Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems/Problem 11"
(Created page with "== Problem == The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temper...") |
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The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range? | The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range? | ||
| − | <math>\text{(A)}\ Monday \qquad \text{(B)}\ Tuesday \qquad \text{(C)}\ Wednesday \qquad \text{(D)}\ Thursday \qquad \text{(E)}\ Friday</math> | + | <math>\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Thursday} \qquad \text{(E)}\ \text{Friday}</math> |
<asy> | <asy> | ||
size(300); | size(300); | ||
draw((0,-10)--(0,10),EndArrow); | draw((0,-10)--(0,10),EndArrow); | ||
| − | draw((0,0)--(16,0),EndArrow); | + | // Comments this line out for reading purposes |
| + | //draw((0,0)--(16,0),EndArrow); | ||
| + | draw((0,0)--(16,0),arrow=Arrow(TeXHead));//smaller arrowhead | ||
picture temp; | picture temp; | ||
label(temp,"Temperature ($^\circ$C)"); | label(temp,"Temperature ($^\circ$C)"); | ||
| Line 24: | Line 26: | ||
label(Thurs,"Thurs."); | label(Thurs,"Thurs."); | ||
add(rotate(90)*Thurs,(8,5.4)); | add(rotate(90)*Thurs,(8,5.4)); | ||
| − | picture Fri; | + | |
| − | label(Fri,"Fri."); | + | //picture Fri; |
| − | add(rotate(90)*Fri,(10,9)); | + | //label(Fri,"Fri."); |
| + | //add(rotate(90)*Fri,(10,9)); | ||
| + | MP(90,"\textup{ Fri.}",(10,8),N);//MarkPoint(Rotation,Label,Coordinates) textup(upright no-italics) | ||
draw((-0.3,-8)--(0.3,-8)); | draw((-0.3,-8)--(0.3,-8)); | ||
draw((-0.3,-6)--(0.3,-6)); | draw((-0.3,-6)--(0.3,-6)); | ||
| Line 33: | Line 37: | ||
draw((-0.3,2)--(0.3,2)); | draw((-0.3,2)--(0.3,2)); | ||
draw((-0.3,4)--(0.3,4)); | draw((-0.3,4)--(0.3,4)); | ||
| − | draw((-0.3,6)--(0.3,6)); | + | //draw((-0.3,6)--(0.3,6)); |
| − | draw((-0.3,8)--(0.3,8)); | + | //draw((-0.3,8)--(0.3,8)); |
| + | path Tick=((-.3,0)--(.3,0));draw(shift(0,6)*Tick);draw(shift(0,8)*Tick); | ||
dot((2,6)); | dot((2,6)); | ||
dot((4,3)); | dot((4,3)); | ||
| Line 44: | Line 49: | ||
draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle); | draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle); | ||
draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle); | draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle); | ||
| − | draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle); | + | //draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle); |
| + | path Square=((-.2,-.2)--(-.2,.2)--(.2,.2)--(.2,-.2)--cycle); | ||
| + | filldraw(shift(10,0)*Square,white);// this hides the x-axis behind white filling -- try green | ||
label("-8",(-0.3,-8),W); | label("-8",(-0.3,-8),W); | ||
label("-6",(-0.3,-6),W); | label("-6",(-0.3,-6),W); | ||
Revision as of 23:12, 22 October 2014
Problem
The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?
![[asy] size(300); draw((0,-10)--(0,10),EndArrow); // Comments this line out for reading purposes //draw((0,0)--(16,0),EndArrow); draw((0,0)--(16,0),arrow=Arrow(TeXHead));//smaller arrowhead picture temp; label(temp,"Temperature ($^\circ$C)"); add(rotate(90)*temp,(-2,0)); picture mon; label(mon,"Mon."); add(rotate(90)*mon,(2,7.3)); picture tues; label(tues,"Tues."); add(rotate(90)*tues,(4,4.3)); picture Wed; label(Wed,"Wed."); add(rotate(90)*Wed,(6,5.3)); picture Thurs; label(Thurs,"Thurs."); add(rotate(90)*Thurs,(8,5.4)); //picture Fri; //label(Fri,"Fri."); //add(rotate(90)*Fri,(10,9)); MP(90,"\textup{ Fri.}",(10,8),N);//MarkPoint(Rotation,Label,Coordinates) textup(upright no-italics) draw((-0.3,-8)--(0.3,-8)); draw((-0.3,-6)--(0.3,-6)); draw((-0.3,-4)--(0.3,-4)); draw((-0.3,-2)--(0.3,-2)); draw((-0.3,2)--(0.3,2)); draw((-0.3,4)--(0.3,4)); //draw((-0.3,6)--(0.3,6)); //draw((-0.3,8)--(0.3,8)); path Tick=((-.3,0)--(.3,0));draw(shift(0,6)*Tick);draw(shift(0,8)*Tick); dot((2,6)); dot((4,3)); dot((6,4)); dot((8,4)); dot((10,8)); draw((1.8,-3.8)--(2.2,-3.8)--(2.2,-4.2)--(1.8,-4.2)--cycle); draw((3.8,-5.8)--(4.2,-5.8)--(4.2,-6.2)--(3.8,-6.2)--cycle); draw((5.8,-1.8)--(6.2,-1.8)--(6.2,-2.2)--(5.8,-2.2)--cycle); draw((7.8,-4.8)--(8.2,-4.8)--(8.2,-5.2)--(7.8,-5.2)--cycle); //draw((9.8,0.2)--(10.2,0.2)--(10.2,-0.2)--(9.8,-0.2)--cycle); path Square=((-.2,-.2)--(-.2,.2)--(.2,.2)--(.2,-.2)--cycle); filldraw(shift(10,0)*Square,white);// this hides the x-axis behind white filling -- try green label("-8",(-0.3,-8),W); label("-6",(-0.3,-6),W); label("-4",(-0.3,-4),W); label("-2",(-0.3,-2),W); label("0",(-0.3,0),W); label("2",(-0.3,2),W); label("4",(-0.3,4),W); label("6",(-0.3,6),W); label("8",(-0.3,8),W); dot((12,-6.5)); label("Daily High",(12,-6.5),E); draw((11.8,-7.7)--(11.8,-7.3)--(12.2,-7.3)--(12.2,-7.7)--cycle); label("Daily Low",(12,-7.5),E); [/asy]](http://latex.artofproblemsolving.com/4/5/1/45181873ab5def18ecc7b0be1b1b95d3dd13b09f.png)
Solution
On each day, the temperature range is the difference between the daily high and daily low temperatures.
On Monday, the range is 
degrees Celsius.
On Tuesday, the range is 
degrees Celsius.
On Wednesday, the range is 
degrees Celsius.
On Thursday, the range is 
degrees Celsius.
On Friday, the range is 
degrees Celsius.
The day with the greatest range is Monday. Therefore, the answer is 
.
