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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
x-6=9
With this problem you have to isolate (Leave it by itself) X. In order to do this, You need to take away the -6, correct? to get rid of the -6, you have to add 6 to the left side. In algebra you always need to know, whatever you do to one side, you need to do to the other. So, then you add 6 to the 9. Then, you're left with x=15. Wa, La! In simpler terms,
x-6=9
+6, +6
x=15
What is 6x2-2x plus 36 equals 5x2 plus 10x?
6x2-2x+36 = 5x2+10x
6x2-5x2-2x-10x+36 = 0
x2-12x+36 = 0
(x-6)(x-6) = 0
x = 6 or x = 6 It has two equal roots.
Can you solve x2 minus 9x equals -20?
Yes, it can be solved for x = ? because there is one equation and one variable.
x2 - 9x = -20
x2 - 9x + 20 = 0
(x-4)(x-5) = 0
The factoring takes some practice. Now we set each parenthesis equal to zero, and we get two possible values for x: x = 4 and x = 5.
Add the mileage for each day and divide by the number of days to get the average: (x + y + z) ÷ 3 = Average
What is another way to say liter?
Most Europeans countries would say litre. As would many Asian and African countries with historic links with Europe.
X plus 5 equals 9 what is the answer complete solution and check?
if x+5=9 than x=4 solved by subtraction property of equality check by substation property 4+5=9
How many cubic meters is 9 cubic centimeters?
Ans: 1 cm = 1 / 100 m; so 9 cu.cm = 9 x 1 cu.cm = 9 x [1 / 100000] cu. metre = 0.000009 cu.m
What is true 15 plus 0 equals 0 15-0 equals 0 15 percent 0 equals 0 0 percent 15 equals 0?
15 percent 0 equals 0;
0 percent 15 equals 0.
Both the above are true
Which length of the pendulum made the most number of swings?
A shorter pendulum will make more swings per second. Or per minute. Or whatever.
What is the second derivative of x to the fourth power?
d/dx(X^4)
= 4X^3 ( first derivative )
d/dx(4X^3)
= 12X^2 ( second derivative )
What is the derivative of lnx raised to 4?
ln(x4)?
d/dx(ln(u))=1/u*d/dx(u)
d/dx(ln(x4))=[1/x4]*d/dx(x4)
-The derivative of x4 is:
d/dx(x4)=4x4-1
d/dx(x4)=4x3
d/dx(ln(x4))=[1/x4]*(4x3)
d/dx(ln(x4))=4x3/x4
d/dx(ln(x4))=4/x
(lnx)4?
Chain rule: d/dx(ux)=x(u)x-1*d/dx(u)
d/dx(lnx)4=4(lnx)4-1*d/dx(lnx)
d/dx(lnx)4=4(lnx)3*d/dx(lnx)
-The derivative of lnx is:
d/dx(ln(u))=1/u*d/dx(u)
d/dx(lnx)=1/x*d/dx(x)
d/dx(lnx)=1/x*(1)
d/dx(lnx)=1/x
d/dx(lnx)4=4(lnx)3*(1/x)
d/dx(lnx)4=4(lnx)3/x
How do you graph y equals 2x plus 0.5?
y=2x+1/2
when x=0, y=1/2 so one point is (0, 1/2)
when y=0, x=-1/4 so another point is (-1/4, 0)
then you plot both points on the graph and draw a line.
What is the relationship between y equals -5x-2 and y-5x equals 4?
Both equations are equal to each other and when solved x = -3/5 and y = 1
Is the simultaneous equation x2 plus y2 equals 25 y equals x plus 1 even possible?
Yes, it's possible
(1) x2 + y2 = 25
(2) y = x + 1
Substituting (2) into (1) gives:
(3) x2 + (x + 1)2 = 25
(4) x2 + x2 + 2x + 1 = 25
(5) 2x2 + 2x - 24 = 0
(6) x2 + x - 12 = 0
Plugging 1, 1, and -12 into the quadratic equation gives us two answers:
x = 3, y - 4 and x = -4, y = -3
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Another contributor was working this at exactly the same time as the first
contributor, and posts his work here, just to demonstrate how great minds
run in the same gutter:
Shouldn't be a big problem. When you think about this for a while, it might seem like it might not be very difficult; but then, when you dig into it a little further, it turns out to be downright easy.
The first glance:
x2+y2=25 is a circle, centered at the origin, with radius=25.
y=x+1 is a 45-degree line, shifted one unit above the origin.
They have two common points ... the two points where the 45-degree line cuts
the circle. Those two points are the solutions to the simultaneous equations.
Since they're on a circle, we can't tell right away where the points will be, and
with fear and trembling, we hesitantly write them down and try to solve them
algebraically.
The drudge work:
Substitute [y=x+1] into [x2 + y2 = 25]:
x 2 + (x+1)2 = 25
x2 + x2 + 2x + 1 = 25
2x2 + 2x -24 = 0
x2 + x - 12 = 0
We don't even need to resort to the quadratic formula to solve this! We can
just look at it and factor it:
(x-4)(x+3) = 0
x = 4, (y = -3)
x = -3, (y = 4)
Well, you and I can factor it just by looking at it, but the middle-schooler whose homework we're doing probably needs to show his (our) work.
