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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
This is done by solving either of the equations for one of the two variables, and then plugging that solution in to the other equation in place of that variable. In this case both equations equal the same variable, y, so it is very easy to do:
Given:
y = 2x + 3
y = 3x + 1
Therefore:
2x + 3 = 3x + 1
∴ 3x - 2x = 3 - 1
∴ x = 2
And then you could plug that value of x back into one of the original equations to find the value of y:
y = 2x + 3
∴ y = 2(2) + 3
∴ y = 4 + 3
∴ y = 7
So you know that x is equal to two, and y is equal to seven. You can solve for either variable first. In this case, y is the simpler value to substitute, but x can be exchanged in exactly the same way:
y = 2x + 3
∴ y - 3 = 2x
∴ (y - 3)/2 = x
Now we substitute that equation for x in our other equation:
y = 3x + 1
∴ y = 3(y - 3)/ 2 + 1
∴ y = 3y/2 - 9/2 + 1
∴ y = (3y - 9 + 2) / 2
∴ 2y = 3y - 9 + 2
∴ -y = -7
∴ y = 7
and then solve for x:
y = 2x + 3
∴ 7 = 2x + 3
∴ 2x = 4
∴ x = 2
giving you the same results.
How do you solve problems like -2 plus 5x equals 13?
This is how I learned:
-2 + 5x = 13
5x + -2 + 2 = 13 + 2
5x = 15
-- --
5 5
x = 3
Then check:
-2 + 5 x 3 = ?
-2 + 15 = ?
13 =13
This is because when you add and subtract integers, adding negative is subtracting.
Subtracting negatives is like adding, but the result is negative. So, when you take
-2 + 2 it equals 0.
Yes, a set can be infinitely large. For instance, the set of all odd integers is infinitely large.
What is the square root of 121-8 to the second power divided by 32 x 4?
(sqrt(121)-8)**2/(32*4)
(11-8)**2/(128)=9/128
(-11-8)**2/(128)=361/128
sqrt121-8**2/(32*4)
11-64/128=10.5
-11-64/128=-11.5
sqrt(121-8**2)/(32*4)
sqrt(57)/128
-sqrt(57)/128
(sqrt(121)-8)**2/32*4
(11-8)**2/32*4=9/8
(-11-8)**2/32*4=361/8
sqrt121-8**2/32*4
11-64/32*4=3
-11-64/32*4=-19
sqrt(121-8**2)/32*4
sqrt(57)/8
-sqrt(57)/8
The mean value theorem can be applied to all continuous functions (or expressions), and so it is applicable here.
There is no equation in te question and furthermore, no c (other than the first letter of cos in the expression so there are no values for c to satisfy anything!
What is the solution to 7over8b-1 equals -15over16b plus 4?
If you mean: 7/8b - 1 = -15/16b + 4
Then the value of b works out as 0.3625
Solve this equation 9h plus 2 - 79?
That's not an equation, and there's no solution required.
An equation has an 'equals' sign ( " = " ) somewhere in it.
That expression is just 9h - 77. Its numerical value depends on what 'h' is. Every time
'h' changes, the value of that expression changes. That's all there is to say about it.
Can multiplication principle be used to solve equations like 7x equals 63?
Just divide both sides by 7...
Subtract 12x from each side: 3x - 5 = 7
Add 5 to each side: 3x = 12
Divide each side by 3: x = 4
Find its nth derivative e to the power x sq By 2 multiply cosx?
I suggest you calculate the first 2 or 3 derivatives, and see whether you can find a pattern.
What is the anti derivative of ax plus b whole raised to the power 2?
First expand the equation to get the following:
(ax+b)2 = (ax+b)*(ax+b) = a2x2+2abx+b2
Now do the integral, remember a&b are just coefficients, so:
∫a2x2 + 2abx + b2 dx
So this integral becomes the following after integrating each term:
(a2/3)x3 + abx2 + b2x + C
You can always take the derivative of the answer to check & see if it is correct.
What is the value of x in x plus 15?
The information given places no restriction at all on the value that x can have. It can be any number - integer, rational, irrational or complex - of any magnitude.
What is A equation for -2x plus 8 equals 7x-10?
-2x + 8 = 7x - 10 is technically an equation, in and of itself.
What is the domain and range of the equation x² plus y² equals 36?
The domain and range are both [-6, +6].
