document.write( "Question 1142489: Hi Please help me.
\n" ); document.write( "1. The depth d of a liquid in a bottle with a hole of area 0.5 cm2 in its side can be approximated by
\n" ); document.write( "d = 0.0034t2 − 0.52518t + 20,
\n" ); document.write( "where t is the time since a stopper was removed from the hole. When will the depth be 1 cm? Round to the nearest tenth of a second.\r
\n" ); document.write( "\n" ); document.write( "2. A small pipe can fill a tank in 9 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 6 min. How long would it take each pipe, working alone, to fill the tank?\r
\n" ); document.write( "\n" ); document.write( "3. A car travels 238 mi. A second car, traveling 9 mph faster than the first car, makes the same trip in 1 h less time. Find the speed of each car.\r
\n" ); document.write( "\n" ); document.write( "4. A homeowner hires a mason to lay a brick border around a rectangular patio that measures 8 ft by 10 ft. If the total area of the patio and border is 168 ft2, what is the width of the border?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #763196 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "1.   d = 0.0034t2 − 0.52518t + 20.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     To find \" t \" when the depth \"d\" is equal to 1 cm, you need to solve the quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "         0.0034t2 − 0.52518t + 20 = 1.\r\n" );
document.write( "\r\n" );
document.write( "     To solve this equation, first write it in the standard form and then use the quadratic formula.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     If you don't know how to use the quadratic formula, learn it from the lessons\r\n" );
document.write( "\r\n" );
document.write( "          - Introduction into Quadratic Equations\r\n" );
document.write( "\r\n" );
document.write( "          - PROOF of quadratic formula by completing the square\r\n" );
document.write( "\r\n" );
document.write( "     in this site.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Let \" t \" be the time for the larger pipe to fill the tank working alone.\r\n" );
document.write( "\r\n" );
document.write( "    Then the time to fill the tank for the smaller pipe is (t+9) minutes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Now, in one minute the larger pipe fills        of the tank volume;\r\n" );
document.write( "\r\n" );
document.write( "                       the smaller pipe fills   of the tank volume.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Working together, the two pipes fill   +   of the tank volume per minute.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     From the other side,  the two pipes, working together, fill    of the tank volume, according to the condition.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It gives you an equation\r\n" );
document.write( "\r\n" );
document.write( "         +  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    To solve it, multiply both sides by 6t*(t+9). You will get\r\n" );
document.write( "\r\n" );
document.write( "        6(t+9) + 6t = t*(t+9).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Transform this equation to the standard form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         6t + 54 + 6t = t^2 + 9t\r\n" );
document.write( "\r\n" );
document.write( "         t^2 - 3t - 54 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Now you can solve it by factoring\r\n" );
document.write( "\r\n" );
document.write( "         (t-9)*(t+6) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     It has two roots t= -6  and  t= 9.\r\n" );
document.write( "\r\n" );
document.write( "     Of these two roots, only positive t= 9 is the valid solution to the problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     ANSWER.  Large pipe can fill the tank in 9 minutes, working alone.\r\n" );
document.write( "\r\n" );
document.write( "              Small pipe can fill the tank in (9+9) = 18 minutes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     CHECK.   +  =  =  = .    ! Correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The rule of this forum is THIS :\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

ONE and ONLY ONE problem per post.

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not put more than one problem into your posts.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you do it, you CAN NOT expect to get full scale solutions to each of your problem, and the tutors' posts become unreadable.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Respect your tutors, respect yourself and respect the rules of this forum.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Happy learning !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );