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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
5 over x plus 2 equals x over 3?
x={3, -5} This is if the equation is: 5/(x+2) = x/3.
But if you wanted: (5/x) + 2 = x/3, that is different, then x = 3±2*sqrt(6)
Which is a solution what system of equations 2X-y equals 6 and X-3y equals 8?
Method 1: Solving by Elimination
This can be done with either x or y. Either x or y is made equal in each equation and then subtracted. The set of equations looks like:
2x-y=6
x-3y=8
Step 1: X can be made equal if the bottom equation is multiplied by 2. The set of equations now looks like:
2x-y=6
2x-6y=16
Step 2: Subtract the second equation from the first and solve.
5y=-10
y=-2
Step 3: Now substitute -2 for y in either equation to solve x.
x-3y=8
x-3(-2)=8
x+6=8
x=2
The solution is (2, -2).
Method 2: Solving by Substitution
Solve for y in one of the equations, then substitute it into the other for x. This can be done with either x or y and in either equation.
Step 1: Solve for y in one equation
2x-y=6
2x=6+y
2x-6=y
y=2x-6
Step 2: Substitute y into the other equation and solve for x
x-3y=8
x-3(2x-6)=8
x-6x+18=8
-5x+18=8
-5x=-10
x=2
Step 3: Substitute x into the first equation
y=2x-6
y=2(2)-6
y=4-6
y=-2
The solution is (2,-2)
What is the difference between finding the dot product and using scalar multiplication?
They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
Is y equals 2x-2 and y equals 2 parallel?
No. The slope of the first is 2 - ie a change in the horizontal direction results in double the change in the vertical direction. The second line is horizontal (slope = 0).
-x + 8 = 3
Add x to each side:
8 = 3 + x
Subtract 3 from each side:
5 = x
Write an indirect proof for the following given 4y divided by6y 6 equals 20 prove y not equal to -1?
Assuming the given is written as:
4y/6y6=20
First off, this can be simplified down to:
2/3y5=20
Since this is an indirect proof, we must first assume the opposite of what you are trying to prove. You are trying to prove that y is not equal to -1.
Let y=-1
If this was done, then the following substitution would be made:
2/3(-1)5=20
2/3(-1)=20
2/(-3)=20
-2/3 =20
Clearly, -2/3 does not equal 20. Since y=-1 causes a mathematically impossible statement, then y cannot equal -1.
As far as formatting it for a formal indirect proof, I'm no help there. Different teachers like different formatting.
3x + 2x - 20 = 180
5x - 20 = 180
Add 20 to both sides: 5x = 200
Divide both sides by 5: x = 40
What is the solution set of the equation 2x-5 equals -15?
2x-5=15
+5 +5
2x=-10
--- ---
2x 2x
x=-5
I hope it helped. i showed the work the best i could.
---- that means divide
+ is add, obviously
and - means negative.
Your welcome.(:
What is y equals 3x minus 7 and y equals negative x plus 1?
y=3x-7
y=-x+1
We're looking for when their x=x and y=y, so set the problems equal to each other.
3x-7=-x+1
3x+x-7=x-x+1
4x-7=1
4x-7+7=1+7
4x=8
4x/4=8/4
x=2
Let x=2 and solve for y in one of the equations.
y=-(2)+1
y=-1
The solution is:(2,-1)
How can study more than 15 hours per day.?
Well it will be hard or is should say very hard but it is not impossible.
like straight after coming for school then sit straight for study and create a atmosphere that you are in a exam and study for 3 hours not even getting up for drinking water then take a break and think what you would achieve by studying this much during break and again study.
Hope it will be useful.
Basically you write a series of if statements, to cover the different cases. For example, in Java, something like this:
...
if (x = 0)
System.out.println("On y-axis")
else if (y = 0)
System.out.println("On x-axis")
else if (x > 0)
if (y > 0)
System.out.println("First quadrant")
else
...
First, the line would intercept the y-axis at positive 3. Then for every one you go left on the x, then you would go down one on the y.
If you mean: 32x-3x+1 then it can be simplified to 29x-1
How does graph of y equals x square-1 different from the graph of y equals x square plus 7?
They're exactly the same shape and size, but every point on the graph of the first one
is 8 units directly below the corresponding point on the graph of the second one.
What is the conditional statement if x equals 8?
For all y, if y = x, y = 8. Like that?
x = 8 is a condition, or result. Not both. e.g.
Condition:
if x = 8, then x + 1 = 9
Result:
If x + 1 = 9 then x = 8.
