![y'''+2y''-4y'-8y=0](https://tex.z-dn.net/?f=y%27%27%27%2B2y%27%27-4y%27-8y%3D0)
has characteristic equation
![r^3+2r^2-4r-8=r^2(r+2)-4(r+2)=(r^2-4)(r+2)=(r-2)(r+2)^2=0](https://tex.z-dn.net/?f=r%5E3%2B2r%5E2-4r-8%3Dr%5E2%28r%2B2%29-4%28r%2B2%29%3D%28r%5E2-4%29%28r%2B2%29%3D%28r-2%29%28r%2B2%29%5E2%3D0)
which has roots at
![r=\pm2](https://tex.z-dn.net/?f=r%3D%5Cpm2)
. The negative root has multiplicity 2. So the general solution is
Hello!
The sum of all angle measures in a heptagon in 900°. We will subtract all of these angles from 900 to find our answer.
900-146-122-142-140-110-142=98
x=98°
I hope this helps!
Answer:
- D(5, 4), E(14, 7), M(9.5, 5.5)
Step-by-step explanation:
As AD = 1/4AB and DE ║ AC, the ratio CE/CB = 1/4, or CE = 1/4CB
<u>Find the coordinates of D:</u>
- x = 1 + 1/4(17 - 1) = 1 + 4 = 5
- y = 5 + 1/4(1 - 5) = 5 - 1 = 4
<u>Find the coordinates of E:</u>
- x = 13 + 1/4(17 - 13) = 13 + 1 = 14
- y = 9 + 1/4(1 - 9) = 9 - 2 = 7
<u>Find the coordinates of the midpoint M of DE:</u>
- x = (5 + 14)/2 = 19/2 = 9.5
- y = (4 + 7)/2 = 11/2 = 5.5
Answer:
Yes
Step-by-step explanation:
![\frac{1}{4} = \frac{1 \times 18}{4 \times 18} = \frac{18}{72} \\ \because \: 19 > 18 \\ \therefore \: \frac{19}{72} > \frac{1}{4} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%20%5Ctimes%2018%7D%7B4%20%5Ctimes%2018%7D%20%20%3D%20%20%5Cfrac%7B18%7D%7B72%7D%20%20%5C%5C%20%20%5Cbecause%20%5C%3A%2019%20%3E%2018%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20%20%5Cfrac%7B19%7D%7B72%7D%20%20%3E%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20)