Mellel 4.0.2 Mac OS X 98 MB. Mellel is a sophisticated and reliable processor texts, proven, specially designed to handle long and complicated, books, manuscripts, papers, theses, etc. Mellel is equipped with a great set of tools for the job, allowing you to control every little. TextExpander 4.0.2.1 (2012-10-10) Fixes issue when%key:return% or%key:enter% appear at the end of a snippet TextExpander 4.0.2 (2012-10-10) Avoids expanding “extra” line breaks when optional parts of a fill-in are not checked Restores ability to click to expand snippets found by Suggest Matching. Mellel has always been my favorite wordprocessor and Mellel 4.2 has notably enhanced its “table” features. Its developer is dedicated to make it better and better. He listens to his customers’ suggestions and carries them out without fail. What is so great in this process is that he doesn’t charge extra fees for all his hard work.
One solution was found :
m = 2Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
m^2-4*m-(-4)=0
m^2-4*m-(-4)=0
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring m2-4m+4
The first term is, m2 its coefficient is 1.
The middle term is, -4m its coefficient is -4.
The last term, 'the constant', is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4.
The first term is, m2 its coefficient is 1.
The middle term is, -4m its coefficient is -4.
The last term, 'the constant', is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4.
-4 | + | -1 | = | -5 | |
-2 | + | -2 | = | -4 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2
m2 - 2m - 2m - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m-2)
Add up the last 2 terms, pulling out common factors :
2 • (m-2)
Step-5 : Add up the four terms of step 4 :
(m-2) • (m-2)
Which is the desired factorization
Multiplying Exponential Expressions :
Mellel 4 4.0.2 Pc
1.2 Multiply (m-2) by (m-2)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (m-2) and the exponents are :
1 , as (m-2) is the same number as (m-2)1
and 1 , as (m-2) is the same number as (m-2)1
The product is therefore, (m-2)(1+1) = (m-2)2
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (m-2) and the exponents are :
1 , as (m-2) is the same number as (m-2)1
and 1 , as (m-2) is the same number as (m-2)1
The product is therefore, (m-2)(1+1) = (m-2)2
Equation at the end of step 1 :
Step 2 :
Solving a Single Variable Equation :
2.1 Solve : (m-2)2 = 0
(m-2)2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : m-2 = 0
Add 2 to both sides of the equation :
m = 2
(m-2)2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : m-2 = 0
Add 2 to both sides of the equation :
m = 2
Supplement : Solving Quadratic Equation Directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex :
3.1 Find the Vertex of y = m2-4m+4
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting 'y' because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Am2+Bm+C,the m -coordinate of the vertex is given by -B/(2A) . In our case the m coordinate is 2.0000
Plugging into the parabola formula 2.0000 for m we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 + 4.0
or y = 0.000
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting 'y' because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Am2+Bm+C,the m -coordinate of the vertex is given by -B/(2A) . In our case the m coordinate is 2.0000
Plugging into the parabola formula 2.0000 for m we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 + 4.0
or y = 0.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = m2-4m+4
Vertex at {m,y} = { 2.00, 0.00}
m-Intercept (Root) :
One Root at {m,y}={ 2.00, 0.00}
Note that the root coincides with
the Vertex and the Axis of Symmetry
coinsides with the line m = 0
Vertex at {m,y} = { 2.00, 0.00}
m-Intercept (Root) :
One Root at {m,y}={ 2.00, 0.00}
Note that the root coincides with
the Vertex and the Axis of Symmetry
coinsides with the line m = 0
Solve Quadratic Equation by Completing The Square
3.2 Solving m2-4m+4 = 0 by Completing The Square .
Subtract 4 from both side of the equation :
m2-4m = -4
Now the clever bit: Take the coefficient of m , which is 4 , divide by two, giving 2 , and finally square it giving 4
Add 4 to both sides of the equation :
On the right hand side we have :
-4 + 4 or, (-4/1)+(4/1)
The common denominator of the two fractions is 1 Adding (-4/1)+(4/1) gives 0/1
So adding to both sides we finally get :
m2-4m+4 = 0
Adding 4 has completed the left hand side into a perfect square :
m2-4m+4 =
(m-2) • (m-2) =
(m-2)2
Things which are equal to the same thing are also equal to one another. Since
m2-4m+4 = 0 and
m2-4m+4 = (m-2)2
then, according to the law of transitivity,
(m-2)2 = 0
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(m-2)2 is
(m-2)2/2 =
(m-2)1 =
m-2
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
m-2 = √ 0
Add 2 to both sides to obtain:
m = 2 + √ 0
The square root of zero is zero
This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.
The solution is:
m = 2
Subtract 4 from both side of the equation :
m2-4m = -4
Now the clever bit: Take the coefficient of m , which is 4 , divide by two, giving 2 , and finally square it giving 4
Add 4 to both sides of the equation :
On the right hand side we have :
-4 + 4 or, (-4/1)+(4/1)
The common denominator of the two fractions is 1 Adding (-4/1)+(4/1) gives 0/1
So adding to both sides we finally get :
m2-4m+4 = 0
Adding 4 has completed the left hand side into a perfect square :
m2-4m+4 =
(m-2) • (m-2) =
(m-2)2
Things which are equal to the same thing are also equal to one another. Since
m2-4m+4 = 0 and
m2-4m+4 = (m-2)2
then, according to the law of transitivity,
(m-2)2 = 0
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(m-2)2 is
(m-2)2/2 =
(m-2)1 =
m-2
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
m-2 = √ 0
Add 2 to both sides to obtain:
m = 2 + √ 0
The square root of zero is zero
This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.
The solution is:
m = 2
Solve Quadratic Equation using the Quadratic Formula
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3.3 Solving m2-4m+4 = 0 by the Quadratic Formula .
According to the Quadratic Formula, m , the solution for Am2+Bm+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
m = ———————--
2A
In our case, A = 1
B = -4
C = 4
Accordingly, B2 - 4AC =
16 - 16 =
0
Applying the quadratic formula :
4 ± √ 0
m = ———--
2
The square root of zero is zero
This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.
The solution is:
m = 4 / 2 = 2
According to the Quadratic Formula, m , the solution for Am2+Bm+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
m = ———————--
2A
In our case, A = 1
B = -4
C = 4
Accordingly, B2 - 4AC =
16 - 16 =
0
Applying the quadratic formula :
4 ± √ 0
m = ———--
2
The square root of zero is zero
This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.
The solution is:
m = 4 / 2 = 2
One solution was found :
m = 2Processing ends successfully
Mellel 4 4.0.2
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• Fixed a bug that caused added characters and locations not to be saved in a story point when document is saved and closed right after adding while creating a story point or location.
• Disabling virtual target popup when there are no virtual targets available in bookmark popover and edit cell
• Fixed an issue that caused Mellel to turn on the discrete GPU (higher energy consumption) when launched
• Fixed an issue that caused the “mention” popup in edit page style (header/footer editor) to be empty.
• Fixed an issue that caused the placeholder “title” element for mentions to become chopped in header/footer editor in page style editor.
• Fixed shortcut for soft hyphen in french localisation
(Improvements in Mellel 4.0.1)
• Updated localisations
• Updated user guide
• Fixed typo (Autotitiles->Autotitles) in The auto-title pane blocker view
• Fixed an issue that caused the symbols & numbers group heading fields not to appear correctly according to the numbers & symbols grouping setting in “Edit Index Attributes” window
• Matched order of side pane items in View menu and side pane
• Fixed spelling Seperate -> Separate in Edit Index attributes and Index style editor
• Changed “Show Comments” to “Show Remarks” in outline context menu
• Fixed many issues under 10.6, including missing palettes, misbehaving side pane
• Fixed an issue that caused Mellel to crash when displaying a text box or an image with a frame with rounded corners in mac os 10.8 and previous versions
• Fixed an issue that cased Mellel to hang and behave oddly when opening documents with list that had old style (pre 4.0) level overrides specifying only character style variation.
• Fixed an issue that caused Mellel to crash when switching autotitle setups while still editing a tag flow that will be deleted as a result of the operation
• Fixed an issue that caused final citation order to become mangled for citations in notes referenced from a single table cell.
• Fixed an issue that caused bad rendering of references inside notes
• Fixed an issue that caused Mellel to crash when choosing “Capture selection from screen” from context menu while editing a comment.
• Some performance improvements to find/replace application
• Improved appearance for preferences toolbar with some localisations
• Fixed an issue that caused the Mellel 4 trial day counter to go to zero after migrating an older Mellel 3 installation settings.
• Fixed an issue that caused the “13” entry in the font size popup to be replaced by whatever “other” value a user enters in some circumstances.
• Fixed problem that caused the left border of the “Characters” field in a story point on the side pane not to be drawn on some systems
• Fixed a bug that caused added characters and locations not to be saved in a story point when document is saved and closed right after adding while creating a story point or location.
• Disabling virtual target popup when there are no virtual targets available in bookmark popover and edit cell
• Fixed an issue that caused Mellel to turn on the discrete GPU (higher energy consumption) when launched
• Fixed an issue that caused the “mention” popup in edit page style (header/footer editor) to be empty.
• Fixed an issue that caused the placeholder “title” element for mentions to become chopped in header/footer editor in page style editor.
• Fixed shortcut for soft hyphen in french localisation
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