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
What is the equation of x squared plus y squared equals 16 with a horizontal compression of a half?
In order to take your circle and squash it horizontally to 1/2 of its original width (2),
change the equation to
4x2 + y2 = 16
How would you gaph the equation y equals 2x minuis3?
You know that y = 2x - 3, so to draw the graph:
(a) You work out where this equation meets the horizontal axis of the graph and put a mark there.
(b) You also work out where it meets the vertical axis of the graph and put a mark there.
You then draw a straight line through the two points which carries on on either side.
For (a) the equation meets the horizontal axis when y = 0.
You know that y = 2x - 3, so put y = 0 into this equation.
0 = 2x - 3
-> 3 = 2x
-> x = 1.5
So the line meets the horizontal axis when x = 1.5
For (b) the equation meets the vertical axis when x = 0
So again put that into y = 2x - 3
So y = 2*0 - 3
-> y = -3
So the line meets the vertical axis when y = -3.
Draw a line through these two points (1.5,0) and (0,-3) and there you have your graph.
What does 14x-2y plus 7x-3y plus -3x equal to?
(14x-2y)+(7x-3y)+(-3x) = 14x-2y+7x-3y-3x
=(14+7-3)x-(2+3)y
=18x-5y
The gradient of the line y equals 4 plus 3 is?
Zero, the line is parallel to the x-axis at a distance 4+3 = 7
Solve this equation using subtitution x plus 2y equals 7 and 2x plus y equals 8?
x + 2y = 7
So x = 7 - 2y
Substitute this value for x in the second equation
which then is: 2(7 - 2y) + y = 8
Simplify: 14 - 4y + y = 8
-3y = -6
y = 2
Put this value of y back into the first equation:
x + 2*2 = 7
ie x + 4 = 7
x = 3
How would you factor x2-2x plus 3 when trying to find the zeros of a function?
That doesn't factor neatly. Applying the quadratic equation, we find two imaginary solutions: 1 plus or minus i times the square root of 2
x = 2.4142135623730951i
x = 0.4142135623730951i
where i is the square root of -1
How do you make a fraction into the simplest form?
Any fraction can be written in many different ways.
For example, 1/2 of a cake is the same amount of cake as 4/8ths, or 8/16ths. 3/4 of 100 dollars is the same as 75/100ths of 100 dollars.
We say that 1/2, and 4/8 and 8/16 are equivalent fractions. 3/4 and 75/100 are equivalent too.
If you take any fraction and multiply both the top number and the bottom number by the same amount, the fraction means the same as before. It doesn't matter what that amount is, as long as it's the same.
This also means that you can divide the top and bottom numbers by the same amount too. 12/18 = 6/9. We divided the top and bottom numbers by 2. But we can divide by 3 as well. 6/9 = 2/3. This is the simplest form we can write the fraction in.
So to turn a fraction into its simplest form, you go on dividing the top and bottom numbers by whatever whole number you can until you can't divide any more.
90/150 = 9/15 (dividing by 10)
9/15 = 3/5 (dividing by 3)
So 90/150 in its simplest form is 3/5
What is the square root or 5 x cubed 9 plus 5?
sqrt(5x^3+5) = sqrt(5)sqrt(x^3+1)=sqrt(5)sqrt(x+1)sqrt(x^2-x+1)
I have just factored the internal terms and still keeping the square roots. you might use these factors in solving or simplifying.
There is no equation (nor inequality) in the question. There is also no unknown variable. So there is nothing to solve.
The relevant formula here is Newton's Second Law, meaning that you need to divide the force by the mass. If you want to estimate the answer in your head - if that's what you mean by "guess" - you can round the mass to 700 or 800, and the force to 1000 or 1100.
How do you know which is the r and the s in factored equations?
The Answers community requires more information for this question. Please edit your question to include more context. There is no standardisation in the use of r and s in factored equations.
Belair X 6-12 is the first 6 x 12 zoom auto-exposure medium format camera.
What is 2 over 3 plus 5 over 7 plus 2 over 5?
figure it out ur self
********************
2/3 + 5/7 + 2/5
Make each of the denominators the same, by finding the LCD, i.e. 105.
To make 2/3 have a denominator of 105, multiply it by 35/35.
Similarly, multiply 5/7 by 15/15, and 2/5 by 21/21.
Therefore,
2/3*35/35 + 5/7*15/15 + 2/5*21/21
= 70/105 + 75/105 + 42/105
= (70 + 75 + 42)/105
= 187/105
How many gallons is in 1 cusec?
1 cusec, or 1 cubic foot per second, would be 7.48 gallons per second.
What is the answer to y - 4 equals 0?
so you first want to wright down the equation (it helps later in math) like this...
y - 4 = 0
then you want to isolate "y" so to cancel out the -4 you have to make it 0. however if you add 4 to the equation then you have to do the same on the other side of the equation such as...
y - 4 + 4 = 0 + 4
From there it is simple arithmetic...
Y = 4
and there is your answer
That completely depends on the value of 'x', and every different value of 'x'
produces a different answer.
We suspect, however, that whatever 'x' happens to be, exponentiating it
to the 542,497 power will introduce such inaccuracy that the answer will be
worthless.
This also leads us to strongly suspect that the question is whimsical, and has
no serious useful purpose.
1.
What are the equations of the two lines that define the maximum and minimum values for the graphs of y = sin x and y = cos x ?
(1 point)
- (1 pt) y = 1 and y = -1
- (0 pts) y = 0
- (0 pts) y = 2 and y = -2
- (0 pts) y = 1 and y = 0
