Pollution. In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by P ( x ) = 2 x 1 − x 0 ≤ x < 1 where x is the percentage (expressed as a decimal fraction) of the total contaminant removed. (A) Where is P ( x ) increasing? Decreasing? (B) Where is the graph of P concave upward? Downward? (C) Find any horizontal or vertical asymptotes. (D) Find the x and y intercepts. (E) Sketch a graph of P .
Pollution. In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by P ( x ) = 2 x 1 − x 0 ≤ x < 1 where x is the percentage (expressed as a decimal fraction) of the total contaminant removed. (A) Where is P ( x ) increasing? Decreasing? (B) Where is the graph of P concave upward? Downward? (C) Find any horizontal or vertical asymptotes. (D) Find the x and y intercepts. (E) Sketch a graph of P .
Solution Summary: The author explains how the function P(x) is increasing or decreasing. The function is not defined when its denominator is 0. The domain can be divided into 2 intervals.
Pollution. In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by
P
(
x
)
=
2
x
1
−
x
0
≤
x
<
1
where x is the percentage (expressed as a decimal fraction) of the total contaminant removed.
(A) Where is P(x) increasing? Decreasing?
(B) Where is the graph of P concave upward? Downward?
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with
two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair
of adjacent entries (G3 shown below). Prove that G,, is connected.
132
123
213
312
321
231
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