Answer:
32 : 24 is smaller
Step-by-step explanation:
32 : 24 = 32/56, reduced is 4/7
30 : 22 = 30/52, reduced is 15/26
a common denominator is 182:
4/7 = 104/182
15/26 = 105/182
Answer:
![y=1-e^{c_{2}}}*e^{-x} *e^{x^2}](https://tex.z-dn.net/?f=y%3D1-e%5E%7Bc_%7B2%7D%7D%7D%2Ae%5E%7B-x%7D%20%2Ae%5E%7Bx%5E2%7D)
Step-by-step explanation:
We begin with the differential equation ![\frac{dy}{dx} =(1-x)(1-y)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%281-x%29%281-y%29)
Firstly, we need to get the
and
as well as the
and
on the same sides as each other
To do this, we can multiply each side by
and divide each side by ![(1-y)](https://tex.z-dn.net/?f=%281-y%29)
Doing this will give us the following differential
![\frac{1}{1-y} dy=(1-x)dx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1-y%7D%20dy%3D%281-x%29dx)
Now, we can integrate each side
![\int\limits\frac{1}{1-y} \, dy =\int (1-x) \, dx\\\\-ln(1-y)=x-x^2+c_{1}](https://tex.z-dn.net/?f=%5Cint%5Climits%5Cfrac%7B1%7D%7B1-y%7D%20%20%5C%2C%20dy%20%3D%5Cint%20%281-x%29%20%5C%2C%20dx%5C%5C%5C%5C-ln%281-y%29%3Dx-x%5E2%2Bc_%7B1%7D)
Now, we need to solve for y
![-ln(1-y)=x-x^2+c_{1}\\\\ln(1-y)=x^2-x+c_{2} \\\\1-y=e^{x^2-x+c_{2}} \\\\y=1-e^{x^2-x+c_{2}}\\\\y=1-e^{c_{2}}}*e^{-x} *e^{x^2}](https://tex.z-dn.net/?f=-ln%281-y%29%3Dx-x%5E2%2Bc_%7B1%7D%5C%5C%5C%5Cln%281-y%29%3Dx%5E2-x%2Bc_%7B2%7D%20%5C%5C%5C%5C1-y%3De%5E%7Bx%5E2-x%2Bc_%7B2%7D%7D%20%5C%5C%5C%5Cy%3D1-e%5E%7Bx%5E2-x%2Bc_%7B2%7D%7D%5C%5C%5C%5Cy%3D1-e%5E%7Bc_%7B2%7D%7D%7D%2Ae%5E%7B-x%7D%20%2Ae%5E%7Bx%5E2%7D)
1. (77+x)/2=84
2. Harold needs at least a 91
Work:
first, you multiply both sides by 2; 77+x=168
then you subtract 77 from both sides; x=91
then you plug it back in to check; (77+91)/2=84 ; 168/2=84 ; 84=84
Answer:
d)
because that would be the same as ![11x * 11x](https://tex.z-dn.net/?f=11x%20%2A%2011x)