![\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cunderline%7B%5Cunderline%7B%5Cpmb%7B%5Csf%20%7B%5Ccolor%20%7Bblue%7D%7BSolution%3A%7D%7D%7D%7D%7D%7D)
Given,
Area = 225 yd²
Base = 30 yd
Height = [To be calculated]
To find:
The height of the given triangle.
We know that, area of a triangle is:
![\frac{1}{2} \times (b \times h) \\ \\ \leadsto \frac{1}{2} \times (30 \times h) \\ \\ \leadsto \frac{1}{2} \times 30h \\ \\ \leadsto \frac{1}{ \cancel{2}} \times \cancel{30}h \\ \\ \leadsto1 \times 15h \\ \\ \leadsto \: h = 15 \: yd](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%28b%20%5Ctimes%20h%29%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%2830%20%5Ctimes%20h%29%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%5Cfrac%7B1%7D%7B2%7D%20%20%20%5Ctimes%2030h%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%20%5Cfrac%7B1%7D%7B%20%5Ccancel%7B2%7D%7D%20%5Ctimes%20%20%5Ccancel%7B30%7Dh%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto1%20%5Ctimes%2015h%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%5C%3A%20h%20%3D%2015%20%5C%3A%20yd)
Therefore, the require height is 15 yd.
Proof:
![\frac{1}{2} \times (b \times h) \\ \\ \leadsto \frac{1}{2} \times (30 \times 15) \\ \\ \leadsto \frac{1}{ \cancel{2}} \times \cancel{450} \\ \\ \leadsto1 \times 225 \\ \\ area = 225 {yd}^{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%28b%20%5Ctimes%20h%29%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%2830%20%5Ctimes%2015%29%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto%20%5Cfrac%7B1%7D%7B%20%5Ccancel%7B2%7D%7D%20%20%20%5Ctimes%20%20%5Ccancel%7B450%7D%20%5C%5C%20%20%5C%5C%20%20%5Cleadsto1%20%5Ctimes%20225%20%20%5C%5C%20%20%5C%5C%20%20area%20%3D%20225%20%20%7Byd%7D%5E%7B2%7D%20)
![\boxed{ \frak \red{brainlysamurai}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cfrak%20%5Cred%7Bbrainlysamurai%7D%7D)
Answer: Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.
Step-by-step explanation:
The square root of 16 is a rational number. The square root of 16 is 4, an integer
Answer:
-10
Step-by-step explanation:
the upper right is the same (105°), therefore the left 75°
now you have 180 = 75 + x + 115
therefore: -10
You can see the Steps but the answer is
X > 15
For any equation,
![a_ny^(n)+\dots+a_1y'+a_0y=0](https://tex.z-dn.net/?f=a_ny%5E%28n%29%2B%5Cdots%2Ba_1y%27%2Ba_0y%3D0)
assume solution of a form, ![e^{yt}](https://tex.z-dn.net/?f=e%5E%7Byt%7D)
Which leads to,
![(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0](https://tex.z-dn.net/?f=%28e%5E%7Byt%7D%29%27%27%27-%28e%5E%7Byt%7D%29%27%27%2B4%28e%5E%7Byt%7D%29%27-4e%5E%7Byt%7D%3D0)
Simplify to,
![e^{yt}(y^3-y^2+4y-4)=0](https://tex.z-dn.net/?f=e%5E%7Byt%7D%28y%5E3-y%5E2%2B4y-4%29%3D0)
Then find solutions,
![\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}](https://tex.z-dn.net/?f=%5Cunderline%7By_1%3D1%7D%2C%20%5Cunderline%7By_2%3D2i%7D%2C%20%5Cunderline%7By_3%3D-2i%7D)
For non repeated real root y, we have a form of,
![y_1=c_1e^t](https://tex.z-dn.net/?f=y_1%3Dc_1e%5Et)
Following up,
For two non repeated complex roots
where,
![y_2=a+bi](https://tex.z-dn.net/?f=y_2%3Da%2Bbi)
and,
the general solution has a form of,
![y=e^{at}(c_2\cos(bt)+c_3\sin(bt))](https://tex.z-dn.net/?f=y%3De%5E%7Bat%7D%28c_2%5Ccos%28bt%29%2Bc_3%5Csin%28bt%29%29)
Or in this case,
![y=e^0(c_2\cos(2t)+c_3\sin(2t))](https://tex.z-dn.net/?f=y%3De%5E0%28c_2%5Ccos%282t%29%2Bc_3%5Csin%282t%29%29)
Now we just refine and get,
![\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}](https://tex.z-dn.net/?f=%5Cboxed%7By%3Dc_1e%5Et%2Bc_2%5Ccos%282t%29%2Bc_3%5Csin%282t%29%7D)
Hope this helps.
r3t40