than 144 and is too large
2 + 72 = more than 72 and is too large
3 + 48 = more than 48 and is too large
4 + 36 = more than 36 and is too large
6 + 24 = 30
8 + 18 = 26
12 + 12 = 24!
so,
(X +12) * (x + 12) = X^2 + 24 +144 = 0
So either (X +12) or the other (X +12) is going to be zero because you can only get zero from multiplying something by 0.
If X+12 =0, then put -12 on both sides of the equation:
X+12 -12 = 0 -12
x + 12-12 = -12
x + 0 = -12
x = -12.
Normally you would then solve for the other (X+12) = 0, but that's the same thing as what we just did. So this time, there is only one answer x = -12.
