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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
What is y plus x minus 20 equals 3?
One equation
y equals 9
x equals 14
Don't forget to add it to 23.
You should generally state that the function is continuous and differentiable over the interval you are using (or throughout the entire function).
Can you explain what a borehole log is?
A borehole geophysical log is the science of recording and analysing measurements of physical properties made in wells or test holes.
Borehole Geophysical logs provide a borehole record of the lithology, fractures, permeability, porosity and water quality.
What is the answer for 48 equals 8x plus 2?
48=8x+2
we must isolate x :)
subtract 2 from both sides
48-2=8x+2-2
46 =8x
x is annoyed of number 8. we must exterminate it.
divide both sides by 8 :D
46/8=8x/8
46/8=x
therefore:
23/4=x
yay!
How do you work out the problem 2x plus 3 equals x?
2x + 3 = x
Subtract 3 from both sides so that...
2x = x - 3
Subtract x from both sides so that...
2x - x = -3
Now you have to simplify the left side so that it equals...
x(2-1) = -3
Now divide both sides by (2-1), the equation should now look like...
x = -3/(2-1)
x = -3/1
x = -3
Now obviously, you could have made (2-1) into 1 and left it as 1x = -3 so x = -3, but if the inside of that equation equaled something such as... (21-13) or something, you need to know you take the entire ( ) over to the other side. Also, don't forget to check your answer
2(-3) + 3 = (-3)
solved, it equals...
-3 = -3 so it is correct.
2x+5y=8
8-2x=5y
y=-0.4x+1.6
for y=mx+c, m is the gradient, -2/5. The perpendicular line will have a gradient of a negative reciprocal of the first, so 5/2 or 2.5.
kx-4y=9
kx-9=4y
y=(k/4)x-2.25
as such, k/4=2.5
k=10
What is the gradient of y equals 3x plus c?
Three, each time that x changes 1 y changes 3. C is where the start is.
What is the discriminant in the quadradic equation x squared plus 11x plus 121 equals x plus 96?
x^(2)+121=x+96
Standard form of quadratic eqn.:
ax^(2)+bx+c=0
Thus,
x^(2)-x+25=0
Discriminant formula:
We let, a= 1; b= -1; c= 25
D=b^(2)-4ac
Thus,
D=(-1)^2-4(1)(25)
D=-99
y=-3
-3 times -3= 9, 9+11= 20.
-3y + 11 =20
subtract 11 from each side, then -3y = 9
divide each side by -3, then y = -3
How do you Solve the equation w equals Cr to the negative second power for r?
Assuming the equation described is: w = (Cr)-2...
Remember that any value to a negative power can also be represented like this:
(Cr)-2 = 1/(Cr)2
Also note that we can distribute the power over multiplication. (This doesn't apply to addition!)
(Cr)2 = C2r2
So if we rewrite the equation with this, we get
w = 1/(C2r2)
If we invert both sides and then divide by C2 on both sides, we get
1/w = C2r2 → 1/(wC2) = r2
Take the square root of both sides, and you'll have the equation in terms of r:
r = sqrt[1/(wC2)]
The biggest step was realizing that anything to a negative power can be inverted to find the same with a positive power. For example, 2-2, if you type it in your calculator, gives you 0.25, or 1/4. If we do what we did above, we can take 2-2 and make it 1/(22), which also equals 1/4. This applies to any negative power, and is a powerful technique for solving equations with negative exponents.
What is the solution for X plus 7y equals 39 and 3x-2y equals 2 is?
x + 7y = 39 ....... Eq.1
3x - 2y = 2 ....... Eq.2
multiply Eq.1 with (-3) and so Eq.1 will be :
-3x - 21y = -117
3x - 2y = 2
_________________ by Elimination method ( Eq.1 + Eq.2 ) the result will we :
- 21y - 2y = - 115
-23y = -115
Y = 5
to find the value of x, put the value of y in Eq.1 :
x + 7y = 39
x = 39 - 7y
x = 39 - 7(5)
X = 4
___________________________________________________________
you can solve it in another way by using substitution method:
x + 7y = 39 ....... Eq.1 ,, you can write it in another form, x = 39 - 7y
3x - 2y = 2 ....... Eq.2
Put the value of Eq.1 on Eq.2
3(39 - 7y) - 2y = 2
117 - 21y - 2y = 2
117 - 23y = 2
23y = 115 ............ Y = 5
to find the value of X , put the value of Y in Eq.1
x = 39 - 7y
x = 39 - 7(5)
x = 39 - 35 .............. X = 4
and so in both ways....you got the same answer choose the easiest way for you :)
good luck my friend...
How many times does the graph of 3x2 plus 8x plus 5 cross the x-axis?
Twice. Between negative two and negative one.
Why do we find the limit of a function?
Typically, it's to give you an idea of a function graphically. Sometimes you deal with functions that are really hectic in design and they don't really have all the points smoothly in place (for example, a graph with an empty point or ^, a peak). A limit gives you an idea of what's happening with the graph as you get close to that point or area (as with infinity not being an actual point), hence the "as x approaches N," N being either some number, or negative or positive infinity.
2x2 + 1 = 16
2x2 = 15
x2 = 7.5
x = sqrt(7.5)
x = positive or negative 2.7386 (rounded)
How do you find the rule of a function that doesn't have a relation between the x and y?
With great difficulty: and it may even be impossible.
With great difficulty: and it may even be impossible.
With great difficulty: and it may even be impossible.
With great difficulty: and it may even be impossible.
What is the easiest way to find area between two functions?
You have to integrate. There is usually no easy shortcut, except for some very simple functions.
When finding the area between to functions subtract the bottom function from the bottom function. Then integrate that from the starting to ending points. (If the functions switch which is on top and which is on the bottom over the interval you're integrating over, you'll have to split the problem into smaller problems around that point and add the areas together.)
