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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 do i solve x x-2 equals 7x?
assuming the gap before x-2 is a +, then x+x-2=7x, so 2x-2=7x, so 5x=-2, so x=-.4
If a equals 2.34 and y equals 8.92 what does axy equal?
There is no definite answer for what axy will equal to if we are not given x's value. If we were given the value of axy we could solve for x if only two variables are known, or if x were know we could solve for axy. We do know that axy will equal to 20.8728 multiplied by x's value.
(2.34)(8.92)x = axy
20.8728x = axy
You can try to factor the LHS to get:
(x - 3) (x - 1) = 0
we then know the two solutions are:
x - 3 = 0
or
x - 1 = 0
so, x = 3, 1.
What is the highest common multiple of 21 and 84?
The highest common multiple of 21 and 84 is infinity.
The least common multiple, on the other hand, is 84, while the greatest common divisor is 21.
x2 + 2x + 4 can be expressed in the form ax2 + bx + c, where a=1, b=2, c=4.
So you will be looking for two numbers that add to 2 [b], and multiply to 4 [ac]. Clearly, there are no two real numbers that can do this. Therefore the expression above cannot be factorised.
Why does the time period of pendulum does not depend on the mass of the bob?
T=2pi sqrt(m/k) here,
m=mass of the body which is oscillating
k=force or spring constant
k=m.w2 after substituting value of k in the first equation we get,
T=2pi/w
and hence we can see in any case it does not depend on the mass of the body as it cancels down when we put the value of k in the equation.
The logarithm of 1 to the base 1 is indeterminate. The logarithm of a number x to the base a is a number y, such that ay = x. The most common base a is 10, or the natural base a is e (2.718281828...). It is invalid to think of logarithms base 1, because 1 to the power of anything is still 1.
The addition method for x plus y equals 8 and -x plus 2y equals 7?
Add the two equations: x + y - x + 2y = 8 + 7 ie 3y = 15 so y = 5 making x = 3.
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
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.
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.
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.
How do you find zeros on each function?
Set the equation equal to zero. For example, take the function
F(x) = x^2 - 4
Find the zeroes by
x^2 - 4 = 0
x^2 = 4
sqrt(x^2) = sqrt(4)
x = +/- 2
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
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.
