Lichobežník MO


#0  xxx() called at [/LinSys.php:671]
#1  LinSys::tryIntegerEquations(Array ([0] => D,[1] => S,[2] => a,[3] => b,[4] => c,[5] => e,[6] => i,[7] => m,[8] => n,[9] => o,[10] => p,[11] => r,[12] => t,[13] => u,[14] => v,[15] => x,[16] => y), Array ([0] => x^2 +0.667x -1 =0,[1] => a=1,[2] => b=0.667,[3] => c=-1,[4] => D = b^2 - 4ac = 0.667^2 - 4** 1 ** (-1) = 4.4444444444444,[5] => xx{1.2} = frac{ -b pm sqrt{ D } }{ 2a } = frac{ -0.67 pm sqrt{ 4.44 } }{ 2 },[6] => xx{1.2} = -0.33333333 pm 1.0540925533895,[7] => xx{1} = 0.72075922338946,[8] => xx{2} = -1.3874258833895,[9] => (x -0.72075922338946) (x +1.3874258833895) = 0), 1) called at [/LinSys.php:344]
#2  LinSys::SolveInner(x^2 +0.667x -1 =0
a=1; b=0.667; c=-1
D = b^2 - 4ac = 0.667^2 - 4** 1 ** (-1) = 4.4444444444444
D>0

xx{1.2} = frac{ -b pm sqrt{ D } }{ 2a } = frac{ -0.67 pm sqrt{  4.44 } }{ 2 } 
xx{1.2}  = -0.33333333 pm 1.0540925533895
xx{1}  = 0.72075922338946
                xx{2}  = -1.3874258833895

text{ Sucinovy tvar: }
		 (x -0.72075922338946) (x +1.3874258833895) = 0, , 1, linsys, 1, , 1, 1) called at [/LinSys.php:220]
#3  LinSys::Solve(x^2 +0.667x -1 =0
a=1; b=0.667; c=-1
D = b^2 - 4ac = 0.667^2 - 4** 1 ** (-1) = 4.4444444444444
D>0

x_{1,2} = \frac{ -b \pm \sqrt{ D } }{ 2a } = \frac{ -0.67 \pm \sqrt{  4.44 } }{ 2 } 
x_{1,2}  = -0.33333333 \pm 1.0540925533895
x_{1}  = 0.72075922338946
                x_{2}  = -1.3874258833895

\text{ Sucinovy tvar: }
		 (x -0.72075922338946) (x +1.3874258833895) = 0, , 1, linsys, 1, , 1) called at [/Example_Generic.php:87]
#4  Example_Generic->GenerateSolveVector(stdClass Object ([example_id] => 543,[title_sk] => Lichobežník MO,[title_en] => Trapezoid MO,[title_cz] => Lichoběžník MO,[add_date] => 2013-01-02 12:09:29,[img] => right_trapezium.jpg,[visible] => 1,[text_sk] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, $e, uhlopriečky sú na seba kolmé.

Vypočítajte obvod a obsah takéhoto lichobežníka.,[text_en] => The rectangular trapezoid ABCD with right angle at point B, $e, diagonals are perpendicular to each other.

Calculate the perimeter and area of ​​the trapezoid.,[text_cz] => Je dán pravouhlý lichoběžník ABCD s pravým uhlem u bodu B, $e, uhlopříčky jsou na sebe kolmé.

Vypočítejte obvod a obsah takéhoto lichobežníka.,[input_vector] => $ac = 12;
$cd = 8;

$e = "|AC| = $ac, |CD| = $cd";,[output_vector] => $oo = Str('o','p','o');
$ss = Str('S','A','S');

list($x1,$x2)= QER(1,$cd/$ac, -1, false);

$alfa1=  acos($x1);
$alfa2=  acos($x2);

if(!is_nan($alfa1))
{
    $alfa = $alfa1;
}
else
{
  $alfa = $alfa1;
}

$u = '\\Theta';

$aa = ShowDeg(r2d($alfa));

$bc = $ac*sin($alfa);
$ab = $ac * cos($alfa);
//$bd = $cd/ sin($alfa);
$ad = sqrt(pow($bc,2)+ pow($ab-$cd,2));

$o->in= $oo . '=';
$o->N = 2;
$o->val = "$ab+$bc+$cd +$ad";

$S->N = 2;
$S->in= $ss . '=';

$eq = QTex(1, $cd/$ac, -1, 'x', 1);

$S->val = "($ab+$cd)*$bc/2";

$o->tex = "\\sin $u = \\frac{|BC|}{|AC|}
\\cos $u = \\frac{|BC|}{|BD|}

\\cos^2 $u + \\frac{ |CD|}{|AC|}\\cos $u - 1 =0
x^2 + \\frac{ |CD|}{|AC|}x - 1 =0

$eq

$u = $aa

|BC| = |AC| \\sin $u = $bc
|AB| = |AC| \\cos $u = $ab
|AD| = \\sqrt{ |BC|^2 + (|AB|-|CD|)^2} = $ad

o = |AB|+|BC|+|CD| + |AD| = RES";

$S->tex = "$ss = \\frac{(|AB|+|CD|)**|BC|}{2}= RES";

,[user_id] => 12,[approved] => 1,[cnt_views] => 104595,[cnt_solved] => 4502,[cnt_solved_ok] => 16,[focus] => 1,[preview_sk] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, |AC| = 12, |CD| = 8, uhlopriečky sú na seba kolmé.  Vypočítajte obvod a obsah takéhoto lichobežníka.,[preview_en] => The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other.  Calculate the perimeter and area of ​​the trapezoid.,[preview_cz] => Je dán pravouhlý lichoběžník ABCD s pravým uhlem u bodu B, |AC| = 12, |CD| = 8, uhlopříčky jsou na sebe kolmé.  Vypočítejte obvod a obsah takéhoto lichobežníka.,[preview_vector_sk] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[preview_vector_en] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[preview_vector_cz] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[last_regenerate] => 2019-07-14 19:55:16,[external_url] => ,[suggestion_id] => 0,[fulltext_sk] => ~ lichobeznik mo je dany pravouhly lichobeznik abcd s pravym uhlom pri bode b |ac| = 12 |cd| 8 uhlopriecky su na seba kolme vypocitajte obvod a obsah takehoto lichobeznika planimetria pytagorova veta kvadraticka rovnica algebra trojuholnik zakladne funkcie uvaha sinus goniometria trigonometria kosinus tangens arkustangens uhlopriecka arkussinus zlomky arkuskosinus 9 rocnik stredna skola 543 ~,[fulltext_en] => ~ trapezoid mo the rectangular trapezoid abcd with right angle at point b |ac| = 12 |cd| 8 diagonals are perpendicular to each other calculate the perimeter and area of the pythagorean theorem planimetrics quadratic equation algebra triangle shape basic functions reason goniomentry trigonometry sine cosine tan arctangent diagonal arcsine fractions arccosine 9t 9 th grade 14y 4 y high school 543 ~,[fulltext_cz] => ~ lichobeznik mo je dan pravouhly lichobeznik abcd s pravym uhlem u bodu b |ac| = 12 |cd| 8 uhlopricky jsou na sebe kolme vypocitejte obvod a obsah takehoto lichobeznika pythagorova veta planimetrie algebra kvadraticka rovnice pravouhly trojuhelnik uvaha zakladni funkce goniometrie trigonometrie sinus kosinus tangens arkustangens uhlopricka arkussinus zlomky arkuskosinus 9 rocnik stredni skola 543 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Lichobežník MO,[text] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, $e, uhlopriečky sú na seba kolmé.

Vypočítajte obvod a obsah takéhoto lichobežníka.), stdClass Object ([ac] => 12,[cd] => 8,[e] => |AC| = 12, |CD| = 8)) called at [/Example_Generic.php:869]
#5  Example_Generic->Run(stdClass Object ([example_id] => 543,[title_sk] => Lichobežník MO,[title_en] => Trapezoid MO,[title_cz] => Lichoběžník MO,[add_date] => 2013-01-02 12:09:29,[img] => right_trapezium.jpg,[visible] => 1,[text_sk] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, $e, uhlopriečky sú na seba kolmé.

Vypočítajte obvod a obsah takéhoto lichobežníka.,[text_en] => The rectangular trapezoid ABCD with right angle at point B, $e, diagonals are perpendicular to each other.

Calculate the perimeter and area of ​​the trapezoid.,[text_cz] => Je dán pravouhlý lichoběžník ABCD s pravým uhlem u bodu B, $e, uhlopříčky jsou na sebe kolmé.

Vypočítejte obvod a obsah takéhoto lichobežníka.,[input_vector] => $ac = 12;
$cd = 8;

$e = "|AC| = $ac, |CD| = $cd";,[output_vector] => $oo = Str('o','p','o');
$ss = Str('S','A','S');

list($x1,$x2)= QER(1,$cd/$ac, -1, false);

$alfa1=  acos($x1);
$alfa2=  acos($x2);

if(!is_nan($alfa1))
{
    $alfa = $alfa1;
}
else
{
  $alfa = $alfa1;
}

$u = '\\Theta';

$aa = ShowDeg(r2d($alfa));

$bc = $ac*sin($alfa);
$ab = $ac * cos($alfa);
//$bd = $cd/ sin($alfa);
$ad = sqrt(pow($bc,2)+ pow($ab-$cd,2));

$o->in= $oo . '=';
$o->N = 2;
$o->val = "$ab+$bc+$cd +$ad";

$S->N = 2;
$S->in= $ss . '=';

$eq = QTex(1, $cd/$ac, -1, 'x', 1);

$S->val = "($ab+$cd)*$bc/2";

$o->tex = "\\sin $u = \\frac{|BC|}{|AC|}
\\cos $u = \\frac{|BC|}{|BD|}

\\cos^2 $u + \\frac{ |CD|}{|AC|}\\cos $u - 1 =0
x^2 + \\frac{ |CD|}{|AC|}x - 1 =0

$eq

$u = $aa

|BC| = |AC| \\sin $u = $bc
|AB| = |AC| \\cos $u = $ab
|AD| = \\sqrt{ |BC|^2 + (|AB|-|CD|)^2} = $ad

o = |AB|+|BC|+|CD| + |AD| = RES";

$S->tex = "$ss = \\frac{(|AB|+|CD|)**|BC|}{2}= RES";

,[user_id] => 12,[approved] => 1,[cnt_views] => 104595,[cnt_solved] => 4502,[cnt_solved_ok] => 16,[focus] => 1,[preview_sk] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, |AC| = 12, |CD| = 8, uhlopriečky sú na seba kolmé.  Vypočítajte obvod a obsah takéhoto lichobežníka.,[preview_en] => The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other.  Calculate the perimeter and area of ​​the trapezoid.,[preview_cz] => Je dán pravouhlý lichoběžník ABCD s pravým uhlem u bodu B, |AC| = 12, |CD| = 8, uhlopříčky jsou na sebe kolmé.  Vypočítejte obvod a obsah takéhoto lichobežníka.,[preview_vector_sk] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[preview_vector_en] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[preview_vector_cz] => O:8:"stdClass":3:{s:2:"ac";i:12;s:2:"cd";i:8;s:1:"e";s:19:"|AC| = 12, |CD| = 8";},[last_regenerate] => 2019-07-14 19:55:16,[external_url] => ,[suggestion_id] => 0,[fulltext_sk] => ~ lichobeznik mo je dany pravouhly lichobeznik abcd s pravym uhlom pri bode b |ac| = 12 |cd| 8 uhlopriecky su na seba kolme vypocitajte obvod a obsah takehoto lichobeznika planimetria pytagorova veta kvadraticka rovnica algebra trojuholnik zakladne funkcie uvaha sinus goniometria trigonometria kosinus tangens arkustangens uhlopriecka arkussinus zlomky arkuskosinus 9 rocnik stredna skola 543 ~,[fulltext_en] => ~ trapezoid mo the rectangular trapezoid abcd with right angle at point b |ac| = 12 |cd| 8 diagonals are perpendicular to each other calculate the perimeter and area of the pythagorean theorem planimetrics quadratic equation algebra triangle shape basic functions reason goniomentry trigonometry sine cosine tan arctangent diagonal arcsine fractions arccosine 9t 9 th grade 14y 4 y high school 543 ~,[fulltext_cz] => ~ lichobeznik mo je dan pravouhly lichobeznik abcd s pravym uhlem u bodu b |ac| = 12 |cd| 8 uhlopricky jsou na sebe kolme vypocitejte obvod a obsah takehoto lichobeznika pythagorova veta planimetrie algebra kvadraticka rovnice pravouhly trojuhelnik uvaha zakladni funkce goniometrie trigonometrie sinus kosinus tangens arkustangens uhlopricka arkussinus zlomky arkuskosinus 9 rocnik stredni skola 543 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Lichobežník MO,[text] => Je daný pravouhlý lichobežník ABCD s pravým uhlom pri bode B, $e, uhlopriečky sú na seba kolmé.

Vypočítajte obvod a obsah takéhoto lichobežníka.)) called at [/index_real.php:185]
#6  HackMath->ExampleDetail() called at [/index_real.php:316]
#7  HackMath->ExampleAction() called at [/index_real.php:461]
#8  HackMath->Run() called at [/index_real.php:815]
#9  include(/index_real.php) called at [/index.php:41]