0
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
Here are possibilities of what you mean:
a: (3-2)(x-2)=10
Solution:
(3-2)(x-2)=10
1(x-2)=10
x-2=10/1
x=10+2=12
b: 3-2(x-2)=10
Solution:
3-2(x-2)=10
3-10=2(x-2)
-7=2x-4
-3=2x
x=-3/2=-1.5
How do you calculate y equals 0.5x?
- y=0.5x is an equation that cannot be solved unless you have a known value for either y or x.
What is the derivative of 5x-1?
The idea is to use the addition/subtraction property. In other words, take the derivative of 5x, take the derivative of 1, and subtract the results.
Do all logarithms require a base of 10?
No. The so-called "natural" logarithms have a base of ' e ', and you can find
the log of any positive number to any base you like.
How do you solve this equation - 9 - 2x plus x equals - 13?
-9-2x+x = -13
-2x+x = -13+9
-x = -4
x = 4
What is the solution to x plus y equals 5 and 2x plus y equals 6?
Given:
x + y = 5
2x + y = 6
We can subtract the second equation from the first to get:
-x = -1
x = 1.
From there, substituting back in to the first equation yields:
1 + y = 5
y = 4.
The solution is (1, 4).
How do you graph x plus three y equals nine?
x+3y=9
First I would solve for y
3y=-x+9
Now divide by 3
y=-x/3 + 3
This is what is called slope - intercept form.
The y-intercept is 3. So, you have your first point (0,3)
now to make this easy - choose any number that is a multiple of 3 (other than 0). How about 3.
Plug x=3 into the equation. y=-3/3+3 => y=-1+3 => y=2
So (3,2) is another point on this equation.
Now that you have 2 points you can draw the graph since it is linear. Just draw a straight line from (0,3) to (3,2) and continue drawing to the right and to the left.
x^2+y^4=10x+7 @ (1,-2)
Rearrange to isolate y.
y=(-x^2+10x+7)^(1/4)
Take derivative.
y'=(1/4)*((-x^2+10x+7)^(-3/4))*(-2x+10)
y'=(-2x+10)/4*(-x^2+10x+7)^(3/4)
Sub in x=1.
y'=8/2*(16)^(3/4)
y'=2/8
y'=1/4
y'=m=slope=1/4
Sub m and (1,-2) into linear equation (tangent line).
m*(x-x1)=y-y2
(1/4)(x-1)=y+2
Isolate y.
Equation of tangent line: y=(1/4)x-(9/4).
The third question is unclear.
Why in the water formula q equals 7.48 x a x v WHERE v equals fps BUT q equals gpm?
We've never seen this formula before, but from what you've told us with your question,
we think we have it figured out, and we also think you made a tiny mistake.
It looks like this is a formula to calculate the amount of water that flows through
some kind of opening ... like maybe a big fire-hose ... if you know the area of the
opening and the speed of the flow.
'a' is the area of the opening, and 'v' is the speed of the flow .
The reason for the units that you're asking about is simple: If you're trying to find out
how much water you'll use up, the most convenient unit to use is: gallons for every
minute it keeps flowing. And if you have something stuck in the pipe or the hose that
measures the speed of the flow, it's going to be something like a little propeller that
spins as the water flows past it; the faster the water flows, the faster it spins, and
it measures the speed of the water, in something like miles-per-hour or feet-per-second.
Those are the most convenient units to use for volume of flow and speed of flow.
Now, you might not completely understand the next paragraph. It's just here to fill in
a gap for some other readers. But we do want to make sure that you do read the
last paragraph.
7.48 is the number of gallons in 1 cubic foot. So if [ 'a' x 'v' ] is the number of cubic feet
per minute, then the formula gives gallons per minute. So 'a' must be the cross-section
area in square-feet, and 'v' must be the flow-rate in feet per minute.
Finally, we think there's a tiny mistake in the question ... in order to make everything
work out right, we think 'v' must be 'feet per minute', not 'feet per second'.
What is the ordered pair of y equals 9x plus 4 and x equals 6?
x = 6
So y = 9*6 + 4 = 54 + 4 = 58
The ordered pair is (6, 58)
How do you solve this equation for x y equals x minus x squared?
It is not possible, in general to solve one equation in two unknown variables. The best that you can do is rewrite the eqaution so that one variable is defined in terms of the other.
xy = x - x2 = x(1 - x)
Assuming x not 0 (else the original equation degerates to 0 = 0)
we can divide both sides by x to give: y = 1 - x
What is the value of y when x equals 12?
The answer depends on the relationship between x and y. But since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
Why does the derivative of e to the power of lnx equal 1?
eln x is the same as x, since the exponential function and the natural logarithm are inverse functions.
Using the chain rule,
(eln x)' = eln x * (ln x)' = x* 1/x = 1
How do you differentiate exp exp exp x?
By using the chain rule. Since the derivative of exp(x) is exp(x), the derivative of exp(exp(exp(x))) is exp(exp(exp(x))) times the derivative of what is inside the parentheses, i.e., exp(exp(exp(x))) times derivate of exp(exp(x)). Continue using the chain rule once more, for this expression.
Determine the graph of the quadratic function y equals 8x2 plus 10x plus 3?
i am 12 and the answer is:
The vertex is: -5/8, 7/8
X intercepts are: -3/8 AND -12 7/8
* * *
I believe the following answers will be found correct:
y = 8x2 + 10x + 3 = (4x + 3)(2x + 1).
The x-intercepts occur at x = -¾ and x = -½.
The vertex occurs at x = -5/8, y = (-5/2 + 3)(-5/4 + 1) = (1/2)(-1/4) = -1/8;
that is, at (-5/8, -1/8).
The parabola is, of course, concave-upwards.
