Facit

Sommarmatte 1

(Skillnad mellan versioner)
Hoppa till: navigering, sök
Versionen från 16 juli 2007 kl. 09.32 (redigera)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

← Gå till föregående ändring
Nuvarande version (17 juli 2007 kl. 11.00) (redigera) (ogör)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

 
(4 mellanliggande versioner visas inte.)
Rad 1: Rad 1:
__NOTOC__ __NOTOC__
'''Svar 1.1:1''' '''Svar 1.1:1'''
-<div class="ovning" style="margin-top:-15px; margin-bottom:-5px;">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 19: Rad 19:
'''Svar 1.1:2''' '''Svar 1.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 37: Rad 37:
'''Svar 1.1:3''' '''Svar 1.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left" valign="top"> <tr align="left" valign="top">
Rad 75: Rad 75:
'''Svar 1.1:4''' '''Svar 1.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 93: Rad 93:
'''Svar 1.1:5''' '''Svar 1.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 110: Rad 110:
'''Svar 1.1:6''' '''Svar 1.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 132: Rad 132:
'''Svar 1.2:1''' '''Svar 1.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 152: Rad 152:
'''Svar 1.2:2''' '''Svar 1.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 170: Rad 170:
'''Svar 1.2:3''' '''Svar 1.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
Rad 183: Rad 183:
'''Svar 1.2:4''' '''Svar 1.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 197: Rad 197:
'''Svar 1.2:5''' '''Svar 1.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
Rad 212: Rad 212:
'''Svar 1.2:6''' '''Svar 1.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table> <table width="100%"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table>
</div> </div>
'''Svar 1.3:1''' '''Svar 1.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 233: Rad 233:
'''Svar 1.3:2''' '''Svar 1.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 247: Rad 247:
'''Svar 1.3:3''' '''Svar 1.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 265: Rad 265:
'''Svar 1.3:4''' '''Svar 1.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 285: Rad 285:
'''Svar 1.3:5''' '''Svar 1.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 307: Rad 307:
'''Svar 1.3:6''' '''Svar 1.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 329: Rad 329:
'''Svar 2.1:1''' '''Svar 2.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 357: Rad 357:
'''Svar 2.1:2''' '''Svar 2.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 379: Rad 379:
'''Svar 2.1:3''' '''Svar 2.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 401: Rad 401:
'''Svar 2.1:4''' '''Svar 2.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 419: Rad 419:
'''Svar 2.1:5''' '''Svar 2.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 437: Rad 437:
'''Svar 2.1:6''' '''Svar 2.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 455: Rad 455:
'''Svar 2.1:7''' '''Svar 2.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 469: Rad 469:
'''Svar 2.1:8''' '''Svar 2.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 483: Rad 483:
'''Svar 2.2:1''' '''Svar 2.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 501: Rad 501:
'''Svar 2.2:2''' '''Svar 2.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 519: Rad 519:
'''Svar 2.2:3''' '''Svar 2.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 541: Rad 541:
'''Svar 2.2:4''' '''Svar 2.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 556: Rad 556:
'''Svar 2.2:5''' '''Svar 2.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 582: Rad 582:
'''Svar 2.2:6''' '''Svar 2.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 604: Rad 604:
'''Svar 2.2:7''' '''Svar 2.2:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 619: Rad 619:
'''Svar 2.2:8''' '''Svar 2.2:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 634: Rad 634:
'''Svar 2.2:9''' '''Svar 2.2:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 653: Rad 653:
'''Svar 2.3:1''' '''Svar 2.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 669: Rad 669:
'''Svar 2.3:2''' '''Svar 2.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 691: Rad 691:
'''Svar 2.3:3''' '''Svar 2.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 715: Rad 715:
'''Svar 2.3:4''' '''Svar 2.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 733: Rad 733:
'''Svar 2.3:5''' '''Svar 2.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 751: Rad 751:
'''Svar 2.3:6''' '''Svar 2.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 765: Rad 765:
'''Svar 2.3:7''' '''Svar 2.3:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 779: Rad 779:
'''Svar 2.3:8''' '''Svar 2.3:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 789: Rad 789:
'''Svar 2.3:9''' '''Svar 2.3:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 803: Rad 803:
'''Svar 2.3:10''' '''Svar 2.3:10'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 811: Rad 811:
</div> </div>
'''Svar 3.1:1''' '''Svar 3.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 827: Rad 827:
'''Svar 3.1:2''' '''Svar 3.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 853: Rad 853:
'''Svar 3.1:3''' '''Svar 3.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 871: Rad 871:
'''Svar 3.1:4''' '''Svar 3.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 889: Rad 889:
'''Svar 3.1:5''' '''Svar 3.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 905: Rad 905:
'''Svar 3.1:6''' '''Svar 3.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 923: Rad 923:
'''Svar 3.1:7''' '''Svar 3.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 937: Rad 937:
'''Svar 3.1:8''' '''Svar 3.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 955: Rad 955:
'''Svar 3.2:1''' '''Svar 3.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 964: Rad 964:
'''Svar 3.2:2''' '''Svar 3.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 973: Rad 973:
'''Svar 3.2:3''' '''Svar 3.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 982: Rad 982:
'''Svar 3.2:4''' '''Svar 3.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 991: Rad 991:
'''Svar 3.2:5''' '''Svar 3.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 000: Rad 1 000:
'''Svar 3.2:6''' '''Svar 3.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 009: Rad 1 009:
'''Svar 3.3:1''' '''Svar 3.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 027: Rad 1 027:
'''Svar 3.3:2''' '''Svar 3.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 053: Rad 1 053:
'''Svar 3.3:3''' '''Svar 3.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 081: Rad 1 081:
'''Svar 3.3:4''' '''Svar 3.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 095: Rad 1 095:
'''Svar 3.3:5''' '''Svar 3.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 117: Rad 1 117:
'''Svar 3.3:6''' '''Svar 3.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%" > <table width="100%" >
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
Rad 1 136: Rad 1 136:
'''Svar 3.4:1''' '''Svar 3.4:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 150: Rad 1 150:
'''Svar 3.4:2''' '''Svar 3.4:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 164: Rad 1 164:
'''Svar 3.4:3''' '''Svar 3.4:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 180: Rad 1 180:
'''Svar 4.1:1''' '''Svar 4.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 198: Rad 1 198:
'''Svar 4.1:2''' '''Svar 4.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 214: Rad 1 214:
'''Svar 4.1:3''' '''Svar 4.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 228: Rad 1 228:
'''Svar 4.1:4''' '''Svar 4.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 246: Rad 1 246:
'''Svar 4.1:5''' '''Svar 4.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 260: Rad 1 260:
'''Svar 4.1:6''' '''Svar 4.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 276: Rad 1 276:
'''Svar 4.1:7''' '''Svar 4.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 296: Rad 1 296:
'''Svar 4.1:8''' '''Svar 4.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 306: Rad 1 306:
'''Svar 4.1:9''' '''Svar 4.1:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 316: Rad 1 316:
'''Svar 4.1:10''' '''Svar 4.1:10'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 325: Rad 1 325:
'''Svar 4.2:1''' '''Svar 4.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Facit till alla delfrågor<br \> Facit till alla delfrågor<br \>
<table width="100%"> <table width="100%">
Rad 1 350: Rad 1 350:
'''Svar 4.2:2''' '''Svar 4.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 374: Rad 1 374:
'''Svar 4.2:3''' '''Svar 4.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 396: Rad 1 396:
'''Svar 4.2:4''' '''Svar 4.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 418: Rad 1 418:
'''Svar 4.2:5''' '''Svar 4.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 434: Rad 1 434:
'''Svar 4.2:6''' '''Svar 4.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 443: Rad 1 443:
'''Svar 4.2:7''' '''Svar 4.2:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 453: Rad 1 453:
'''Svar 4.2:8''' '''Svar 4.2:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 462: Rad 1 462:
'''Svar 4.2:9''' '''Svar 4.2:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 471: Rad 1 471:
'''Svar 4.3:1''' '''Svar 4.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 485: Rad 1 485:
'''Svar 4.3:2''' '''Svar 4.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 497: Rad 1 497:
'''Svar 4.3:3''' '''Svar 4.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 521: Rad 1 521:
'''Svar 4.3:4''' '''Svar 4.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 545: Rad 1 545:
'''Svar 4.3:5''' '''Svar 4.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 554: Rad 1 554:
'''Svar 4.3:6''' '''Svar 4.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 572: Rad 1 572:
'''Svar 4.3:7''' '''Svar 4.3:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 586: Rad 1 586:
'''Svar 4.3:8''' '''Svar 4.3:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 596: Rad 1 596:
'''Svar 4.3:9''' '''Svar 4.3:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 606: Rad 1 606:
'''Svar 4.4:1''' '''Svar 4.4:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 634: Rad 1 634:
'''Svar 4.4:2''' '''Svar 4.4:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 677: Rad 1 677:
'''Svar 4.4:3''' '''Svar 4.4:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 715: Rad 1 715:
'''Svar 4.4:4''' '''Svar 4.4:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%" cellpadding="10px"> <table width="100%" cellpadding="10px">
<tr> <tr>
Rad 1 726: Rad 1 726:
'''Svar 4.4:5''' '''Svar 4.4:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 738: Rad 1 738:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td> <td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 752: Rad 1 750:
'''Svar 4.4:6''' '''Svar 4.4:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 766: Rad 1 764:
x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$ x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$
</td> </td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 780: Rad 1 776:
'''Svar 4.4:7''' '''Svar 4.4:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 793: Rad 1 789:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $</td> <td class="ntext" width="50%">$x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 807: Rad 1 801:
'''Svar 4.4:8''' '''Svar 4.4:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 820: Rad 1 814:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\displaystyle \frac{\pi}{3}+n\pi$</td> <td class="ntext" width="50%">$x=\displaystyle \frac{\pi}{3}+n\pi$</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 832: Rad 1 824:
</table> </table>
</div> </div>
 +
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br>

Nuvarande version

Svar 1.1:1

a)    $-7$ b)    $1$
c)    $11$ d)    $1$

Svar 1.1:2

a)    $0$ b)    $-1$
c)    $-25$ d)    $-19$

Svar 1.1:3

a)    naturliga talen, heltalen, rationella talen b)    heltalen, rationella talen c)    naturliga talen, heltalen, rationella talen
d)    heltalen, rationella talen e)    heltalen, rationella talen f)    naturliga talen, heltalen, rationella talen
g)    rationella talen h)    naturliga talen, heltalen, rationella talen i)    irrationella talen
j)    naturliga talen, heltalen, rationella talen k)    irrationella talen l) irrationella talen

Svar 1.1:4

a)    $\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$
b)    $\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$
c)    $\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$

Svar 1.1:5

a)    $1{,}167$ b)    $2{,}250$ c)    $0{,}286$ d)    $1{,}414$

Svar 1.1:6

a)    Talet är rationellt och lika med $\,314/100 = 157/50\,$.
b)    Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.
c)    Talet är rationellt och lika med $\,1999/9990\,$.
d)    Talet är irrationellt.

Svar 1.2:1

a)    $\displaystyle \frac{93}{28}$ b)    $\displaystyle \frac{3}{35}$ c)    $\displaystyle -\frac{7}{30}$
d)    $\displaystyle \frac{47}{60}$ e)    $\displaystyle \frac{47}{84}$

Svar 1.2:2

a)    $\displaystyle {30}$ b)    $\displaystyle {8}$
c)    $\displaystyle {84}$ d)    $\displaystyle {225}$

Svar 1.2:3

a)    $\displaystyle \frac{19}{100}$ b)    $\displaystyle \frac{1}{240}$

Svar 1.2:4

a)    $\displaystyle \frac{6}{7}$ b)    $\displaystyle \frac{16}{21}$ c)    $\displaystyle \frac{1}{6}$

Svar 1.2:5

a)    $\displaystyle \frac{105}{4}$ b)    $-5$ c)    $\displaystyle \frac{8}{55}$

Svar 1.2:6

$\displaystyle \frac{152}{35}$

Svar 1.3:1

a)    $72$ b)    $3$ c)    $-125$ d)    $\displaystyle \frac{27}{8}$

Svar 1.3:2

a)    $2^6$ b)    $2^{-2}$ c)    $2^0$

Svar 1.3:3

a)    $3^{-1}$ b)    $3^5$ c)    $3^4$ d)    $3^{-3}$ e)    $3^{-3}$

Svar 1.3:4

a)    $4$ b)    $3$ c)    $625$
d)    $16$ e)    $\displaystyle \frac{1}{3750}$

Svar 1.3:5

a)    $2$ b)    $\displaystyle \frac{1}{2}$ c)    $27$
d)    $2209$ e)    $9$ f)    $\displaystyle \frac{25}{3}$

Svar 1.3:6

a)    $256^{1/3}>200^{1/3}$ b)    $0{,}4^{-3}>0{,}5^{-3}$ c)    $0{,}2^{5}>0{,}2^{7}$
d)    $\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$ e)    $125^{1/2}>625^{1/3}$ f)    $3^{40}>2^{56}$

Svar 2.1:1

a)    $3x^2-3x$ b)    $xy+x^2y-x^3y$ c)    $-4x^2+x^2y^2$
d)    $x^3y-x^2y+x^3y^2$ e)    $x^2-14x+49$ f)    $16y^2+40y+25$
g)    $9x^6-6x^3y^2+y^4$ h)    $9x^{10}+30x^8+25x^6$

Svar 2.1:2

a)    $-5x^2+20$ b)    $10x-11$
c)    $54x$ d)    $81x^8-16$
e)    $2a^2+2b^2$

Svar 2.1:3

a)    $(x+6)(x-6)$ b)    $5(x+2)(x-2)$ c)    $(x+3)^2$
d)    $(x-5)^2$ e)    $-2x(x+3)(x-3)$ f)    $(4x+1)^2$

Svar 2.1:4

a)    $5\,$ framför $\,x^2\,$, $\,3\,$ framför $\,x$
b)    $2\,$ framför $\,x^2\,$, $\,1\,$ framför $\,x$
$\textrm{c)    }$ $6\,$ framför $\,x^2\,$, $\,2\,$ framför $\,x$

Svar 2.1:5

a)    $\displaystyle \frac{1}{1-x}$ b)    $-\displaystyle \frac{1}{y(y+2)}$
c)    $3(x-2)(x-1)$ d)    $\displaystyle \frac{2(y+2)}{y^2+4}$

Svar 2.1:6

a)    $2y$ b)    $\displaystyle\frac{-x+12}{(x-2)(x+3)}$
c)    $\displaystyle\frac{b}{a(a-b)   }$ d)    $\displaystyle\frac{a(a+b)   }{4b}$

Svar 2.1:7

a)    $\displaystyle \frac{4}{(x+3)(x+5)}$ b)    $\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$ c)    $\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$

Svar 2.1:8

a)    $\displaystyle \frac{x}{(x+3)(x+1)}$ b)    $\displaystyle \frac{2(x-3)}{x}$ c)    $\displaystyle \frac{x+2}{2x+3}$

Svar 2.2:1

a)    $x=1$ b)    $x=6$
c)    $x=-\displaystyle\frac{3}{2}$ d)    $x=-\displaystyle\frac{13}{3}$

Svar 2.2:2

a)    $x=1$ b)    $x=\displaystyle\frac{5}{3}$
c)    $x=2$ d)    $x=-2$

Svar 2.2:3

a)    $x=9$
b)    $x=\displaystyle\frac{7}{5}$
c)    $x=\displaystyle\frac{4}{5}$
d)    $x=\displaystyle\frac{1}{2}$

Svar 2.2:4

a)    $-2x+y=3$
b)    $y=-\displaystyle\frac{3}{4}x+\frac{5}{4}$

Svar 2.2:5

a)    $y=-3x+9$
b)    $y=-3x+1$
c)    $y=3x+5$
d)    $y=-\displaystyle \frac{1}{2}x+5$
e)    $k = \displaystyle\frac{8}{5}$

Svar 2.2:6

a)    $\bigl(-\frac{5}{3},0\bigr)$ b)    $(0,5)$
c)    $\bigl(0,-\frac{6}{5}\bigr)$ d)    $(12,-13)$
e)    $\bigl(-\frac{1}{4},\frac{3}{2}\bigr)$

Svar 2.2:7

a)    Bild:Svar_o2_2_7a.gif‎ b)    Bild:Svar_o2_2_7b.gif‎
c)    Bild:Svar_o2_2_7c.gif‎

Svar 2.2:8

a)    Bild:Svar_o2_2_8a.gif‎ b)    Bild:Svar_o2_2_8b.gif‎
c)    Bild:Svar_o2_2_8c.gif‎

Svar 2.2:9

a)    $4\,$ a.e.
b)    $5\,$ a.e.
c)    $6\,$ a.e.


Svar 2.3:1

a)    $(x-1)^2-1$ b)    $(x+1)^2-2$ c)    $-(x-1)^2+6$ d)    $\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$

Svar 2.3:2

a)    $\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right.$ b)    $\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right.$ c)    saknar (reella)    lösning
d)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right.$ e)    $\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right.$ f)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right.$

Svar 2.3:3

a)    $\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right.$ b)    $\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. $
c)    $\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. $ d)    $\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. $
e)    $\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. $ f)    $\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. $

Svar 2.3:4

a)    $ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
b)    $ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
c)    $ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.

Svar 2.3:5

a)    Exempelvis $\ x^2+14x+49=0\,$.
b)    $3< x<4$
c)    $b=-5$

Svar 2.3:6

a)    $0$ b)    $-2$ c)    $\displaystyle \frac{3}{4}$

Svar 2.3:7

a)    $1$ b)    $\displaystyle -\frac{7}{4}$ c)    saknar max

Svar 2.3:8

Se lösningen i webmaterialet när du loggat in till kursen.

Svar 2.3:9

a)    $(-1,0)\ $ och $\ (1,0)$ b)    $(2,0)\ $ och $\ (3,0)$ c)    $(1,0)\ $ och $\ (3,0)$

Svar 2.3:10

Se lösningen i webmaterialet när du loggat in till kursen

Svar 3.1:1

a)    $2^{1/2}$ b)    $7^{5/2}$ c)    $3^{4/3}$ d)    $3^{1/4}$

Svar 3.1:2

a)    $3$ b)    $3$ c)    ej definierad d)    $5^{11/6}$
e)    $12$ f)    $2$ g)    $-5$

Svar 3.1:3

a)    $3$ b)    $\displaystyle \frac{4\sqrt{3}}{3}$
c)    $2\sqrt{5}$ d)    $2-\sqrt{2}$

Svar 3.1:4

a)    $0{,}4$ b)    $0{,}3$
c)    $-4\sqrt{2}$ d)    $2\sqrt{3}$

Svar 3.1:5

a)    $\displaystyle \frac{\sqrt{3}}{3}$ b)    $\displaystyle \frac{7^{2/3}}{7}$ c)    $3-\sqrt{7}$ d)    $\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$

Svar 3.1:6

a)    $6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$ b)    $-\displaystyle \frac{5+4\sqrt{3}}{23}$
c)    $\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$ d)    $\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$

Svar 3.1:7

a)    $\sqrt{5}-\sqrt{7}$ b)    $-\sqrt{35}$ c)    $\sqrt{17}$

Svar 3.1:8

a)    $\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$ b)    $7 > \sqrt7$
c)    $\sqrt7 > 2{,}5$ d)    $\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$

Svar 3.2:1

$x=5$

Svar 3.2:2

$x=1$

Svar 3.2:3

$\left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right.$

Svar 3.2:4

Saknar lösning.

Svar 3.2:5

$x=1$

Svar 3.2:6

$x=\displaystyle\frac{5}{4}$

Svar 3.3:1

a)    $x=3$ b)    $x=-1$
c)    $x=-2$ d)    $x=4$

Svar 3.3:2

a)    $-1$ b)    $4$ c)    $-3$ d)    $0$
e)    $2$ f)    $3$ g)    $10$ h)    $-2$

Svar 3.3:3

a)    $3$ b)    $-\displaystyle \frac{1}{2}$ c)    $-3$
d)    $\displaystyle \frac{7}{3}$ e)    $4$ f)    $-2$
g)    $1$ h)    $\displaystyle \frac{5}{2}$

Svar 3.3:4

a)    $1$ b)    $0$ c)    $-\displaystyle \frac{1}{2}\lg{3}$

Svar 3.3:5

a)    $5$ b)    $0$ c)    $0$
d)    $0$ e)    $-2$ f)    $e^2$

Svar 3.3:6

a)    $1{,}262$
b)    $1{,}663$
c)    $4{,}762$

Svar 3.4:1

a)    $x=\ln 13$ b)    $x=\displaystyle\frac{\ln 2 - \ln 13}{1+\ln 3}$ c)    $x=\displaystyle\frac{\ln 7 - \ln 3}{1-\ln 2}$

Svar 3.4:2

a)    $ \left\{ \eqalign{ x_1&=\sqrt2 \cr x_2&=-\sqrt2 } \right. $ b)    $x=\ln \left(\displaystyle\frac{\sqrt17}{2}-\frac{1}{2}\right)$ c)    Saknar lösning

Svar 3.4:3

a)    $x=-\,\displaystyle\frac{1}{\ln{2}}\pm\sqrt{\left(\displaystyle\frac{1}{\ln{2}}\right)^2-1}$ b)    $x=\displaystyle \frac{5}{2}$
c)    $x=1$

Svar 4.1:1

a)    $90^\circ\ $ och $\ \displaystyle \frac{\pi}{2} \textrm{ rad} $ b)    $135^\circ\ $ och $\ \displaystyle \frac{3\pi}{4} \textrm{ rad}$
c)    $-240^\circ\ $ och $\ \displaystyle -\frac{4\pi}{3} \textrm{ rad}$ d)    $2910^\circ\ $ och $\ \displaystyle \frac{97\pi}{6} \textrm{ rad}$

Svar 4.1:2

a)    $\displaystyle \frac{\pi}{4}\textrm{ rad}$ b)    $\displaystyle \frac{3\pi}{4}\textrm{ rad}$ c)    $-\displaystyle \frac{7\pi}{20}\textrm{ rad}$ d)    $\displaystyle \frac{3\pi}{2}\textrm{ rad}$

Svar 4.1:3

a)    $x=50$ b)    $x=5$ c)    $x=15$

Svar 4.1:4

a)    $5 \textrm{ l.e.}$
b)    $\sqrt{61} \textrm{ l.e.}$
c)    $(2,0)$

Svar 4.1:5

a)    $(x-1)^2+(y-2)^2=4$
b)    $(x-2)^2+(y+1)^2=13$

Svar 4.1:6

a)    En cirkel med radie 3 och medelpunkt i origo. b)    En cirkel med radie $\sqrt 3$ och medelpunkt i punkten (1, 2).
c)    En cirkel med radie $\frac{1}{3}\sqrt 10$ och medelpunkt i punkten (1/3, -7/3).

Svar 4.1:7

a)    En cirkel med medelpunkt (-1, 1) och radie $\sqrt 3$. b)    En cirkel med medelpunkt (0, -2) och radie 2.
c)    En cirkel med medelpunkt (1, -3) och radie $\sqrt 7$.
d)    Endast punkten (1, -1).

Svar 4.1:8

$\displaystyle \frac{10}{\pi}\textrm{ varv }\approx 3,2 \textrm{ varv} $

Svar 4.1:9

$\displaystyle \frac{32\pi}{3} \textrm{ cm}^2 \approx 33,5 \textrm{ cm}^2$

Svar 4.1:10

$x=9$ dm

Svar 4.2:1

Facit till alla delfrågor

a)    $x=13\cdot\tan {27 ^\circ} \approx 6{,}62$ b)    $x=25\cdot\cos {32 ^\circ} \approx 21{,}2$
c)    $x=\displaystyle\frac{14}{\tan {40 ^\circ}} \approx 16{,}7$ d)    $x=\displaystyle\frac{16}{\cos {20 ^\circ}} \approx 17{,}0$
e)    $x=\displaystyle\frac{11}{\sin {35 ^\circ}} \approx 19{,}2$ f)    $x=\displaystyle\frac{19}{\tan {50 ^\circ}} \approx 15{,}9$

Svar 4.2:2

a)    $\tan v=\displaystyle\frac{2}{5}$ b)    $\sin v=\displaystyle\frac{7}{11}$
c)    $\cos v=\displaystyle\frac{5}{7}$ d)    $\sin v=\displaystyle\frac{3}{5}$
e)    $v=30 ^\circ$ f)    $\sin \displaystyle\frac{v}{2}=\displaystyle\frac{1}{3}$

Svar 4.2:3

a)    $-1$ b)    $1$ c)    $0$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{2}}$ f)    $\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.2:4

a)    $\displaystyle \frac{\sqrt{3}}{2}$ b)    $\displaystyle \frac{1}{2}$ c)    $-1$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{3}}$ f)    $\sqrt{3}$

Svar 4.2:5

a)    $-\displaystyle \frac{1}{\sqrt{2}}$ b)    $1$ c)    $\displaystyle \frac{\sqrt{3}}{2}$ d)    $-1$

Svar 4.2:6

$x= \sqrt{3}-1$

Svar 4.2:7

Älvens bredd är $\ \displaystyle\frac{100}{\sqrt{3}-1}$ m $\approx 136{,}6$ m.


Svar 4.2:8

$\ell\cos \gamma=a \cos \alpha - b\cos \beta $

Svar 4.2:9

Avståndet är $\ \sqrt{205-48\sqrt{3}} \approx 11{,}0$ km.

Svar 4.3:1

a)    $v = \displaystyle \frac{9\pi}{5}$ b)    $v = \displaystyle \frac{6\pi}{7}$ c)    $v = \displaystyle \frac{9\pi}{7}$

Svar 4.3:2

a)    $v=\displaystyle \frac{\pi}{2}$ b)    $v=\displaystyle \frac{3\pi}{5}$

Svar 4.3:3

a)    $-a$ b)    $a$
c)    $\sqrt{1-a^2}$ d)    $\sqrt{1-a^2}$
e)    $-a$ f)    $\displaystyle \frac{\sqrt{3}}{2}\sqrt{1-a^2}+\displaystyle \frac{1}{2}\cdot a $

Svar 4.3:4

a)    $1-b^2$ b)    $\sqrt{1-b^2}$
c)    $2b\sqrt{1-b^2}$ d)    $2b^2-1$
e)    $\sqrt{1-b^2}\cdot\displaystyle \frac{1}{\sqrt{2}} + b\cdot \displaystyle \frac{1}{\sqrt{2}} $ f)    $b\cdot\displaystyle \frac{1}{2}+\sqrt{1-b^2}\cdot\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.3:5

$\cos{v}=\displaystyle \frac{2\sqrt{6}}{7}\quad$ och $\quad\tan{v}=\displaystyle \frac{5}{2\sqrt{6}}\,$.

Svar 4.3:6

a)    $\sin{v}=-\displaystyle \frac{\sqrt{7}}{4}\quad$ och $\quad\tan{v}=-\displaystyle \frac{\sqrt{7}}{3}\,$.
b)    $\cos{v}=-\displaystyle \frac{\sqrt{91}}{10}\quad$ och $\quad\tan{v}=-\displaystyle \frac{3}{\sqrt{91}}\,$.
c)    $\sin{v}=-\displaystyle \frac{3}{\sqrt{10}}\quad$ och $\quad\cos{v}=-\displaystyle \frac{1}{\sqrt{10}}\,$.

Svar 4.3:7

a)    $\sin{(x+y)}=\displaystyle \frac{4\sqrt{2}+\sqrt{5}}{9}$
b)    $\sin{(x+y)}=\displaystyle \frac{3\sqrt{21}+8}{25}$

Svar 4.3:8

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.3:9

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.4:1

a)    $\displaystyle v=\frac{\pi}{6}\,$, $\,\displaystyle v=\frac{5\pi}{6}$ b)    $\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$
c)    $\displaystyle v=\frac{\pi}{2}$ d)    $\displaystyle v=\frac{\pi}{4}\,$, $\,\displaystyle v=\frac{5\pi}{4}$
e)    lösning saknas f)    $\displaystyle v=\frac{11\pi}{6}\,$, $\,\displaystyle v=\frac{7\pi}{6}$
g)    $\displaystyle v=\frac{5\pi}{6}\,$, $\,\displaystyle v=\frac{11\pi}{6}$

Svar 4.4:2

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$

c)    $x=n\pi$
d)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$

e)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.$

f)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.$

Svar 4.4:3

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{6}+2n\pi\cr x&=\displaystyle\frac{11\pi}{6}+2n\pi }\right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{5}+2n\pi\cr x&=\displaystyle\frac{4\pi}{5}+2n\pi }\right.$

c)   

$\left\{\eqalign{ x&=25^\circ + n\cdot 360^\circ\cr x&=75^\circ + n\cdot 360^\circ }\right.$

d)   

$\left\{\eqalign{ x&=5^\circ + n \cdot 120^\circ \cr x&= 55^\circ + n \cdot 120^\circ }\right.$

Svar 4.4:4

$v_1=50^\circ$, $\ \ v_2=120^\circ$, $\ \ v_3=230^\circ\ \ $ och $\ \ v_4=300^\circ$

Svar 4.4:5

a)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2} }\right.$

b)    $x=\displaystyle \frac{n\pi}{3}$ c)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3} }\right.$

Svar 4.4:6

a)   

$x=n\pi$

b)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$

c)   

$\left\{\eqalign{ x&=\displaystyle \frac{2n\pi}{3}\cr x&=\displaystyle \pi + 2n\pi\cr }\right.$

Svar 4.4:7

a)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{6}+2n\pi\cr x=\displaystyle \frac{5\pi}{6}+2n\pi\cr x=\displaystyle \frac{3\pi}{2}+2n\pi }\right.$

b)    $x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $ c)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{2}+2n\pi\cr x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7} }\right.$

Svar 4.4:8

a)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi }\right.$

b)    $x=\displaystyle \frac{\pi}{3}+n\pi$ c)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{3\pi}{4}+n\pi }\right.$












































































Den här artikeln är hämtad från http://wiki.math.se/wikis/sf0600_0701/index.php/Facit
Personliga verktyg