Let
Substitute into differential equation:
Factor out t^r and solve for 'r':
<span><span>(<span><span>5x</span>+7</span>)</span><span>(<span>1/5</span>)</span></span>=<span><span>(<span>8−<span>6x</span></span>)</span><span>(<span>1/5</span><span>)
</span></span></span>Simplify both sides. In order to do this you need to distribute 1/5 in each expression.
<span><span><span>(<span>5x</span>)</span><span>(<span>1/5</span>)</span></span>+<span><span>(7)</span><span>(<span>1/5</span>)</span></span></span>=<span><span><span>(8)</span><span>(<span>1/5</span>)</span></span>+<span><span>(<span>−<span>6x</span></span>)</span><span>(<span>1/5</span><span>)
</span></span></span></span><span>x+<span>7/5</span></span>=<span><span>8/5</span>+<span><span><span>−6/</span>5</span><span>x
</span></span></span><span>x+<span>7/5</span></span>=<span><span><span><span>−6/</span>5</span>x</span>+<span>8/<span>5
Now you need to add (-6/5)x to both sides. This leaves you with
</span></span></span><span><span><span>(5/11)</span>x</span>+<span>7/5</span></span>=<span>8/<span>5
Now subtract 7/5 from both sides.
</span></span><span><span>(5/11)</span>x</span>=<span>1/<span>5
Divide both sides by 5/11
x=1/11</span></span>
Let's assume the pool is a rectangular block
If you know the length width and depth (or height) of the pool, then you can find the volume.
For example
length = 30 feet
width = 10 feet
depth = 8 feet
volume = length*width*depth = 30*10*8 = 300*8 = 2400 cubic feet
This is assuming that the depth stays the same throughout the pool. Though some pools (or most?) have the depth gradually get deeper as you move toward the deep-end. To keep things simple however, the assumption is that the bottom is completely flat and it doesn't gradually get deeper.
X^2 + x = 5
hope that helps
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Answer:
The full answer is in the media.Good luck!
