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1 + 4 x 2 = ? .. 10 or 9 ?

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  • McDuck
    replied
    Originally posted by Wayne View Post

    SOH CAH TOA
    Tan(50)=opposite/adjacent.
    Adjacent is 80
    Rearranging Opposite (the height)=Tan(50)x80ft = 95.3ft
    Sanity checking - if the angle was 45deg then the height would equal the distance of 80ft (right angle triangle - a 1-1-root2 triangle).
    As the angle gets bigger the height gets bigger so 95.3ft is in the right ballpark and the calculator says it is right.
    Nice answer. Nice check procedure.

    This one requires quite a lot of information to solve.

    The first step is to understand that you are now in the field of math called Trigonometry, or "measuring triangles".
    People have been fudging around for thousands of years trying to figure out a good way to do this.



    Some kind chap wrote down a set of tables that connect the angles in triangles to the lengths of the sides.
    If you know an angle and a length, you can use these tables to figure out the other sides.




    The first step is to know the names of the sides of the triangle.
    They are:
    The side opposite to the angle, abbreviated to "O"
    The longest side, called the hypotenuse , abbreviated to " H"
    And the side next to, or adjacent to the angle, abbreviated to "A"

    You are then given three formula. S=O/H C=A/H T=O/A

    Most people remember them with the memory aid SOHCAHTOA.

    Where the first three letters (SOH) give the first equation. the Sine of the angle = the Opposite side divided by the Hypotenuse side.

    So, we look at the problem and see what sides we have.
    We have the Adjacent side = to 80 feet
    and we want to find the Opposite side (the height of the tree).
    So we know to use the last three letter in the memory aid.
    TOA

    It means the Tan of the angle equals the opposite side divided by the adjacent side.

    In other words.
    Tan of angle 50 degrees = opposite side divided by 80 feet.

    Rearrange the formula so the unknown item is by itself.
    (multiply both sides by the Adjacent side 80).

    T x A = O

    Tan50 times by 80 = Opposite side length.

    1.19175359259 x 80 = O

    95.3402874075 feet = O

    Since the tree is growing and defoliating, we can round the answer to 95.3 feet for practicality.
    ( if you were using this in GPS navigation, or to construct a Tesla electric car motor, you would probably go a bit more accurate).



    Inside the TESLA ELECTRIC MOTOR. Yes, the triangle is there for a reason.
    Last edited by McDuck; 28-05-2021, 09:07 AM.

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  • Wayne
    replied
    Originally posted by McDuck View Post

    .
    SOH CAH TOA
    Tan(50)=opposite/adjacent.
    Adjacent is 80
    Rearranging Opposite (the height)=Tan(50)x80ft = 95.3ft
    Sanity checking - if the angle was 45deg then the height would equal the distance of 80ft (right angle triangle - a 1-1-root2 triangle).
    As the angle gets bigger the height gets bigger so 95.3ft is in the right ballpark and the calculator says it is right.

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  • McDuck
    replied


    Some bright spark in history decided to notice the length of shadows.
    And broke a circle up into even segments called degrees.




    Turned out pretty handy for sailors and navigators.

    Here are the relationships.

    S O/H

    C A/H

    T O/A

    Show your working.

    * H stands for " Hypotenuse", the longest side of the triangle.
    Greek hupoteinein (from hupo ‘under’ + teinein ‘stretch’).
    Last edited by McDuck; 27-05-2021, 09:08 AM.

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  • McDuck
    replied
    Originally posted by Wayne View Post

    grapes = 1000/4=250
    watermelon can't be worth anything = 0 because 2xgrapes =500
    500 - grapes (250) = 250, so 2 bananas = 250 (since watermelon = 0). 1 banana = 125
    so 250 (grapes) + 125 (banana) - (0x250) = 375
    Perfect answer.
    Looks like that brain has been dusted off.
    The two traps are
    A Mellon being equal to nothing.

    * it's worth a note that a Mellon times a bunch of grapes = 0
    Because something times nothing is.. nothing.

    Which really screws with the field of geometry,
    As a line has length, but no width.
    In other words, something x nothing.

    Shhhh,
    Last edited by McDuck; 27-05-2021, 08:42 AM.

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  • Wayne
    replied
    Originally posted by McDuck View Post
    And since you had such fun with then last one. ..



    grapes = 1000/4=250
    watermelon can't be worth anything = 0 because 2xgrapes =500
    500 - grapes (250) = 250, so 2 bananas = 250 (since watermelon = 0). 1 banana = 125
    so 250 (grapes) + 125 (banana) - (0x250) = 375

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  • McDuck
    replied
    And since you had such fun with then last one. ..



    Last edited by McDuck; 25-05-2021, 09:01 AM.

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  • McDuck
    replied
    Originally posted by Wayne View Post

    2+(4x2/2)+4+(2x2x2) = 2+4+4+8 = 18
    Note 2 squared is just 2x2
    PEMDAS
    Very nice, you skipped over both traps with ease.
    The main trick here is to see it as problem that requires you know "the order of operations"
    Or, what to do first.
    And there are a few memory aids to help.
    "PEDMAS" is one.

    Parentheses
    Exponents
    Division
    Multiplication
    Addition
    Subtraction.

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  • Wayne
    replied
    Originally posted by McDuck View Post
    Few more traps in this one, since you're on a roll.


    2 + 4 × 2 ÷ 2 + 4 + 22 × 2 = ?
    2+(4x2/2)+4+(2x2x2) = 2+4+4+8 = 18
    Note 2 squared is just 2x2
    PEMDAS

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  • McDuck
    replied

    Few more traps in this one, since you're on a roll.


    2 + 4 × 2 ÷ 2 + 4 + 22 × 2 = ?
    Last edited by McDuck; 24-05-2021, 01:41 PM.

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  • Wayne
    replied
    Originally posted by McDuck View Post
    Few traps in this one, for the unpracticed.


    2 + 4 ÷ 2 + 4 + 2 × 2 = ?
    2+(4/2)+4+(2x2) = 2+2+4+4 = 12

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  • McDuck
    replied
    Few traps in this one, for the unpracticed.


    2 + 4 ÷ 2 + 4 + 2 × 2 = ?

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  • McDuck
    replied
    Originally posted by Wayne View Post

    Not used by me for years and years.
    Computer graphics, cryptography
    The uses are many.
    From recollection, the first use they are put to in normal school math is linear transformations.
    You have a line segment on a graph and you want it to shift to become another line segment, so you apply a transformational matrix.



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  • Wayne
    replied
    Originally posted by McDuck View Post

    Perfect.

    But what's it for?
    Not used by me for years and years.
    Computer graphics, cryptography

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  • McDuck
    replied
    Originally posted by Wayne View Post

    Takes me back - matrices or arrays
    The answer is (imagine the square brackets)
    4 -3
    -2 3
    Perfect.

    But what's it for?
    hint.


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  • Wayne
    replied
    Originally posted by McDuck View Post


    What is it?
    What is it for?
    What is the answer?
    Takes me back - matrices or arrays
    The answer is (imagine the square brackets)
    4 -3
    -2 3

    Leave a comment:

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