When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation
2 answers:
Answer:
Step-by-step explanation:
You have that x varies directly with p*m (which means that if the result of m*p increase, x increase)
And you have too that x is inversely with y (which means that if y increase, x decrease).
Then you must get:
If the problem says that x is 2, y is 4, p is 0.5, and m is 2
the constant value should be 8, in this way:
If you replace:
The result is x=2
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Step-by-step explanation:
3 to 8= 5
8 to 17= 9
17 to 30= 13
30 to 47= 17
47 to 68= 21
68 to 93= 25
93 to 122= 29
122 to 155= 33
155 to 192= 37
difference is 4
solve by
Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)