we know that
The <u>Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Let
s------> the length of the third side
![10\ cm < s < 60\ cm](https://tex.z-dn.net/?f=10%5C%20cm%20%3C%20s%20%3C%2060%5C%20cm)
therefore
<u>The answer part a) is</u>
![10\ cm < s < 60\ cm](https://tex.z-dn.net/?f=10%5C%20cm%20%3C%20s%20%3C%2060%5C%20cm)
we know that
the perimeter of a triangle is the sum of the length sides
In this problem
![P=25+35+s\\P=60+s](https://tex.z-dn.net/?f=P%3D25%2B35%2Bs%5C%5CP%3D60%2Bs)
<u>For
</u>
the perimeter is equal to
![P > 60+10\\ P>70\ cm](https://tex.z-dn.net/?f=P%20%3E%2060%2B10%5C%5C%20P%3E70%5C%20cm)
<u>For
</u>
the perimeter is equal to
![P < 60+60\\ P](https://tex.z-dn.net/?f=P%20%3C%2060%2B60%5C%5C%20P%3C120%5C%20cm)
so
![70\ cm < P < 120\ cm](https://tex.z-dn.net/?f=70%5C%20cm%20%3C%20P%20%3C%20120%5C%20cm)
therefore
<u>the answer part b) is</u>
![70\ cm < P < 120\ cm](https://tex.z-dn.net/?f=70%5C%20cm%20%3C%20P%20%3C%20120%5C%20cm)
X(-x^4)(-x^4)=
The answer is x^9
Answer:
f(x inv)=-1/2x-3
Step-by-step explanation:
You pretty much just have to flip all the numbers to fractions and all the positives to negatives.
Answer:
5
Step-by-step explanation:
According to the described rule, we have
![a_1=7\\ \\a_1^2=7^2=49\Rightarrow a_2=4+9+1=14\\ \\a_2^2=14^2=196\Rightarrow a_3=1+9+6+1=17\\ \\a_3^2=17^2=289\Rightarrow a_4=2+8+9+1=20\\ \\a_4^2=20^2=400\Rightarrow a_5=4+0+0+1=5\\ \\a_5^2=5^2=25\Rightarrow a_6=2+5+1=8\\ \\a_6^2=8^2=64\Rightarrow a_7=6+4+1=11\\ \\a_7^2=11^2=121\Rightarrow a_8=1+2+1+1=5\\ \\\text{and so on...}](https://tex.z-dn.net/?f=a_1%3D7%5C%5C%20%5C%5Ca_1%5E2%3D7%5E2%3D49%5CRightarrow%20a_2%3D4%2B9%2B1%3D14%5C%5C%20%5C%5Ca_2%5E2%3D14%5E2%3D196%5CRightarrow%20a_3%3D1%2B9%2B6%2B1%3D17%5C%5C%20%5C%5Ca_3%5E2%3D17%5E2%3D289%5CRightarrow%20a_4%3D2%2B8%2B9%2B1%3D20%5C%5C%20%5C%5Ca_4%5E2%3D20%5E2%3D400%5CRightarrow%20a_5%3D4%2B0%2B0%2B1%3D5%5C%5C%20%5C%5Ca_5%5E2%3D5%5E2%3D25%5CRightarrow%20a_6%3D2%2B5%2B1%3D8%5C%5C%20%5C%5Ca_6%5E2%3D8%5E2%3D64%5CRightarrow%20a_7%3D6%2B4%2B1%3D11%5C%5C%20%5C%5Ca_7%5E2%3D11%5E2%3D121%5CRightarrow%20a_8%3D1%2B2%2B1%2B1%3D5%5C%5C%20%5C%5C%5Ctext%7Band%20so%20on...%7D)
We can see the pattern
![a_5=a_8=a_{11}=a_{14}=...=5\\ \\a_6=a_9=a_{12}=a_{15}=...=8\\ \\a_7=a_{10}=a_{13}=a_{16}=...=11](https://tex.z-dn.net/?f=a_5%3Da_8%3Da_%7B11%7D%3Da_%7B14%7D%3D...%3D5%5C%5C%20%5C%5Ca_6%3Da_9%3Da_%7B12%7D%3Da_%7B15%7D%3D...%3D8%5C%5C%20%5C%5Ca_7%3Da_%7B10%7D%3Da_%7B13%7D%3Da_%7B16%7D%3D...%3D11)
In other words, for all ![k\ge 2](https://tex.z-dn.net/?f=k%5Cge%202)
![a_{3k-1}=5\\ \\a_{3k}=8\\ \\a_{3k+1}=11](https://tex.z-dn.net/?f=a_%7B3k-1%7D%3D5%5C%5C%20%5C%5Ca_%7B3k%7D%3D8%5C%5C%20%5C%5Ca_%7B3k%2B1%7D%3D11)
Now,
![a_{2018}=a_{3\cdot 673-1}=5](https://tex.z-dn.net/?f=a_%7B2018%7D%3Da_%7B3%5Ccdot%20673-1%7D%3D5)
Answer:
5
Step-by-step explanation: