![\bf \cfrac{x}{4x+x^2}\implies \cfrac{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(4+x)}\implies \cfrac{1}{4+x}\qquad \{x|x\in \mathbb{R}, x\ne -4\}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bx%7D%7B4x%2Bx%5E2%7D%5Cimplies%20%5Ccfrac%7B%5Cbegin%7Bmatrix%7D%20x%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D%7D%7B%5Cbegin%7Bmatrix%7D%20x%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%284%2Bx%29%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B4%2Bx%7D%5Cqquad%20%5C%7Bx%7Cx%5Cin%20%5Cmathbb%7BR%7D%2C%20x%5Cne%20-4%5C%7D)
if you're wondering about the restriction of x ≠ -4, is due to that would make the fraction with a denominator of 0 and thus undefined.
Answer:
Actual volume: 150.8
Step-by-step explanation:
the equation to find the volume of a cylinder is:
V= pi (r)^2 (h)
r= radius
h= height
To get the radius, you divide the diameter by 2.
when you plug in the numbers is looks like this:
V= pi (2)^2 (12)
you'll get 150.8 ft^3
I'm not really sure which volume would be the closest, but it should be around the answer I provided
Answer:
9 mph = the speed in still water
Step-by-step explanation:
Let r = the speed in still water
Then the speed going down stream is r + 3
and the speed going upstream is r - 3
d = rt or t = d/r
time going downstream is 16/(r + 3) and time going upstream is 16/(r - 3)
The total time was 4 hours, so
Multiply thru the equation by (r + 3)(r - 3)
Then 16(r - 3) + 16(r + 3) = 4(r + 3)(r - 3)
16r - 48 + 16r + 48 =
- 36
- 36 = 32r
- 32r - 36 = 0

4(r - 9)(r + 1) = 0
r = 9 or -1
But a rate of speed cannot be negative, so x ≠ -1
So, r = 9 mph = the speed in still water
Answer:
10 quarters and 12 dimes :)
Step-by-step explanation: