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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 you factor the expression x cubed minus 5x plus 4?
By inspection, the sum of the coefficients is 1 - 5 + 4 = 0Therefore x = 1 is a root. That is (x - 1) is a factor.
Then suppose the other factor is ax^2 + bx + c
SInce the coefficient of x^3 is 1, then a = 1 so that the second factor is x^2 + bx + c
Therefore (x - 1)*(x^2 + bx + c) = x^3 - 5x + 4
x^3 - x^2 + bx^2 - bx + cx - c = x^3 - 5x + 4
Comparing coefficient of x^2 gives -1 + b = 0 so that b = 1
Comparing coefficient of x gives -b + c = -5 so that c = b - 5 = -4
Comparing constant terms gives -c = 4 or c = -4 which confirms above calculations.
Thus, the second factor is (x^2 + x - 4) which does not have rational factors.
What is the least common multiple for 48 and 70?
Taking each number in turn we factor it into primes :- 1) 48 = 2 * 2 * 2 * 2 * 3 = 2 ^4 * 3 ^1 2) 70 = 2 * 5 * 7 = 2 ^1 * 5 ^1 * 7^1 For each prime factor we take the one with the largest number as the index, eg for the factor 2 , we have 4 and 1. The largest is 4 and so on for each prime factor that occurs and then multiply them together so we have all together 2 ^4 * 3 ^1 * 5^1 * 7^1 = 16*3*5*7 = 1680 which is the Lowest Common Multiple of 48 and 70.
There are many different kinds of analyses within mathematics.
How many centimeters are there in 300 millimetres?
There are 10 millimetres in one centimetre. Therefore, 300 millimetres is equal to 300 / 10 = 30 centimetres.
30 cm
What is is the speed of light?
The speed of light in a vacuum is 299,792,458ms-1 or 183,000 miles per second.
In scientific notation and rounding for ease of memorization, this is usually written as 3.00 x 108 m/s
It's value however is different for other media and can be calculated using the following formula:
v=c/n
That depends on what it's traveling through.
When it's traveling through nothing ... empty space, vacuum ... the speed
is 299,792,458 meters per second.
The speed is somewhat less in any material that light might travel through ...
air, water, glass, diamond, jello, etc. It's different in each material.
186,282.397 miles per second or 299,792,458 metres per second
The number to remember is: 300,000 kilometres per second
Find the point of intersection of y equals x2-6x plus 11 and the lines y equals x and y equals 2x?
y = x^2 - 6x + 11
x + y = 2x
x + y = 2x
x - x + y = 2x - x
y = x
Substitute x for y in the first equation:
y = x^2 - 6x + 11
x = x^2 - 6x + 11
x - x = x^2 - 6x - x + 1
0 = x^2 - 7x + 11
x = [-(-7) ± √[(-7)^2 - 4(1)(11)]]/(2)(1)
x = (7 ± √5)/2
x = (7 + √5)/2 or x = (7 - √5)/2
x ≈ 4.618 or x ≈ 2.382
Since y = x, then y ≈ 4.618 or y ≈ 2.382.
Thus, we can say that the solution of the system are (2.382, 2.382) and (4.618, 4.618).
How can you find out if your 86 prelude is a si or a dx?
The DX has the 1.8 liter dual carb engine whereas the Si has the 2.o litre fuel injected engine.
Placing a question mark at the end of a phrase does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered.
How do you find the sides of a right triangle?
Use Pythagorean theorem if you have a right triangle with legs a and b and hypotenuse c. a^2+b^2=c^2 a=sqrt(c^2-b^2) it is possible to find b and c in a similar way.
There cannot be a polygon with 6 diagonals.
A polygon with n vertices has n*(n-3)/2 diagonals.
If this is 6, then n*(n-3)/2 = 6
therefore n*(n-3) = 12
and so n^2 - 3n - 12 = 0
The only solutions to this equation are n = 1.5-sqrt(57)/2 or 1.5+sqrt(57)/2.
However, n, being the NUMBER of vertices cannot be an irrational number and so there is no solution.
3x - y equals 3 y equals 2x plus 2?
3x-y = 3y
3x = 4y
y = 0.75x
3x-0.75x = 2x+2
2.25x = 2x+2
0.25x = 2
x = 8
y = 6
What is the answer to y plus 3 equals negative 1 third x?
y + 3 = -(1/3)x
y = -(1/3)x -3
There is no question.
This is the equation of a line, with a slope of (-1/3) and a y-intercept of (-3).
Every point on the line has a set of (x,y) coordinates that make the equation
a true statement. There are an infinite number of them.
The trick here is to give those terms a common denominator so that the numerators can be added together. This can be done by multiplying each term by 1 (which does not change any values in the expression), but by expressing 1 in a unique way. Any value other than zero is equal to 1 when you divide it by itself, so in this case, you would multiply the first term by (x + 4)/(x + 4) and the second one by (x + 1) / (x + 1):
5 / (x + 1) + 3 / (x + 4)
= 5(x + 4) / (x + 1)(x + 4) + 3(x + 1)/(x + 1)(x + 4)
Now both terms have a common denominator, so you can add them together and simplify:
= [ 5(x + 5) + 3(x + 1) ] / (x + 1)(x + 4)
= (5x + 25 + 3x + 3) / (x + 1)(x + 4)
= (8x + 28) / (x + 1)(x + 4)
= 4(2x + 7) / (x + 1)(x + 4)
Why is 2 plus -2 equals 0 while 2 x -2 equals -4 Isn't multiplication just fast addition?
Well, now isn't 2 plus 2 equals 4
2 times 2 equals 4
2 times 2 equals 2 plus 2 equals 4
2 times -2 equals 2 plus -2 equals 0 WAIT 2 times -2 equals negative 4 according to mathematics. No teacher nor professor has been able to even do more than stutter explaining this.
3 times 3 equals 9
3 times -3 equals -9
So why is the digit 2 different?
How do you solve the equation x plus 6 equals x plus 8?
X + 6 = X + 8
This is a nice example of an equation that has no solution.
If you subtract 'X' from both sides of the "equation", it says: " 6 = 8 " .
This should immediately lead us to suspect that something here is not kosher, (that is to say, unorthodox).
