https://peda.net/id/31a330247da 2017-08-10T11:37:50+03:00 https://peda.net/:static/532/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/c7b633567e7 2017-08-11T13:06:44+03:00 Taneli Kotamäki https://peda.net/p/er%C3%A4.jorma a. 45 itraa maksaa 60€<br/> b. 2017-08-11T13:06:44+03:00 https://peda.net/id/5d6e5e36889 2017-08-24T10:18:02+03:00 <span>A, Ei, </span><img src="https://math-demo.abitti.fi/math.svg?latex=a_4%3D7%5Ccdot4-9%3D19" alt="a_4=7\cdot4-9=19"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a_5%3D7%5Ccdot5-9%3D35" alt="a_5=7\cdot5-9=35"/><br/> <div> </div> <div>B, Ei, </div> <img src="https://math-demo.abitti.fi/math.svg?latex=a_4%3D-9" alt="a_4=-9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a_5%3D-14" alt="a_5=-14"/><br/> <div> </div> <div>C, On</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=a_4%3D3%2B%5Cleft(4-1%5Cright)%5Ccdot4%3D15" alt="a_4=3+\left(4-1\right)\cdot4=15"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a_5%3D3%2B%5Cleft(5-1%5Cright)%5Ccdot4%3D19" alt="a_5=3+\left(5-1\right)\cdot4=19"/><br/> <br/> <span>D, Ei, Seitsemäs</span><br/> <div> </div> <img src="https://math-demo.abitti.fi/math.svg?latex=a_7%3D4%2B%5Cleft(7-1%5Cright)%5Ccdot%5Cleft(-3%5Cright)" alt="a_7=4+\left(7-1\right)\cdot\left(-3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%3D4%2B6%5Ccdot%5Cleft(-3%5Cright)" alt="=4+6\cdot\left(-3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%3D-14" alt="=-14"/> 2017-08-24T10:18:02+03:00 https://peda.net/id/e9a5bb1a889 2017-08-24T10:21:57+03:00 A, <img src="https://math-demo.abitti.fi/math.svg?latex=a_n%3D79-2n" alt="a_n=79-2n"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a_5%3D79-2%5Ccdot5%3D69" alt="a_5=79-2\cdot5=69"/><br/> <div> </div> <div>Viidennellä harjoituskerralla oli 69 osallistujaa</div> <div> </div> <div>B, </div> <img src="https://math-demo.abitti.fi/math.svg?latex=-2n%5C%20%3D17%5C%20-79" alt="-2n\ =17\ -79"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-2n%5C%20%3D%5C%20-62" alt="-2n\ =\ -62"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=n%3D%5C%20%5Cfrac%7B-62%7D%7B-2%7D%3D31" alt="n=\ \frac{-62}{-2}=31"/> <div><span>31. harjoituskerralla osallistujien määrä on 17.</span><br/> <br/> </div> 2017-08-24T10:21:57+03:00 https://peda.net/id/1fde89548c7 2017-08-29T08:37:19+03:00 <span>A,</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=13%5Ex%3D26%5C%20%5C%20%5C%20%5C%20%5C%20Log" alt="13^x=26\ \ \ \ \ Log"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Log13%5Ex%3D%5C%20%5Clog26" alt="Log13^x=\ \log26"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Ccdot%5Clog13%3D%5Clog26" alt="x\cdot\log13=\log26"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B%5Clog26%7D%7B%5Clog13%7D%3D1%2C27..." alt="x=\frac{\log26}{\log13}=1,27..."/></div> <div> </div> <div>B,</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=4%5Ex%3D%5C%202%5C%20300%5C%20000" alt="4^x=\ 2\ 300\ 000"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B%5Clog%5C%202%5C%20300%5C%20000%7D%7B%5Clog%5C%204%7D" alt="x=\frac{\log\ 2\ 300\ 000}{\log\ 4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%3D%5C%2010%2C56.." alt="=\ 10,56.."/><br/> <div> </div> <div>C,</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=10%5Ex%3D154" alt="10^x=154"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5C%20%5Cfrac%7B%5Clog154%7D%7B%5Clog10%7D%3D2%2C18..." alt="x=\ \frac{\log154}{\log10}=2,18..."/><br/> <div> </div> <div>D,</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=9%5Ex%3D-81" alt="9^x=-81"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B%5Clog%5Cleft(-81%5Cright)%7D%7B%5Clog9%7D" alt="x=\frac{\log\left(-81\right)}{\log9}"/><span> = Ei ratkaisua</span> 2017-08-29T08:37:19+03:00 https://peda.net/id/78b414e28ef 2017-09-01T13:22:35+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%5C%20%3D%5C%20250000%5C%20%5Ccdot%5C%201%2C03%5Ex" alt="f\left(x\right)\ =\ 250000\ \cdot\ 1,03^x"/><br/> <div>a, Arviointihetkellä x= 0</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(0%5Cright)%5C%20%3D%5C%20250000%5C%20%5Ccdot%5C%201%2C03%5E0%3D250%5C%20000" alt="f\left(0\right)\ =\ 250000\ \cdot\ 1,03^0=250\ 000"/></div> <br/> <span>B, 3%</span> <div> </div> <div>C,</div> <div> </div> <div>f(5)= 5vuoden päästä oleva arvo</div> <div>f(-5)= asunnon arvo 5 vuotta ennen arviointihetkeä</div> <div> </div> 2017-09-01T13:22:35+03:00 https://peda.net/id/c2094518920 2017-09-05T09:52:18+03:00 <div>428,</div> <div>a.</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=a_4%3D80%5Ccdot0%2C5%5E3%5C%20%3D10" alt="a_4=80\cdot0,5^3\ =10"/></div> <div> </div> <span>b,</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=a_4%3D3%5Ccdot2%5E3%5C%20%3D%5C%2024" alt="a_4=3\cdot2^3\ =\ 24"/></div> 2017-09-05T09:52:18+03:00 https://peda.net/id/8d1eaf74817 2017-08-15T08:35:30+03:00 <br/> <a href="https://peda.net/p/er%C3%A4.jorma/mab4/kpt/s-25-teht-126/s-25-teht-126-png#top" title="s.25.teht.126.png"><img src="https://peda.net/p/er%C3%A4.jorma/mab4/kpt/s-25-teht-126/s-25-teht-126-png:file/photo/6b33ccc1fe3204feb4f9aba6287e7e19fd66a02c/s.25.teht.126.png" alt="" title="s.25.teht.126.png" class="inline" loading="lazy"/></a>b. 1<br/> <br/> 2017-08-15T08:28:21+03:00 https://peda.net/id/9541f74e7e7 2017-08-11T12:58:17+03:00 <a href="https://peda.net/p/er%C3%A4.jorma/mab4/kpt/teht-104/104-105-png#top" class="service">104-105.png</a>​ 2017-08-11T12:58:10+03:00 https://peda.net/id/c395dff87e8 2017-08-11T14:03:54+03:00 <img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1502449402752"/> 2017-08-11T14:03:54+03:00 https://peda.net/id/dce18ff8832 2017-08-17T11:20:00+03:00 a,<img src="https://math-demo.abitti.fi/math.svg?latex=-2%2B5%3Db" alt="-2+5=b"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=b%3D3" alt="b=3"/></div> <br/> <div><br/> <div>b, </div> <img src="https://math-demo.abitti.fi/math.svg?latex=3%5Ccdot2%2B5%3Db" alt="3\cdot2+5=b"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=b%3D11" alt="b=11"/></div> <br/> <div> </div> <div>c, </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-%5Cfrac%7B1%7D%7B2%7D%5Ccdot2%2B5%3Db" alt="-\frac{1}{2}\cdot2+5=b"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=b%3D-4" alt="b=-4"/><br/> <div> </div> </div> 2017-08-17T11:20:00+03:00 https://peda.net/id/5465d0fa833 2017-08-18T13:16:42+03:00 a, y= -4x+2<br/> b, y= -7x + 0<br/> c, y= 5x + 19<br/> d, y= 3x-3<br/> <br/> 2017-08-17T12:49:14+03:00 https://peda.net/id/0ce62b6488a 2017-08-24T11:34:31+03:00 <img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563558119"/><img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563558119"/><img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563558119"/><img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563558119"/><img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563558119"/><img src="https://math-demo.abitti.fi/screenshot/?answerId=answer1&amp;id=1503563655336"/> 2017-08-24T11:34:31+03:00 https://peda.net/id/9aef4d908c8 2017-08-29T09:52:21+03:00 <span>A,</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D49" alt="x^2=49"/><br/> <div>=7</div> <div> </div> <div> </div> <div>B,</div> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E3%5C%20%3D%5C%20-27" alt="x^3\ =\ -27"/><br/> <div> </div> <div> </div> <div> </div> <div>C,</div> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E4%3D%5C%2010%5C%20000" alt="x^4=\ 10\ 000"/><br/> <div> </div> </div> <div> </div> <div> </div> <div>D, </div> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E6%3D0" alt="x^6=0"/> 2017-08-29T09:52:21+03:00 https://peda.net/id/a7f803368e1 2017-08-31T10:26:08+03:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=a)x%5E3%2B7%3D132x%5E3%3D132-7x%5E3%3D125x%3D%5Csqrt%5B3%5D%7B125%7D%3D5" alt="a)x^3+7=132x^3=132-7x^3=125x=\sqrt[3]{125}=5"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=c)x%5E4-5%3D-86x%5E4%3D-86%2B5x%5E4%3D-81Eiratkaisua" alt="c)x^4-5=-86x^4=-86+5x^4=-81Eiratkaisua"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=b)-2x%5E6%3D-1458x%5E6%3D%5Cfrac%7B-1458%7D%7B-2%7Dx%5E6%3D729x%3D%5Csqrt%5B6%5D%7B729%7Dx%3D3%5C%20tai%5C%20x%3D-3" alt="b)-2x^6=-1458x^6=\frac{-1458}{-2}x^6=729x=\sqrt[6]{729}x=3\ tai\ x=-3"/> 2017-08-31T10:26:08+03:00 https://peda.net/id/f4592434818 2017-08-15T09:49:58+03:00 <span>s.40 teht 204</span> <div>a.</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=k%3D%5Cfrac%7B8-0%7D%7B3-1%7D%3D%5C%20%5Cfrac%7B8%7D%7B2%7D%3D4" alt="k=\frac{8-0}{3-1}=\ \frac{8}{2}=4"/> suora on nouseva</div> <div> </div> <div>b.</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=k%3D%5Cfrac%7B-2-3%7D%7B6-%5Cleft(-4%5Cright)%7D%3D%5Cfrac%7B-5%7D%7B10%7D%3D-%5Cfrac%7B1%7D%7B2%7D" alt="k=\frac{-2-3}{6-\left(-4\right)}=\frac{-5}{10}=-\frac{1}{2}"/> suora on laskeva</div> <div> </div> <div>c.</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=k%3D%5Cfrac%7B-8-%5Cleft(-6%5Cright)%7D%7B-2-3%7D%3D%5Cfrac%7B-8%2B6%7D%7B-5%7D%3D%5Cfrac%7B-2%7D%7B-5%7D%3D%5Cfrac%7B2%7D%7B5%7D" alt="k=\frac{-8-\left(-6\right)}{-2-3}=\frac{-8+6}{-5}=\frac{-2}{-5}=\frac{2}{5}"/> suora on nouseva</div> 2017-08-15T09:49:58+03:00 https://peda.net/id/7d97386a8e1 2017-08-31T10:17:47+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Ccdot%20x%5Ccdot%20x%5C%20%3D%5C%205%2C0" alt="x\cdot x\cdot x\ =\ 5,0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E3%3D5%2C0" alt="x^3=5,0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Csqrt%5B3%5D%7B5%2C0%7D%3D1%2C7099...." alt="x\sqrt[3]{5,0}=1,7099...."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Capprox1%2C7%5C%20%5Cleft(dm%5Cright)%5C%20%5C%20%3D%5C%2017%5Cleft(cm%5Cright)" alt="\approx1,7\ \left(dm\right)\ \ =\ 17\left(cm\right)"/><br/> Vastaus: Ruukun särmän pituus on 17cm 2017-08-31T10:17:47+03:00