document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185369>Question 1185369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that\r<BR>\n" );
document.write( "\n" );
document.write( "L{cos(7t)/sqrt(πt)}=e^(−7/s)/sqrt(s)\r<BR>\n" );
document.write( "\n" );
document.write( "find the Laplace transform of sqrt(t/π)cos(7t).\r<BR>\n" );
document.write( "\n" );
document.write( "L{sqrt(t/π)cos(7t)}= \r<BR>\n" );
document.write( "\n" );
document.write( "My answer (cos(3/2tan^(-1)(7/s)))/(2(s^2+49)^(3/4)) , but is wrong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817047 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%28cos%287t%29%2Fsqrt%28pi%2At%29%29+=+e%5E%28-7%2Fs%29%2Fsqrt%28s%29 ALIGN=MIDDLE  ALT=\"L%28cos%287t%29%2Fsqrt%28pi%2At%29%29+=+e%5E%28-7%2Fs%29%2Fsqrt%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28cos%287t%29%2Fsqrt%28pi%2At%29%29%2Ae%5E%28-st%29%2C+dt%2C+0%2C+infinity%29+=+e%5E%28-7%2Fs%29%2Fsqrt%28s%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, by applying the definition of the Laplace transform to the hypothesis.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fds%29int%28%28cos%287t%29%2Fsqrt%28pi%2At%29%29%2Ae%5E%28-st%29%2C+dt%2C+0%2C+infinity%29+=+%28d%2Fds%29%28e%5E%28-7%2Fs%29%2Fsqrt%28s%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, i.e., taking derivatives wrt s.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28cos%287t%29%2Fsqrt%28pi%2At%29%29%2Ae%5E%28-st%29%2A%28-t%29%2C+dt%2C+0%2C+infinity%29+=+-int%28%28sqrt%28t%2Fpi%29%29%2A+cos%287t%29+%2Ae%5E%28-st%29%2C+dt%2C+0%2C+infinity%29=+%28sqrt%28s%29%2Ae%5E%28-7%2Fs%29%2A%287%2Fs%5E2%29+-+e%5E%28-7%2Fs%29%2A%281%2F%282sqrt%28s%29%29%29%29%2Fs+=+e%5E%28-7%2Fs%29%2A%287%2Fs%5E%285%2F2%29+-+1%2F%282s%5E%283%2F2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28sqrt%28t%2Fpi%29%29%2A+cos%287t%29+%2Ae%5E%28-st%29%2C+dt%2C+0%2C+infinity%29+=++e%5E%28-7%2Fs%29%2A%28+1%2F%282s%5E%283%2F2%29%29+-+7%2Fs%5E%285%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%28sqrt%28t%2Fpi%29%2A+cos%287t%29++%29+=++e%5E%28-7%2Fs%29%2A%28+1%2F%282s%5E%283%2F2%29%29+-+7%2Fs%5E%285%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );