diff --git a/OpenProblemLibrary/FortLewis/Calc3/18-4-Greens-theorem/HGM4-18-4-17-Greens-theorem.pg b/OpenProblemLibrary/FortLewis/Calc3/18-4-Greens-theorem/HGM4-18-4-17-Greens-theorem.pg index 3c00710e15..7619ccd65d 100644 --- a/OpenProblemLibrary/FortLewis/Calc3/18-4-Greens-theorem/HGM4-18-4-17-Greens-theorem.pg +++ b/OpenProblemLibrary/FortLewis/Calc3/18-4-Greens-theorem/HGM4-18-4-17-Greens-theorem.pg @@ -134,9 +134,11 @@ $rd2 = $r / 2; $gr[0]->moveTo($rd2,0); $gr[0]->arrowTo($rd2+0.1,0,"red",3); +$grAlt = "A vector field witha wedge shaped path traveled counterclockwise"; +$grDescr = "A vector field with a counterclockwise rotation and magnitude increasing as points go away from the origin. A wedge shaped path going from the origin to (3,0), then along a circular path of radius 3 from the origin for 30 degrees, then back to the origin. "; foreach my $i (0) { - $fig[$i] = image(insertGraph($gr[$i]),width=>"400",height=>"400",tex_size=>"700"); + $fig[$i] = image(insertGraph($gr[$i]),width=>"400",height=>"400",tex_size=>"700", alt=>$grAlt, long_description=>$grDescr) } diff --git a/OpenProblemLibrary/Michigan/Chap12Sec4/Q15.pg b/OpenProblemLibrary/Michigan/Chap12Sec4/Q15.pg index ca5760d67a..1a2cd14464 100644 --- a/OpenProblemLibrary/Michigan/Chap12Sec4/Q15.pg +++ b/OpenProblemLibrary/Michigan/Chap12Sec4/Q15.pg @@ -2,8 +2,20 @@ # Problem from Calculus, multi-variable, Hughes-Hallett et al., # originally from 5ed (with updates) # WeBWorK problem written by Gavin LaRose, + +DOCUMENT(); + +loadMacros( + "PGstandard.pl", + "PGchoicemacros.pl", + "MathObjects.pl", + "PGgraphmacros.pl", + "PGcourse.pl" +); + ## Tagged by glr 05/12/09 + ## DBsubject(Calculus - multivariable) ## DBchapter(Concepts for multivariable functions) ## DBsection(Traces, contours, and level sets) @@ -31,105 +43,123 @@ ## Textbook tags ## HHChapter1('Functions of Several Variables') -DOCUMENT(); +$refreshCachedImages = 1; -loadMacros('PGstandard.pl', 'PGML.pl', 'plots.pl', 'PGcourse.pl'); +Context("Numeric"); +$showPartialCorrectAnswers = 1; ## the cost of a cd -$p = random(6, 10, 2); +$p = random(6,10,2); ## the cost of a dvd -$q = $p + random(2, 6, 2); +$q = $p + random(2,6,2); + +$p = 10; +$q = 14; ## then the revenue is given by ## r = p c + q d, ## so the contour lines are the lines -## d = r/q - (p/q) c - -$plot = Plot( - xmin => 0, - xmax => 400, - ymin => 0, - ymax => 400, - xtick_delta => 100, - xminor => 1, - ytick_delta => 100, - yminor => 1, - xlabel => '\(c\)', - ylabel => '\(d\)', - aria_label => 'The revenue based on number of CDs and DVDs sold', - axes_on_top => 1, -); - -for ($i = 1; $i < 9; $i++) { - $r = 1000 * $i; - $plot->add_function( - "($r - $p*x)/($q)", 'x', 0, $r / $p, - color => 'blue', - weight => 2 - ); - $y1 = $r / ($p + $q); - $plot->add_label($y1 + 20, $y1 + 10, label => "$r", color => 'blue'); +## d = r/q - (p/q) c +$gr = init_graph(0,0,400,400, axes=>[0,0], grid=>[8,8], size=>[300,300]); +$gr->lb('reset'); +foreach my $v ( 100, 200, 300, 400 ) { + $gr->lb( new Label( $v, 0, "$v", 'black', 'right', 'bottom' ) ); + $gr->lb( new Label( 0, $v, "$v", 'black', 'left', 'top' ) ); } +$gr->lb( new Label( 350, 0, "c", 'black', 'right', 'bottom' ) ); +$gr->lb( new Label( 0, 350, " d", 'black', 'left', 'top' ) ); -## nice intersection points are given by -%rpoints = ( - 6 => { - 8 => [ [ 200, 100, 2000 ], [ 100, 300, 3000 ] ], - 10 => [ [ 250, 50, 2000 ], [ 250, 150, 3000 ] ], - 12 => [ [ 100, 200, 3000 ], [ 200, 150, 3000 ] ] - }, - 8 => { - 10 => [ [ 250, 100, 3000 ], [ 250, 200, 4000 ] ], - 12 => [ [ 100, 100, 2000 ], [ 100, 350, 5000 ] ], - 14 => [ [ 200, 100, 3000 ], [ 100, 300, 5000 ] ] - }, - 10 => { - 12 => [ [ 100, 250, 4000 ], [ 200, 250, 5000 ] ], - 14 => [ [ 150, 250, 5000 ], [ 250, 250, 6000 ] ], - 16 => [ [ 100, 250, 5000 ], [ 200, 250, 6000 ] ] - } -); +for ( my $i=1; $i<9; $i++ ) { + my $r = 1000*$i; + add_functions( $gr, "($r - $p*x)/$q for x in <0,400> using color:" . + "blue and weight:2" ); -($c0, $d0, $r0) = @{ $rpoints{$p}->{$q}->[0] }; -($c1, $d1, $r1) = @{ $rpoints{$p}->{$q}->[1] }; + ## put the contour label on the line y=x + my $y1 = $r/($p+$q); + $gr->lb( new Label( $y1, $y1, "$r", 'black', 'right', 'bottom' ) ); +} +$grAlt = "A contour plot with parallel lines going down and to the right."; +$grDescr = "A graph where the horizontal axis is labelled as c, and the vertical axis is labelled as d. On the graph are eight parallel horizontal lines starting at the vertical axis and travelling down and right until they meet the horizontal axis. The lowest such line is labelled with 1000, and each higher line has a label that is 1000 greater than the one below. The line that is labelled $r0 passes through the point ($c0,$d0). The line that is labelled $r1 passes through the point ($c1,$d1)."; -$alt_text = - "A graph where the horizontal axis is labelled as c, and the vertical axis is labelled as d. On the graph are eight parallel horizontal lines starting at the vertical axis and travelling down and right until they meet the horizontal axis. The lowest such line is labelled with 1000, and each higher line has a label that is 1000 greater than the one below. The line that is labelled $r0 passes through the point ($c0,$d0). The line that is labelled $r1 passes through the point ($c1,$d1)."; +Context()->texStrings; +TEXT(beginproblem()); +BEGIN_TEXT -BEGIN_PGML A store sells CDs at one price and DVDs at another price. The figure below shows the revenue (in dollars) -of the music store as a function of the number, [` c `], -of CDs and the number, [` d `], of DVDs that it sells. The +of the music store as a function of the number, \( c \), +of CDs and the number, \( d \), of DVDs that it sells. The values of the revenue are shown on each line. - ->> [! $alt_text !]{$plot}{300} << - -_(Hint: for this problem there are many possible ways to +$PAR +$BCENTER +\{ image( insertGraph( $gr ), tex_size=>350, height=>300, width=>300, + alt=>$grAlt, long_description=>$grDescr) \} + +$ECENTER +$PAR +${BITALIC}(Hint: for this problem there are many possible ways to estimate the requisite values; you should be able to find information from the figure that allows you to give an answer that is essentially -exact.)_ +exact.)$EITALIC +$PAR +${BBOLD}(a)$EBOLD +What is the price of a CD? \{ ans_rule(25) \} dollars +$BR +${BBOLD}(b)$EBOLD +What is the price of a DVD? \{ ans_rule(25) \} dollars -a) What is the price of a CD? [_]{$p}{5} dollars -b) What is the price of a DVD? [_]{$q}{5} dollars -END_PGML -BEGIN_PGML_SOLUTION -The revenue function, [`R`], is linear and so we may write it as: -[``` +END_TEXT +Context()->normalStrings; + +ANS(Compute("$p")->cmp() ); +ANS(Compute("$q")->cmp() ); + +## nice intersection points are given by +%rpoints = ( 6 => { 8 => [ [ 200, 100, 2000 ], + [ 100, 300, 3000 ] ], + 10 => [ [ 250, 50, 2000 ], + [ 250, 150, 3000 ] ], + 12 => [ [ 100, 200, 3000 ], + [ 200, 150, 3000 ] ] }, + 8 => { 10 => [ [ 250, 100, 3000 ], + [ 250, 200, 4000 ] ], + 12 => [ [ 100, 100, 2000 ], + [ 100, 350, 5000 ] ], + 14 => [ [ 200, 100, 3000 ], + [ 100, 300, 5000 ] ] }, + 10 => { 12 => [ [ 100, 250, 4000 ], + [ 200, 250, 5000 ] ], + 14 => [ [ 150, 250, 5000 ], + [ 250, 250, 6000 ] ] } ); +($c0, $d0, $r0) = @{$rpoints{$p}->{$q}->[0]}; +($c1, $d1, $r1) = @{$rpoints{$p}->{$q}->[1]}; + +Context()->texStrings; +SOLUTION(EV3(<<'END_SOLUTION')); +$PAR SOLUTION $PAR + + +The revenue +function, \(R\), is linear and so we may write it as: +\[ R = (p_1)c + (p_2)d -```] -where [`p_1`] is the price of CDs and [`p_2`] is the price of DVDs, in +\] +where \(p_1\) is the price of CDs and \(p_2\) is the price of DVDs, in dollars. -From the diagram, we can pick two points, such as [`c = [$c0]`], [`d=[$d0]`] -on the contour [`R=[$r0]`], and [`c = [$c1]`], [`d = [$d1]`] on the contour -[`R = [$r1]`]. These +From the diagram, we can pick two points, such as \(c = $c0\), \(d=$d0\) +on the contour \(R=$r0\), and \(c = $c1\), \(d = $d1\) on the contour +\(R = $r1\). These points give the following system of linear equations: -[``` -[$r0] = [$c0] p_1 + [$d0] p_2, \mbox{ and } -[$r1] = [$c1] p_1 + [$d1] p_2. -```] -Solving gives [`p_1 = [$p]`] dollars and [`p_2 = [$q]`] dollars. -END_PGML_SOLUTION +\[ +$r0 = $c0 p_1 + $d0 p_2, \mbox{ and } +$r1 = $c1 p_1 + $d1 p_2. +\] +Solving gives \(p_1 = $p\) dollars and \(p_2 = $q\) dollars. + +END_SOLUTION +Context()->normalStrings; + +; ENDDOCUMENT(); diff --git a/OpenProblemLibrary/Michigan/Chap14Sec1/Q09.pg b/OpenProblemLibrary/Michigan/Chap14Sec1/Q09.pg index ca1217af11..565243329f 100644 --- a/OpenProblemLibrary/Michigan/Chap14Sec1/Q09.pg +++ b/OpenProblemLibrary/Michigan/Chap14Sec1/Q09.pg @@ -163,7 +163,8 @@ $fy[3] = PopUp( [ "?", "positive", "negative" ], ## we'll ask for three of these @ask = PGsort( sub { $_[0] < $_[1] }, NchooseK( 4, 3 ) ); - +$grAlt = "A contour plot with circles centered at the origin and the radius of successive circles shrinking."; +$grDescr = "A plot of circles centered at the origin. The smallest circle is labeled 6 and successively larger circles are labeled 9, 12, 15,18,21, 24. The difference in radius between successive circles is decreasing. A point labeled P is on the contour labeled 12 and in the first quadrant. A point labeled Q is on the contour labeled 12 and is in the fourth quadrant. A point labeled S is on the contour labeled 12 and in the second quadrant. A point labeled R is on the contour labeled 12 and is in the third quadrant."; Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -176,7 +177,7 @@ positive \(x\) value and negative \(y\), etc.) $PAR $BCENTER \{ image( insertGraph( $contour ), tex_size=>300, height=>300, width=>300, - extra_html_tags=>'alt="' . $grdesc . '"' ) \} + alt=>$grAlt, long_description=>$grDescr) \} $ECENTER $PAR ${BBOLD}(a)$EBOLD @@ -256,4 +257,4 @@ Context()->normalStrings; ; -ENDDOCUMENT(); +ENDDOCUMENT(); \ No newline at end of file diff --git a/OpenProblemLibrary/Michigan/Chap14Sec1/Q26.pg b/OpenProblemLibrary/Michigan/Chap14Sec1/Q26.pg index bcdfe05b63..85b5b0ccb7 100644 --- a/OpenProblemLibrary/Michigan/Chap14Sec1/Q26.pg +++ b/OpenProblemLibrary/Michigan/Chap14Sec1/Q26.pg @@ -131,6 +131,9 @@ $hw22 = Compute( "($happ{$t2}->{$w2a} - $happ{$t2}->{$w2})/0.1" ); $hw22a = Compute( "($happ{$t2}->{$w2} - $happ{$t2}->{$w2b})/0.1" ); $hw22b = Compute( "($happ{$t2}->{$w2a} - $happ{$t2}->{$w2b})/0.2" ); +$grAlt = "A contour map with four level curves"; +$grDescr = "A graph showing \(H(T,0.1), H(T,0.2), H(T,0.3), H(T,0.4)\), which are decreasing functions of \(T\), each at a higher value of \(H\). As \(H\) increases, the associated level curve is more concave up."; + Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -146,9 +149,7 @@ diagram, but shows cross-sections of \( H \) with \( w \) fixed at $PAR $BCENTER \{ image( insertGraph( $gr ), tex_size=>250, height=>350, width=>350, - extra_html_tags=>'alt="graph showing H(T,0.1), H(T,0.2), ' . - 'H(T,0.3) and H(T,0.4), which are decresaing functions ' . - 'of T, each at a higher value of H."' ) \} + alt=>$grAlt, long_description=>$grDescr) \} $ECENTER $PAR ${BBOLD}(a)$EBOLD @@ -295,4 +296,4 @@ Context()->normalStrings; ; -ENDDOCUMENT(); +ENDDOCUMENT(); \ No newline at end of file diff --git a/OpenProblemLibrary/Michigan/Chap16Sec1/Q03.pg b/OpenProblemLibrary/Michigan/Chap16Sec1/Q03.pg index 14de0d2868..412aa44df1 100644 --- a/OpenProblemLibrary/Michigan/Chap16Sec1/Q03.pg +++ b/OpenProblemLibrary/Michigan/Chap16Sec1/Q03.pg @@ -112,6 +112,9 @@ $tol = ($over - $under)/2; $overTest = Compute( "($oversum)*2*2 - $tol" )->with( tolType=>'absolute', tolerance=>($tol+1) ); $underTest = Compute( "($undersum)*2*2 + $tol" )->with( tolType=>'absolute', tolerance=>($tol+1) ); +$grAlt = "A contour plot of the function g"; +$grDescr = "A contour plot with horizontal range from 5 yo 11 and vertical range from 2 to 8. There are five contours labeled 2, 3, 4, 5, and 6 that are hyperbolas with the labels increasing across the graphs being further up and to the right."; + Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -121,8 +124,7 @@ The figure below shows contours of \( g(x,y) \) on the region $PAR $BCENTER \{ image( insertGraph( $gr ), height=>300, width=>300, tex_size=>300, - extra_html_tags=>'alt="contour graph showing the contours ' . - 'of the function."' ) \} + alt=>$grAlt, long_description=>$grDescr) \} $ECENTER $PAR Using \( \Delta x = \Delta y =2 \), find an overestimate and an diff --git a/OpenProblemLibrary/Michigan/Chap16Sec1/Q27.pg b/OpenProblemLibrary/Michigan/Chap16Sec1/Q27.pg index d05a212593..b66ce6311e 100644 --- a/OpenProblemLibrary/Michigan/Chap16Sec1/Q27.pg +++ b/OpenProblemLibrary/Michigan/Chap16Sec1/Q27.pg @@ -152,6 +152,9 @@ $avgint = Compute( "($max + $min)/2" ); $avg = Compute( "($max + $min)/50" ); $tolval = ($max - $min)/50 + 0.1; +$grAlt = "A contour plot of the temperature in a 5 by 5 meter room"; +$grDescr = "A contour plot with horizontal and vertical range from 0 to 5. There are ten contours labeled from 21 to 30 and the contours become more curved when moving away from the middle of the plot."; + Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -161,8 +164,8 @@ degrees C, in a 5 meter by 5 meter heated room. $PAR $BCENTER \{ image( insertGraph( $gr ), height=>300, width=>300, tex_size=>300, - extra_html_tags=>'alt="contour graph showing the temperatures ' . - 'in the room"' ) \} + alt=>$grAlt, long_description=>$grDescr) \} + $ECENTER Using Riemann sums, estimate the average temperature in the room. $BR @@ -227,4 +230,4 @@ Context()->normalStrings; ; -ENDDOCUMENT(); +ENDDOCUMENT(); \ No newline at end of file diff --git a/OpenProblemLibrary/Michigan/Chap16Sec4/Q07.pg b/OpenProblemLibrary/Michigan/Chap16Sec4/Q07.pg index 01102fe9dc..a6f4af8d8a 100644 --- a/OpenProblemLibrary/Michigan/Chap16Sec4/Q07.pg +++ b/OpenProblemLibrary/Michigan/Chap16Sec4/Q07.pg @@ -126,7 +126,7 @@ if( $whichSec < 3 ) { } @desc = ( "a rectangular region with diagonally opposite corners ($x0,$y0) " . - "and ($x1,y1).", + "and ($x1,$y1).", "a sector of a circle of radius $r0 centered at the origin, with " . "radial endpoints ($rcx0,$rcy0) and ($rcx1,$rcy1)." ); @@ -221,6 +221,8 @@ $chk[1] = MultiAnswer( Compute($sangles[$whichSec]->[0]), @order = NchooseK(2,2); +$grAlt = "A wedge shaped region"; +$grAlt2 = "A rectangular shaped region"; Context()->texStrings; TEXT(beginproblem()); @@ -236,7 +238,8 @@ The region $BR $BCENTER \{ image( insertGraph( $gr[$order[0]] ), tex_size=>250, height=>250, - width=>250, extra_html_tags=>'alt="' . $desc[$order[0]] . '"' ) \} + width=>250, alt=>$grAlt, long_description=>$desc[$order[0]]) \} + $ECENTER With \( a = \) \{ $chk[$order[0]]->ans_rule(5) \}, @@ -254,7 +257,7 @@ The region $BR $BCENTER \{ image( insertGraph( $gr[$order[1]] ), tex_size=>250, height=>250, - width=>250, extra_html_tags=>'alt="' . $desc[$order[1]] . '"' ) \} + width=>250, alt=>$grAlt2, long_description=>$desc[$order[1]]) \} $ECENTER With \( a = \) \{ $chk[$order[1]]->ans_rule(5) \}, diff --git a/OpenProblemLibrary/Michigan/Chap17Sec5/Q25.pg b/OpenProblemLibrary/Michigan/Chap17Sec5/Q25.pg index 4ddab23d8e..2b1969521b 100644 --- a/OpenProblemLibrary/Michigan/Chap17Sec5/Q25.pg +++ b/OpenProblemLibrary/Michigan/Chap17Sec5/Q25.pg @@ -105,6 +105,9 @@ $param = MultiAnswer( $xst, $yst, $zst, $s0, $s1, $t0, $t1 )->with( $vol = NumberWithUnits( "$n0*$po2*pi*(1 + 2*$rb*$rb)", "in^3" ); $volc = $n0*$po2*(1 + 2*$rb*$rb); +$grAlt = "A column that has a sinusoidal radius"; +$grDescr = "figure of a column with a vertically varying outside radius. the maximum radius is r0 inches, the vertical distance between maximum radii is a0 inches, and the difference between the minimum and maximum radii is 2 inches."; + Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -114,11 +117,7 @@ that its profile is sinusoidal as shown in the figure below. $BR $BCENTER \{ image( 'q15f1.png', tex_size=>200, height=>432, width=>173, - extra_html_tags=>'alt="figure of a column with a ' . - 'vertically varying outside radius. the maximum radius ' . - 'is r0 inches, the vertical distance between maximum ' . - 'radii is a0 inches, and the difference between the ' . - 'minimum and maximum radii is 2 inches."' ) \} + alt=>$grAlt, long_description=>$grDescr) \} $ECENTER $BR In this figure, \(r_0 = $r1\) inches and \(a_0 = $p0\) inches. diff --git a/OpenProblemLibrary/Michigan/Chap17Sec5/Q31.pg b/OpenProblemLibrary/Michigan/Chap17Sec5/Q31.pg index af881e9c04..4a3ac0d538 100644 --- a/OpenProblemLibrary/Michigan/Chap17Sec5/Q31.pg +++ b/OpenProblemLibrary/Michigan/Chap17Sec5/Q31.pg @@ -57,6 +57,8 @@ $s0 = Compute( "0" ); $s1 = Compute( "$r0" ); $t0 = Compute( "0" ); $t1 = Compute( "2*pi" ); +$grAlt = "A plot of a cone surface with vertex on the z-axis"; +$grDescr = "figure of a cone with circular base on the xy-plane, centered on the z-axis, and point on the positive z-axis."; Context()->texStrings; TEXT(beginproblem()); @@ -66,9 +68,8 @@ Consider the cone shown below. $BR $BCENTER \{ image( "q31fig.png", tex_size=>250, height=>280, width=>230, - extra_html_tags=>'alt="figure of a cone with circular base ' . - 'on the xy-plane, centered on the z-axis, and point on the ' . - 'positive z-axis."' ) \} + alt=>$grAlt, long_description=>$grDescr) \} + $ECENTER $BR If the height of the cone is $z0 and the base radius is $r0, write @@ -111,4 +112,4 @@ in terms of \(r\) and \(\theta\), as required in this problem. END_SOLUTION Context()->normalStrings; -ENDDOCUMENT(); +ENDDOCUMENT(); \ No newline at end of file diff --git a/OpenProblemLibrary/Michigan/Chap18Sec1/Q21.pg b/OpenProblemLibrary/Michigan/Chap18Sec1/Q21.pg index 0654298db5..5d7e4eed9f 100644 --- a/OpenProblemLibrary/Michigan/Chap18Sec1/Q21.pg +++ b/OpenProblemLibrary/Michigan/Chap18Sec1/Q21.pg @@ -128,7 +128,7 @@ for ( my $i=0; $i<3; $i++ ) { $invMap{$pickem[$i]} = $i; - $desc .= "Curve C" . ($i+1) . " is " . $curves[$pickem[$i]]->[3] . ". "; + $desc .= "Curve C" . ($i+1) . " is " . $curves[$pickem[$i]]->[3] . ". The vector field points with constant length horizontally to the left "; } ## then the popups are @@ -137,7 +137,7 @@ for ( my $i=0; $i<3; $i++ ) { $int1 = PopUp( [ @intdesc ], $intdesc[$invMap{$picked[0]} + 1] ); $int2 = PopUp( [ @intdesc ], $intdesc[$invMap{$picked[1]} + 1] ); $int3 = PopUp( [ @intdesc ], $intdesc[$invMap{$picked[2]} + 1] ); - +$grAlt = "A horizontal vector field with three linear segment paths"; Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -147,7 +147,7 @@ together with the paths \( C_1 \), \( C_2 \), and \( C_3 \). $PAR $BCENTER \{ image( insertGraph( $gr ), tex_size=>250, height=>250, width=>250, - extra_html_tags=>'alt="' . $desc . '"' ) \} + alt=>$grAlt, long_description=>$desc) \} $BR ${BITALIC}(${BBOLD}Note:$EBOLD For the vector field, vectors are shown with a dot at the ${BBOLD}tail$EBOLD of the vector.)$EITALIC diff --git a/OpenProblemLibrary/Michigan/Chap19Sec1/Q12.pg b/OpenProblemLibrary/Michigan/Chap19Sec1/Q12.pg index 4b608380d9..818cf55df4 100644 --- a/OpenProblemLibrary/Michigan/Chap19Sec1/Q12.pg +++ b/OpenProblemLibrary/Michigan/Chap19Sec1/Q12.pg @@ -53,6 +53,9 @@ $z0 = list_random(2,3,4); $flux = Compute( "$x0*($a*$z0 + $c*$x0)" ); +$grAlt = "A tilted plane in the first octant"; +$grDescr = "Figure showing part of a plane intersecting the yz-plane along the line segment between (0,0,b) and (0,a,b), and intersecting the xy-plane along the line segmentn between (a,0,0) and (a,a,0). The orientation is given by an arrow pointing from the part of the plane upwards with positive slope dz/dx."; + Context()->texStrings; TEXT(beginproblem()); BEGIN_TEXT @@ -64,12 +67,8 @@ assuming it is oriented as shown and that \(a = $x0\) and $BR $BCENTER \{ image( "q12fig.png", height=>280, width=>300, tex_size=>250, - extra_html_tags=>'alt="Figure showing part of a plane ' . - 'intersecting the yz-plane along the line segment between ' . - '(0,0,b) and (0,a,b), and intersecting the xy-plane along ' . - 'the line segmentn between (a,0,0) and (a,a,0). The ' . - 'orientation is given by an arrow pointing from the part ' . - 'of the plane upwards with positive slope dz/dx."' ) \} + alt=>$grAlt, long_description=>$grDescr) \} + $ECENTER $PAR flux = \{ ans_rule(35) \} diff --git a/OpenProblemLibrary/Michigan/Chap20Sec3/Q13.pg b/OpenProblemLibrary/Michigan/Chap20Sec3/Q13.pg index d378520c54..fcfb1ec827 100644 --- a/OpenProblemLibrary/Michigan/Chap20Sec3/Q13.pg +++ b/OpenProblemLibrary/Michigan/Chap20Sec3/Q13.pg @@ -103,11 +103,11 @@ $BR ${BCENTER} \{ begintable(3) \} \{ row( image( insertGraph($gr[0]), height=>250, width=>250, tex_size=>250, - extra_html_tags=>'alt="graph of the first vector field"' ), + alt=>"A vector field", long_description=>"A vector field with a slight counterclockwise rotation around the origin that increases in strength as the points get closer to the origin."), image( insertGraph($gr[1]), height=>250, width=>250, tex_size=>250, - extra_html_tags=>'alt="graph of the second vector field"' ), + alt=>"A vector field", long_description=>"A vector field symmetric about the horizontal axis that points to the right and down for positive y values and to the right and up for negative y values."), image( insertGraph($gr[2]), height=>250, width=>250, tex_size=>250, - extra_html_tags=>'alt="graph of the third vector field"' ) ) \} + alt=>"A vector field", long_description=>"A vector field symmetric about the vertical axis that points to the right and up for positive x values and to the left and up for negative x values.") ) \} \{ row( "${BBOLD}(a)$EBOLD", "${BBOLD}(b)$EBOLD", "${BBOLD}(c)$EBOLD" ) \} \{ endtable() \} ${ECENTER} diff --git a/OpenProblemLibrary/Michigan/Chap20Sec3/Q31.pg b/OpenProblemLibrary/Michigan/Chap20Sec3/Q31.pg index 513124c45b..38a0baee37 100644 --- a/OpenProblemLibrary/Michigan/Chap20Sec3/Q31.pg +++ b/OpenProblemLibrary/Michigan/Chap20Sec3/Q31.pg @@ -101,7 +101,7 @@ ${BITALIC}tail$EITALIC of each arrow. $BR $BCENTER \{ image( insertGraph( $gr ), height=>250, width=>250, tex_size=>250, - extra_html_tags=>'alt="graph of the vector field"' ) \} + alt=>"A vector field", long_description=>"A vector field that points to the right and up on the positive x axis, to the right and up on the positive y axis, to the left and down on the negative x axis, and to the left and down on negative y axis.") \} $ECENTER $PAR ${BBOLD}(a)$EBOLD diff --git a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.1_Vector_Fields/16.1.15.pg b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.1_Vector_Fields/16.1.15.pg index ba6bec4ccd..f477b72ee0 100644 --- a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.1_Vector_Fields/16.1.15.pg +++ b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.1_Vector_Fields/16.1.15.pg @@ -38,6 +38,8 @@ if ($perm[1]==2) {$answer='2'; $mc->qa("", "Plot 2"); $mc->extra("Plot 1", "Plot if ($perm[2]==2) {$answer='3'; $mc->qa("", "Plot 3"); $mc->extra("Plot 2", "Plot 1", "Plot 4");}; if ($perm[3]==2) {$answer='4'; $mc->qa("", "Plot 4"); $mc->extra("Plot 2", "Plot 3", "Plot 1");}; +$grAlt = ["A plot of a vector field","A plot of a vector field","A plot of a vector field","A plot of a vector field"]; +$grDescr = ["A vector field over the region from negative a to a. This vector field points up for points below the line y equals x and down above y equals x. This vector field points to the right for points above the line y equals negative x and to the left for points below the line y equals negative x.","A vector field over the region from negative a to a. This vector field points in a swirl around (a,0).", " A vector field over the region from negative a to a. This vector field points up for points above y equals 0 and down for points where y is less than 0. This vector field points to the right for points to the right of x equals negative 1 and to the left for points to the left of x equals negative one. "," A vector field over the region from negative a to a. This vector field points up for points above y equals 0 and down for points where y is less than 0. This vector field points to the right for all points. "]; BEGIN_TEXT \{ textbook_ref_exact("Rogawski ET 2e", "16.1","15") \} @@ -45,13 +47,13 @@ $PAR Match the planar vector field \(\mathbf{F} = \left< $a x + $a, y\right>\) with the corresponding plot in the Figures below. $PAR -\{image("image_16_1_15_$plot[$perm[0]].png", width=>194, height=>199)\} \(\Leftarrow\) $BBOLD Plot 1 \(\quad\) -\{image("image_16_1_15_$plot[$perm[1]].png", width=>194, height=>199)\} -\(\Leftarrow\)Plot 2 $PAR -\{image("image_16_1_15_$plot[$perm[2]].png", width=>194, height=>199)\} -\(\Leftarrow\)Plot 3 \(\quad\) -\{image("image_16_1_15_$plot[$perm[3]].png", width=>194, height=>199)\} -\(\Leftarrow\)Plot 4 $EBOLD $BR +\{image("image_16_1_15_$plot[$perm[0]].png", width=>194, height=>199, alt=>$grAlt[$perm[0]], long_description=>$grDescr[$perm[0]]) \} \(\Leftarrow\) Plot 1 \(\quad\) + +\{image("image_16_1_15_$plot[$perm[1]].png", width=>194, height=>199, alt=>$grAlt[$perm[1]], long_description=>$grDescr[$perm[1]])\} \(\Leftarrow\)Plot 2 $PAR + +\{image("image_16_1_15_$plot[$perm[2]].png", width=>194, height=>199, alt=>$grAlt[$perm[2]], long_description=>$grDescr[$perm[2]])\} \(\Leftarrow\)Plot 3 \(\quad\) + +\{image("image_16_1_15_$plot[$perm[3]].png", width=>194, height=>199, alt=>$grAlt[$perm[3]], long_description=>$grDescr[$perm[3]])\} \(\Leftarrow\)Plot 4 $BR With \(a=$a\) $PAR Answer : \{ $mc->print_a\} diff --git a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.2_Line_Integrals/16.2.41.pg b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.2_Line_Integrals/16.2.41.pg index 4c8e670c39..714dd31c87 100644 --- a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.2_Line_Integrals/16.2.41.pg +++ b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.2_Line_Integrals/16.2.41.pg @@ -40,6 +40,15 @@ $answerA=$sol[$perm[0]]; $answerB=$sol[$perm[1]]; $answerC=$sol[$perm[2]]; +$grAlt = "A vector field with a circle path in the middle"; +$grDescr = "A vector field that moves to the right and down for all points. The length of the vectors increases as you go up and to the right. The circular path is drawn in the middle. "; + +$grAlt2 = "A vector field with a circle path in the middle"; +$grDescr2 = "A vector field that moves horizontally for right for all points. The length of the vectors increases as you go to the right. The circular path is drawn in the middle. "; + +$grAlt3 = "A vector field with a circle path in the middle"; +$grDescr3 = "A vector field that points toward the middle of the circular path. The length of the vectors increases as you move away from the middle of the circular path."; + BEGIN_TEXT \{ textbook_ref_exact("Rogawski ET 2e", "16.2","41") \} $PAR @@ -49,11 +58,10 @@ each case, $BR determine whether the line integral around the circle $PAR Note: Use "0" for zero, "P" for positive, and "N" for negative. $PAR -\{image("image_16_2_13_$plot[$perm[0]].png", width=>167, height=>169)\} $BBOLD (A) \{ans_rule(2)\} $PAR -\{image("image_16_2_13_$plot[$perm[1]].png", width=>167, height=>169)\} -(B) \{ans_rule(2)\} $PAR -\{image("image_16_2_13_$plot[$perm[2]].png", width=>167, height=>169)\} -(C) \{ans_rule(2)\} $PAR +\{image("image_16_2_13_$plot[$perm[0]].png", width=>167, height=>169, alt=>$grAlt, long_description=>$grDescr) \} +$BBOLD (A) \{ans_rule(2)\} $PAR +\{image("image_16_2_13_$plot[$perm[1]].png", width=>167, height=>169, alt=>$grAlt2, long_description=>$grDescr2) \} (B) \{ans_rule(2)\} $PAR +\{image("image_16_2_13_$plot[$perm[2]].png", width=>167, height=>169, alt=>$grAlt3, long_description=>$grDescr3) \} (C) \{ans_rule(2)\} $PAR $EBOLD $PAR @@ -86,3 +94,4 @@ In the vector field below, the vector field is orthogonal to the unit tangent ve END_SOLUTION ENDDOCUMENT(); + diff --git a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.5_Surface_Integrals_of_Vector_Fields/16.5.3.pg b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.5_Surface_Integrals_of_Vector_Fields/16.5.3.pg index 5674cbd999..eb884af697 100644 --- a/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.5_Surface_Integrals_of_Vector_Fields/16.5.3.pg +++ b/OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/16_Line_and_Surface_Integrals/16.5_Surface_Integrals_of_Vector_Fields/16.5.3.pg @@ -44,6 +44,9 @@ $ee="\mathbf{e}"; TEXT('') if $displayMode eq 'HTML_jsMath'; +$grAlt = "A two by two grid of squares with center points of each square labeled A in the top left, B in the top right, C in the bottom left, and D in the bottom right."; +$grDescr = "A two by two grid of squares with center points of each square labeled A in the top left, B in the top right, C in the bottom left, and D in the bottom right."; + Context()->texStrings; BEGIN_TEXT @@ -57,7 +60,7 @@ field whose values at the labeled points are \[\begin{array}{llll} $FF(A) &= $faV,&\qquad $FF(B) &= $fbV\\ $FF(C) &= $fcV,&\qquad $FF(D) &= $fdV\end{array} \] -\{image("image_16_5_3.png", width=>163, height=>167)\} $PAR +\{image("image_16_5_3.png", width=>163, height=>167,alt=>$grAlt, long_description=>$grDescr)\} $PAR \(\iint_{$surf} $FF \cdot \,d\mathbf{S} \approx \) \{ans_rule()\} $PAR