document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109725>Question 109725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My daughters math problems are making me crazy, hope you can help me so I can help her.\r<BR>\n" );
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document.write( "Speed on a hill problem:  The maximum speed your car will go is a linear function of the steepness of the hill it is going up or down.  Suppose that the car can go a maximum of 63 mph up a 2 degree hill, and a max of 105 mph down a 5 degree hill.  (going downhill can be thought of as going up a hill at -5 degrees).<BR>\n" );
document.write( "a)  Write a particular equation expressing max speed in terms of steepness.<BR>\n" );
document.write( "b)  How fast could you go down a 7 degree hill?<BR>\n" );
document.write( "c)  If your top speed is 83 mph, how steep is the hill?  Is it up or down?<BR>\n" );
document.write( "d)  What does the speed-intercept equal, and what does it represent?<BR>\n" );
document.write( "e)  What does the steepness-intercept equal and what does it reprsent?<BR>\n" );
document.write( "f)  Sketch and label the graph using a reasonable domain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79974 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. Suppose that the car can go a maximum of 63 mph up a 2 degree hill, and a max of 105 mph down a 5 degree hill. (going downhill can be thought of as going up a hill at -5 degrees).<BR>\n" );
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document.write( "You have two points: (2,63) and (-5,105)<BR>\n" );
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document.write( "a) Write a particular equation expressing max speed in terms of steepness.<BR>\n" );
document.write( "slope = [105-63]/[-5-2] = 42/-7 = -6<BR>\n" );
document.write( "63 = -6*2+b<BR>\n" );
document.write( "b = 63+12<BR>\n" );
document.write( "b = +75<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "speed = -6(steepness)+75<BR>\n" );
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document.write( "b) How fast could you go down a 7 degree hill?<BR>\n" );
document.write( "speed = -6(-7)+75 <BR>\n" );
document.write( "speed = 42+75 = 117<BR>\n" );
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document.write( "c) If your top speed is 83 mph, how steep is the hill? Is it up or down?<BR>\n" );
document.write( "83 = -6(steepness)+75<BR>\n" );
document.write( "8 = -6(steepness)<BR>\n" );
document.write( "steepness = -4/3<BR>\n" );
document.write( "It's negative so it's down<BR>\n" );
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document.write( "d) What does the speed-intercept equal, and what does it represent?<BR>\n" );
document.write( "When the steepness is zero the maximum speed = 75 mph<BR>\n" );
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document.write( "e) What does the steepness-slope equal and what does it reprsent?<BR>\n" );
document.write( "When steepness increases one-degree max speed decreases by 6 mph<BR>\n" );
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document.write( "f) Sketch and label the graph using a reasonable domain.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C150%2C-6x%2B75%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C150%2C-6x%2B75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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