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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
Use the quadratic formula to solve x2 - 6x plus 6 equals 0?
x=(6±sqrt(36-4*6))/2
x=3±(sqrt(12)/2)
x=3±sqrt(3)
What would be a word phrase for y divided by 5 plus 8?
(y/5) + 8 would be considered a binomial, as there is two terms. Just the same as 3x + 8. Those fall under binomials as well.
7
6 - 1 x 0 + 1
1. Multiplication first (PEMDAS), 1x0 = 0
2. Division, Addition, Subtraction.... 6-0+1= 7
How do you solve the direct variation y equals 5x plus 1?
y = 5x + 1 is nota direct variation.
y = 5x + 1 is nota direct variation.
y = 5x + 1 is nota direct variation.
y = 5x + 1 is nota direct variation.
What is the value of x if x minus 4 over 3 equals negative 7?
I'm assuming the equation looks something like this...
(x-4)/3= -7
If so then the answer is x= -17
How you get there:
(-17-4)= -21
-21/3= -7
What should be added to both sides of this equation to solve for the variable 37 equals -5 plus y?
32
(-4,-6)
What is the ordered pair that satisfies the equation 2x - 5y equals -1?
There are an infinite number of them.
Here are a few:
X . . . . Y
-3 . . . -1
-2 . . . -0.6
-1 . . . -0.2
0 . . . . +0.2
1 . . . . 0.6
2 . . . . 1
3 . . . . 1.4
5 . . . . 2.2
10 . . . 4.2
Advanced Calculus means different things in different context. But in general there are only two different meanings.
i) Multivariable and Vector Calculus, where instead of looking at just the boring and trivial real line, we move up to look into functions over real vector spaces Rn, where functions are not as nice, but much more practical in Physics, Engineering etc. (Space is R3, Space-Times os R4 with a weirdly defined dot product)
ii) "Real Math" Calculus, or more accurately, rigorous Calculus or Modern Calculus where we don't just take what the professor tells us to be the absolute truth, but rather using logic, axioms and tools such as mathematical induction, symbolic logic, and other type of mathematical proofs to come to our own conclusion of what is true (and more importantly why) and what is false. It is "advanced" as there is no direct reason of doing so in Engineering, Physic, or any field of Science. It is a way for people going into research in Mathematics to be prepared as it is how modern Math is really done.
I am in Advanced Calculus myself where it is the second meaning. Clearly, the second case involves discussions and theorem proving for the first case.
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Square root of 3 sinx plus cosx equals 0?
sqrt(3sin(x)=cos(x)=0 // Square both sides
3sin(x) + cos(x) = 0 // subtract cos(x) from both sides
3sin(x) = -cos(x) // rearrange
sin(x)/cos(x) = -1/3 //sin(x)/cos(x) = tan(x)
tan(x) = -1/3
x = tan^-1(-1/3) == -18,43484882 // tan^-1(inverse tan)
What is the answer to the equation x2 plus 6x plus 6 equals 0?
Using the quadratic equation formula:
x = -3 - the square root of 3 or x = -3 + the square root of 3
How do you solve the trigonomic equation sin2x equals negative cosx?
Sin(2x) = -cos(x)
But sin(2x) = 2 sin(x) cos(x)
Substitute it:
2 sin(x) cos(x) = -cos(x)
Divide each side by cos(x):
2 sin(x) = -1
sin(x) = -1/2
x = 210°
x = 330°
What lines are parallel y equals 2x plus 3?
If two lines have the same slope (ie. they rise or fall at the same angle) they are parallel.
With lines, the number before the x determines the slope. So as long as your line has a 2x term, and is written in the same form as y = 2x + 3, it will be parallel.
Therefore,
y = 2x + 7
y = 2x +5556
y = 2x - 3
y = 2x - 0.7561
... are all parallel lines to y = 2x + 3
Do you mean kilometer by kl, or millimeter by ml?
1 cm = 10 mm
1 m = 100 cm = 1,000 mm
1km = 1,000 m = 1,000,000 mm
164 mm = 164/1,000,000 = 0.000164 km or in scientific notation 1.64 x 10^-4 km
or if you mean liter and milliliter
1 L = 1,000 mL
164 mL = 164/1,000 =0.164 L
20 / 4 = 5. Therefore, you have four teams with five players in each team or five teams with four players in each of team.
How many diagonals does a shape with 4 sides have?
Two. If you start from any vertex, the lines to either of the two adjacent vertices will be one of the sides of the original shape. Only the line joining it to the opposite vertex will be a new line - a diagonal. Four vertices might therefore suggest four such lines but remember you're counting each line twice - once from each of its end. From any vertex, you can have only one diagonal - to the next but one vertex. Lines to the next vertex, on either
Is intake of oral isotretinoin a contraindication for sclerotherapy?
At least two weeks before any surgery, all medication that is not life supporting or of extreme importance, should be halted. This is most important in surgeries where blood clotting factor is important. Isotretinoin (Accutane) as well as other medication as contraceptive pills should be re-initiated only two weeks after surgery. It is important that you alert the surgeon and the anesthesiologist about any medication that you are on.
2 sin x plus 1 equals 3 cos x - 1?
2sin(x+1)=3cos(x-1)
Since there is only one variable in this equation, it cannot be implicitly differentiated.
If the speed limit is 65 on the turnpike how many feet would you go per second?
At 65 miles per hour, you are going 95 and a third feet per second.
What is 5x equals 8 equals 98-4x?
This one looks like No Solution. This is how I read it: 5x = 8 = 98-4x. If 5x = 8, then x = 8/5 = 1 3/5 (or 1.6), substitute into 98 - 4x --> 98 - 4(1.6) = 91.6, which does not equal 8, as it should from the equation.
What is the answer to y equals 5x plus 2?
There is no one answer. This is an equation for a straight line.
