The answer is,
Also equivalent to about, 0.185188.
Also equivalent to about, 0.185188.
A dust bunny gathers dust at a rate of 11% per week. The dust bunny, Alfred, originally weighed 0.7 ounces. Write an equation th
1 answer:
Alfred is 0.7 ounces at the beginning.
After one week had passed, he is 11% larger. 0.7 * 1.11
After two weeks, the dust bunny's size is once again 11% larger.
0.7 * 1.11 * 1.11, or 0.7 * 1.11².
From here you can see that each week the dust bunny's size multiplies by 1.11. (1 whole plus 11 percent) How many times it is multiplied can be expressed with exponents.
After one week had passed, he is 11% larger. 0.7 * 1.11
After two weeks, the dust bunny's size is once again 11% larger.
0.7 * 1.11 * 1.11, or 0.7 * 1.11².
From here you can see that each week the dust bunny's size multiplies by 1.11. (1 whole plus 11 percent) How many times it is multiplied can be expressed with exponents.
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Answer:
the comparison must be reversed when multiplying by a negative
Step-by-step explanation:
The rules of equality apply to solving inequalities, with the exception that multiplication or division by a negative number reverses the sense of the comparison:
-x > 1
x < -1 . . . . . multiply both sides by -1
____
Effectively, multiplication (or division) by a negative number is equivalent to reflection across the origin. Things that were ordered left/right (on the number line) are ordered right/left after such a reflection:
-2 < -1
1 < 2
_____
<em>Additional comment</em>
Application of any function requires that you pay attention to ordering. Some functions naturally reverse the order; others do so only on specific domains.
Consider f(x) = 1/x.
1 < 2
f(1) > f(2) . . . . because the slope of the f(x) function is negative everywhere.
__
<em>In the first and second quadrants</em>, the cosine function also reverses order.
20° > 10°
cos(20°) < cos(10°)
__
Probably the most commonly encountered function used with inequalities is the absolute value function.
|x-3| > 2
This function has one domain where the slope is negative, and another domain where the slope is positive.
For x < 3, the function negates its argument, so we have ...
-(x -3) > 2
-x +3 > 2
-x > -1
x < 1 . . . . . everywhere consistent with x < 3
For x ≥ 3, the function does nothing, so we have ...
x -3 > 2
x > 5
The solution to this absolute value inequality is (x < 1) ∪ (x > 5).
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You can also resolve negative coefficients by adding the opposite. Addition and subtraction never require any change to the comparison operator.
-x > 1
0 > x +1 . . . . x is added
-1 > x . . . . . . -1 is added
