II gimnazjum

Matematyka z plusem 2

a) &nbsp; <table style="border: none; border-collapse: collapse; width: 624px;"> <tbody> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">długość boku kwadratu &nbsp;</td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 5 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 22<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 6 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 10<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 7 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 3<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> </tr> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">długość przekątnej &nbsp;</td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 52<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 16<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 62<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 20<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 72<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 6<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ </td> </tr> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">pole kwadratu&nbsp;</td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 25 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 8 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 36 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 10 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 49 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> 3 </td> </tr> </tbody> </table>

a)&nbsp; |CD| =(wysokość trójkąta równobocznego o boku a &nbsp;= 6 ) ,-6 |CD| =&nbsp; 6−a23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​​=6−623<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​​=6−33<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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M834 80h400000v40h-400000z'/></svg>​

C =(x,y) x-połowa odległości między punktami &nbsp;A i B : 3-7=5 y-wysokość trójkąta równobocznego &nbsp;o boku 4 :&nbsp; 4⋅23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​​=23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​ F=(x,y) x - połowa &nbsp;odległości między punktami &nbsp;D &nbsp;i E : 13-19 = 6&nbsp; y- wysokość trójkąta równobocznego o &nbsp;boku 6 : 6⋅23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​​=33<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​

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długość boku kwadratu	$5$	$22$	$6$	$10$	$7$	$3$
długość przekątnej	$52$	$16$	$62$	$20$	$72$	$6$
pole kwadratu	$25$	$8$	$36$	$10$	$49$	$3$

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