III gimnazjum

Matematyka wokół nas 3

Obliczenia:  Paczka makaronu: 2,4złzł+2,4zł⋅5%=2,4zł+2,4zł⋅0,05=2,4zł+0,12zł=2,52zł Karma dla psa: x+x⋅8%=16,20zł   x+0,08x=16,20zł   1,08x=16,20zł   x=16,20:1,08=15zł   Telewizor LCD 1500+1500x=1845   1500x=345   x=345:1500   x=0,23   x=23%     <table style="border: none; border-collapse: collapse; width: 602px;"> <tbody> <tr style="height: 0px;"> <td style="vertical-align: top; background-color: #ff9900; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Towar </td> <td style="vertical-align: top; background-color: #ff9900; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Cena netto (zł) </td> <td style="vertical-align: top; background-color: #ff9900; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">VAT </td> <td style="vertical-align: top; background-color: #ff9900; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Cena brutto (zł) </td> </tr> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">paczka makaronu </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">2,40 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">5% </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">2,52 </td> </tr> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">karma dla psa </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">15 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">8% </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">16,20 </td> </tr> <tr style="height: 0px;"> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">telewizor LCD </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">1500 </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">23% </td> <td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;"> <span style="font-size: 14.666666666666666px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">1845 </td> </tr> </tbody> </table>

Rozwiązanie 1

Podobieństwo w skali  31​  oznacza, że przyprostokątne mają długość 3 cm i 4 cm odpowiednio.

Z danych wynika, że wysokość walca jest równa  10cm  oraz obwód podstawy wynosi  10cm

Z danych wynika, że tworząca stożka wynosi 6 cm. Jednocześnie wiemy, że długość podstawy wynosi  6Π . Promień stożka wynosi zatem  3cm

I. Tworząca stożka jest dwa razy dłuższa od promienia jego podstawy.
TAK

Podstawa ostrosłupa zasadza się na podstawie walca. Mamy zatem kwadrat wpisany w koło. Przekątna tego kwadratu jest równa średnicy koła. Przekątna kwadratu ostrosłupa (oznaczmy przez d) wynosi zatem  d=8

Najwygodniejszy sposób nauki z edukacyjnym Odrabiamy AI

11

Matematyka wokół nas 3