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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
What is the period of y equals 2sinx?
The same as the period of y = sin x. This period is equal to (2 x pi).
How do you solve n square equals 6n by using the zero product property?
n2 = 6n
Rearranging so that all the n's are on the same side gives:
n2 - 6n = 0
Factorizing gives:
n(n - 6) = 0
The zero product property states that for two numbers to multiply together to gives zero, at least one must be 0.
Therefore either n=0 or n - 6 = 0
The two solutions are either n=0, or n=6
What is the binomial factor of x2 plus 2x minus 35?
X2 + 2X - 35
What two factors of - 35 add up to 2?
(X - 5)(X + 7)
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How might you set this up as a quadratic equation x times 'x plus 1' equals 306?
x(x+1)=306
x2+x=306
x2+x-306=0
(x+18)(x-17)
x= -18 or 17
16x to the power of 3 plus 4x to the power of 2 - 144 divided by 4x - 8?
4x - 8 = 0 when x = 2
Substitute this value of x in 16x3 + 4x2 - 144 to give
16*8 + 4*4 - 144 = 128 + 16 - 144 = 144 - 144 = 0
So, by the remainder theorem, (x-2) is a factor of 16x3 + 4x2 - 144
Also, the coeffs are all divisibl by 4 so 4 is also a factor
(x-2) is a factor, 4 is a factor so 4*(x-2) = (4x - 8) is a factor.
How do you graph 3x plus 5y equals 15?
you pick any # for x or y and work from there
ex. x=-5 now the question is 3(-5)+5y=15
multiply 3 and -5 to get -15
add 15 to both sides and the question is now 5y=30
divide both sides by 5 and the answer is y=6
X plus y equals 15 and 4x plus 3y equals 38?
rewrite first equation: x = 15 - y
substitute into second equation for x: 4(15 - y) + 3y = 38
distribute and simplify: 60 - y = 38
solve: y = 22
plug back into first equation: x = -7
-OR-
multiply first equation by -3: -3x - 3y = -45
add new equation to second equation: 1x + 0y = -7 or x = -7
plug back into first equation: y = 22
7y plus 8x plus 4 equals 20 plus 8x?
7y+ 8x + 4= 20 + 8x
- 8x - 8x
7y + 4 = 20
- 4 - 4
7y=16
/7 /7
y= 2.28
the /7 means divide by 7 :)
How do you solve x squared plus y squared equals 13 squared?
You need to get a value for x or y. As it is, the problem has no answer because there is more then one variable and only one equation.
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First, you need to understand clearly what "solve" means.
The "solution" to an equation normally means a set of numerical values for all
of the variables that appear in it, that makes the equation a true statement.
In order to find a solution, you generally need the same number of different
equations as there are variables in them. That is, if the equation has both
'x' and 'y' in it, then you need two different facts about their relationship in
order to figure out what numbers they are.
When you graph the equation in the question ... x2+ y2 = (13)2 ... the graph
is a circle, with its center at the origin, and with a radius of 13. Every point on
that circle has 'x' and 'y' coordinates, and every point is a solution to the equation.
So, just as it stands, there are an infinite number of "solutions".
You have included one dimension too many ! Someone can edit this if they want to.
Which is one of the factors of 2x squared plus 2x minus 60?
None of the items on the list that accompanies the question
satisfies that description.
2x2 + 2x - 60
= 2(x2 + x - 30), b = 1 and c = -30
= 2(x + 6)(x - 5) since 6*-5 = -30 and 6 + -5 = 1
How do you solve for x when its in a fraction?
example:
12X+8=6X+11
-6X -6X
6X+8=11
-8 -8
6X=3
now divide by 6
X=1/3
Which can be factored by multiplying five 2's, fourteen u's, two w's and seventeen y's.
Cloud the pendulum be changed to increase the period of the pendulum?
Yes. You can increase the period by moving the pendulum to a location where the gravitational force is weaker.
Alternatively, you can increase the effective length of the pendulum. The pendulum may be of fixed length, but you can still increase its effective length by adding mass to any point below its centre of gravity.
Yes. You can increase the period by moving the pendulum to a location where the gravitational force is weaker.
Alternatively, you can increase the effective length of the pendulum. The pendulum may be of fixed length, but you can still increase its effective length by adding mass to any point below its centre of gravity.
Yes. You can increase the period by moving the pendulum to a location where the gravitational force is weaker.
Alternatively, you can increase the effective length of the pendulum. The pendulum may be of fixed length, but you can still increase its effective length by adding mass to any point below its centre of gravity.
Yes. You can increase the period by moving the pendulum to a location where the gravitational force is weaker.
Alternatively, you can increase the effective length of the pendulum. The pendulum may be of fixed length, but you can still increase its effective length by adding mass to any point below its centre of gravity.
How do you report sec x equals 2 in class?
I cannot think of any reason why reporting this should be an issue - unless you are not comfortable because sec x sounds like sex. So here are two thoughts:
1. There is nothing wrong or embarrassing about the word.
2. But, if it still bothers you, you can always use the full name for the ratio: "secant x equals 2".
How do you convert an improper fraction to simplest form?
Find the GCF of the numerator and the denominator and divide them both by it. If the GCF is 1, the fraction is in its simplest form.
