https://peda.net/id/12a80e948be 2021-03-23T16:57:22+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/3c1f25da8c1 2021-03-23T22:35:01+02:00 ​<a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/ytl/matematiikka-lyhyt-oppimaara-hyvan-vasta#top" class="service">Matematiikka, lyhyt oppimäärä, hyvän vastauksen piirteet, kevät 2021.pdf</a>​ 2021-03-23T22:34:58+02:00 https://peda.net/id/6898c6b48c0 2021-03-23T22:33:30+02:00 <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10.png#top" title="mab_k21_10.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10.png:file/photo/bbf8454560ec6dbbc5c09864ebbc030a5aa52b28/mab_k21_10.png" alt="" title="mab_k21_10.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10a.png#top" title="mab_k21_10a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10a.png:file/photo/ab70ea3831e71aa0b3bf73facdd9e6ab4b92752c/mab_k21_10a.png" alt="" title="mab_k21_10a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10-b.png#top" title="mab_k21_10_b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-10-b.png:file/photo/afb0a9c48afc6c75ed96eb7be62749a4876b0204/mab_k21_10_b.png" alt="" title="mab_k21_10_b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-11.png#top" title="mab_k21_11.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-11.png:file/photo/a415605a5beea5f6e5f6b89be1a7d888a4753366/mab_k21_11.png" alt="" title="mab_k21_11.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-11a.png#top" title="mab_k21_11a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-11a.png:file/photo/a0e455012fdb6c25e25a6751fe6dfea62fc7e146/mab_k21_11a.png" alt="" title="mab_k21_11a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-12.png#top" title="mab_k21_12.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-12.png:file/photo/9fa1d554ba4df7f0236f06f5a3e595080904ed75/mab_k21_12.png" alt="" title="mab_k21_12.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-12a.png#top" title="mab_k21_12a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-12a.png:file/photo/5db08a18f32cae8778c664af1d4a33ea87c9028c/mab_k21_12a.png" alt="" title="mab_k21_12a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13.png#top" title="mab_k21_13.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13.png:file/photo/88e4f057f62797a343eae0a5805541259a34bc40/mab_k21_13.png" alt="" title="mab_k21_13.png" class="inline" loading="lazy"/></a></span><br/> <br/> 1)<br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13a.png#top" title="mab_k21_13a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13a.png:file/photo/81c2992f9a0633b9d0621be2cc0781fa3598b83f/mab_k21_13a.png" alt="" title="mab_k21_13a.png" class="inline" loading="lazy"/></a></span><br/> <br/> 2) Funktion p(x), koska<br/> <br/> p(0) = |0 - 3|= 3<br/> <br/> 3) Funktion f(x), koska yksi sen derivaatan nollakohta on n. 0,42 ja <br/> <br/> f'(0,4) = 0,35<br/> <br/> 4) Funktio h(x). Se on kasvava, kun x &gt; 1 ja saa arvon<br/> <br/> h(1) = 1,45<br/> <br/> 5) Neljännen asteen funktio f(x), nollakohdat ovat<br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13b.png#top" title="mab_k21_13b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b2-osa/mab-k21-13b.png:file/photo/2fd82c7c05981ce676afdf71029e1c9cb9e144aa/mab_k21_13b.png" alt="" title="mab_k21_13b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <br/> <br/> 2021-03-23T21:03:09+02:00 https://peda.net/id/5b63026c8bf 2021-03-23T21:01:36+02:00 <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-5.png#top" title="mab_k21_5.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-5.png:file/photo/1151788d95da9153f3f5f298f739a512320f7ca8/mab_k21_5.png" alt="" title="mab_k21_5.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-5a.png#top" title="mab_k21_5a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-5a.png:file/photo/f55d9bf3dbec217793871d55f8449d0b5cede8c2/mab_k21_5a.png" alt="" title="mab_k21_5a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-6.png#top" title="mab_k21_6.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-6.png:file/photo/45942c66280dea82f73d33b877355e42fc7c3b9c/mab_k21_6.png" alt="" title="mab_k21_6.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-6a.png#top" title="mab_k21_6a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-6a.png:file/photo/d52e060509811db548d8e5a8359b5af65cd8799a/mab_k21_6a.png" alt="" title="mab_k21_6a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k-21-6b.png#top" title="mab_k_21_6b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k-21-6b.png:file/photo/e27ab95aefe1255cc295ea3c2da31526fa6ddc9a/mab_k_21_6b.png" alt="" title="mab_k_21_6b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7.png#top" title="mab_k21_7.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7.png:file/photo/05ee30e119db63a291e24cc4a8ec403d1cdb2158/mab_k21_7.png" alt="" title="mab_k21_7.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7a.png#top" title="mab_k21_7a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7a.png:file/photo/c2d541d88676552ab1d937d2a38f75b5b9154821/mab_k21_7a.png" alt="" title="mab_k21_7a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7b.png#top" title="mab_k21_7b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-7b.png:file/photo/ffef035c1c06d41c80ce6c46645a1da54ae88e25/mab_k21_7b.png" alt="" title="mab_k21_7b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8.png#top" title="mab_k21_8.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8.png:file/photo/195ababa000ec7cf19a9f6594dd7803fdc3714e7/mab_k21_8.png" alt="" title="mab_k21_8.png" class="inline" loading="lazy"/></a></span><span class="small"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8a.png#top" title="mab_k21_8a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8a.png:file/photo/a00cd8d57700d6f641b0120350bd7fcaab860c05/mab_k21_8a.png" alt="" title="mab_k21_8a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8b.png#top" title="mab_k21_8b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-8b.png:file/photo/e6b5627834f19a9e25ee7521e67717c8de6d5a35/mab_k21_8b.png" alt="" title="mab_k21_8b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9.png#top" title="mab_k21_9.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9.png:file/photo/5b06d5b6c412f3ed5f11fb1c03435e0c20aa7e77/mab_k21_9.png" alt="" title="mab_k21_9.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9a.png#top" title="mab_k21_9a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9a.png:file/photo/693d3a830185cf4c95dd86517d05c5302bd1eb9f/mab_k21_9a.png" alt="" title="mab_k21_9a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9b.png#top" title="mab_k21_9b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9b.png:file/photo/6dcc8eb1d72675dea82f3eec11254321c777aac8/mab_k21_9b.png" alt="" title="mab_k21_9b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9c.png#top" title="mab_k21_9c.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/b-osa/mab-k21-9c.png:file/photo/f6c9e07ab44be8f1bd798b30b965bf24773b2d45/mab_k21_9c.png" alt="" title="mab_k21_9c.png" class="inline" loading="lazy"/></a></span><br/> 2021-03-23T18:32:28+02:00 https://peda.net/id/3eb694468be 2021-03-23T22:41:33+02:00 <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-1.png2#top" title="mab_k21_1.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-1.png2:file/photo/dea7c4f98439c4323640630d757088f4105f66f5/mab_k21_1.png" alt="" title="mab_k21_1.png" class="inline" loading="lazy"/></a></span><br/> <br/> 2. Jalkapallomatematiikkaa<br/> <br/> <span>Jalkapallokentän maalin leveys on 7,32 metriä. Kohtisuoraan 11,0 metrin päässä maaliviivan keskipisteestä sijaitsee rangaistuspotkupiste</span><span>. Kuinka suuressa kulmassa maali näkyy rangaistuspotkupisteeltä katsottuna? Kulma mitataan kentän pintaa pitkin. Anna vastaus asteen tarkkuudella.</span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-2a.png#top" title="mab_k21_2a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-2a.png:file/photo/833b1bc281d7c6139e9bda6931cb5bf810f4e08a/mab_k21_2a.png" alt="" title="mab_k21_2a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="small"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-c.png#top" title="mab_k21_c.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-c.png:file/photo/8bc931458ee885ceed8c0f0eeb6d9c357c4818f7/mab_k21_c.png" alt="" title="mab_k21_c.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="small"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-2b.png#top" title="mab_k21_2b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-2b.png:file/photo/575380308da0fd17c86441bbabde6541efeff3a2/mab_k21_2b.png" alt="" title="mab_k21_2b.png" class="inline" loading="lazy"/></a></span><br/> <br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3.png#top" title="mab_k21_3.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3.png:file/photo/db765e5588df6695ecd708c6c56cd292a78882d6/mab_k21_3.png" alt="" title="mab_k21_3.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3a.png#top" title="mab_k21_3a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3a.png:file/photo/245a1215d3c8438c118e397fe61c749e0ef9a94a/mab_k21_3a.png" alt="" title="mab_k21_3a.png" class="inline" loading="lazy"/></a></span><br/> <br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3b.png#top" title="mab_k21_3b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-3b.png:file/photo/830fbbe08eda21ee9ad51244604f0e8054458f8e/mab_k21_3b.png" alt="" title="mab_k21_3b.png" class="inline" loading="lazy"/></a></span><br/> <span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4a.png#top" title="mab_k21_4a.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4a.png:file/photo/b9f3b56b07e23492d602cdb1bf00c0b73dee397c/mab_k21_4a.png" alt="" title="mab_k21_4a.png" class="inline" loading="lazy"/></a></span><span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4.png#top" title="mab_k21_4.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4.png:file/photo/d01958fc0a3525a13e20a521918c21bfb049ba43/mab_k21_4.png" alt="" title="mab_k21_4.png" class="inline" loading="lazy"/></a></span><br/> <br/> <p><span class="medium"><a href="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4b.png#top" title="mab_k21_4b.png"><img src="https://peda.net/p/Mika%20Lehtola/yo/omat-ratkaisut/k-2021/a-osa/mab-k21-4b.png:file/photo/ff908575dad796c43ed8dde577023b738a65d70d/mab_k21_4b.png" alt="" title="mab_k21_4b.png" class="inline" loading="lazy"/></a></span></p> 2021-03-23T17:05:46+02:00