Answer:
7/12
Step-by-step explanation:
lemon is 5/12
lime is 7/12
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Answer:
Figure A
Step-by-step explanation:
A regular polygon has all sides the same length and all angles the same measure. Only Figure A matches that description.
Answer:
![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)
Step-by-step explanation:
Given: ![y'=\sqrt{4y+25}](https://tex.z-dn.net/?f=y%27%3D%5Csqrt%7B4y%2B25%7D)
Initial value: y(1)=6
Let ![y'=\dfrac{dy}{dx}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7Bdy%7D%7Bdx%7D)
![\dfrac{dy}{dx}=\sqrt{4y+25}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Csqrt%7B4y%2B25%7D)
Variable separable
![\dfrac{dy}{\sqrt{4y+25}}=dx](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7B%5Csqrt%7B4y%2B25%7D%7D%3Ddx)
Integrate both sides
![\int \dfrac{dy}{\sqrt{4y+25}}=\int dx](https://tex.z-dn.net/?f=%5Cint%20%5Cdfrac%7Bdy%7D%7B%5Csqrt%7B4y%2B25%7D%7D%3D%5Cint%20dx)
![\sqrt{4y+25}=2x+C](https://tex.z-dn.net/?f=%5Csqrt%7B4y%2B25%7D%3D2x%2BC)
Initial condition, y(1)=6
![\sqrt{4\cdot 6+25}=2\cdot 1+C](https://tex.z-dn.net/?f=%5Csqrt%7B4%5Ccdot%206%2B25%7D%3D2%5Ccdot%201%2BC)
![C=5](https://tex.z-dn.net/?f=C%3D5)
Put C into equation
Solution:
![\sqrt{4y+25}=2x+5](https://tex.z-dn.net/?f=%5Csqrt%7B4y%2B25%7D%3D2x%2B5)
or
![4y+25=(2x+5)^2](https://tex.z-dn.net/?f=4y%2B25%3D%282x%2B5%29%5E2)
![y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdfrac%7B1%7D%7B4%7D%282x%2B5%29%5E2-%5Cdfrac%7B25%7D%7B4%7D)
![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)
Hence, The solution is
or ![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)