The correct answer is C. 3.0
Hope this helps
-AaronWiseIsBae
You need to note first two things.
1. The function f(x) need to be a continuous function on [-3,-1] (indeed f(x) is a polynomial function, is continuous on every real number x)
2. Take the closed interval [-3,-1]
Now, evaluate f(-3) and f(-1).

So, we have f(-3) < 0 and f(-1). So,
, then by the Intermediate Value Theorem, there exist
such that
.
Answer with Step-by-step explanation:
The given differential euation is
![\frac{dy}{dx}=(y-5)(y+5)\\\\\frac{dy}{(y-5)(y+5)}=dx\\\\(\frac{A}{y-5}+\frac{B}{y+5})dy=dx\\\\\frac{1}{100}\cdot (\frac{10}{y-5}-\frac{10}{y+5})dy=dx\\\\\frac{1}{100}\cdot \int (\frac{10}{y-5}-\frac{10}{y+5})dy=\int dx\\\\10[ln(y-5)-ln(y+5)]=100x+10c\\\\ln(\frac{y-5}{y+5})=10x+c\\\\\frac{y-5}{y+5}=ke^{10x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28y-5%29%28y%2B5%29%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7B%28y-5%29%28y%2B5%29%7D%3Ddx%5C%5C%5C%5C%28%5Cfrac%7BA%7D%7By-5%7D%2B%5Cfrac%7BB%7D%7By%2B5%7D%29dy%3Ddx%5C%5C%5C%5C%5Cfrac%7B1%7D%7B100%7D%5Ccdot%20%28%5Cfrac%7B10%7D%7By-5%7D-%5Cfrac%7B10%7D%7By%2B5%7D%29dy%3Ddx%5C%5C%5C%5C%5Cfrac%7B1%7D%7B100%7D%5Ccdot%20%5Cint%20%28%5Cfrac%7B10%7D%7By-5%7D-%5Cfrac%7B10%7D%7By%2B5%7D%29dy%3D%5Cint%20dx%5C%5C%5C%5C10%5Bln%28y-5%29-ln%28y%2B5%29%5D%3D100x%2B10c%5C%5C%5C%5Cln%28%5Cfrac%7By-5%7D%7By%2B5%7D%29%3D10x%2Bc%5C%5C%5C%5C%5Cfrac%7By-5%7D%7By%2B5%7D%3Dke%5E%7B10x%7D)
where
'k' is constant of integration whose value is obtained by the given condition that y(2)=0\\

Thus the solution of the differential becomes

Answer:
The length of the yard is 102
Step-by-step explanation:
If the width of the yard is 100 feet, and it's a rectangular, that means the other side of the rectangle is also equal to 100 feet. So so far we have 200 feet of the yard covered. Then we do 404-200=204. So the combined length of both the sides is 204. Since they both equal the same length, we can then do 204/2 to get 102. So one side length is 102 and the L, W, L, W of the rectangle is 102, 100, 102, 100. In other words, the rectangle is 102 by 100.