232,000,000 - 2.32E8
0.00000431 - 4.31E-6
2,320,000,000 - 2.32E9
0.000000000000431 - 4.31E-13
Answer:
3. 9.4cm2
4. Any flat surface of a 3-D object or cube.
Step-by-step explanation:
A face is well flat.
Either a histogram or a Dot plot.
The intersection would be at the point (2, 2).
This is because, graphically, the plots of f(x) and its inverse are reflections of one another across the line y = x, and (2, 2) lies on this line.
Put another way, we have f(2) = 2 = f⁻¹(2), so both f(x) and f⁻¹(x) intersect when x = 2.
Put yet another (longer) way, we can find the equation for f(x): it's a line that passes through (0, 6) and (3, 0), so it has slope -6/3 = -2. Then using the point-slope formula,
y - 6 = -2 (x - 0) ⇒ y = f(x) = -2x + 6
By definition of function inverse, we have
f(f⁻¹(x)) = x
so that with the given definition of f(x), we get
f(f⁻¹(x)) = -2 f⁻¹(x) + 6 = x
-2 f⁻¹(x) = x - 6
f⁻¹(x) = -x/2 + 3
Then we solve for x such that f(x) = f⁻¹(x). We would find x = 2 as before.
Answer:
- minimum: 6.75 km²
- maximum: 13.75 km²
Step-by-step explanation:
Such questions generally arise in the context of measurement precision and/or accuracy. Apparently, we're to assume that these dimensions could be arrived at by rounding to the nearest km. In that case, they can be taken to have a possible error of ±0.5 km.
The minimum possible area is the product of the minimum possible dimensions: 1.5 km by 4.5 km = 6.75 km².
The maximum possible area is the product of the maximum possible dimensions: 2.5 km by 5.5 km = 13.75 km².
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<em>Comment on combining measurement values</em>
You will note that the nominal area is 2 km by 5 km = 10 km², and that the middle value between the minimum and maximum is slightly more than this, at 10.25 km².
It is typically the case that when measurements are combined by operations other than addition and subtraction, the nominal result is different from the middle result in the range of possibilities.