A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded.
1 answer:
Answer:
is the fraction of sensors upgraded per unit.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of upgraded sensors in one unit and y be the number of non-upgraded sensors in one unit.
Number of modular units = 30
Since some part of unit is upgraded and some are non-upgraded, then, we can write the equation:
Number of non-upgraded sensors =
Thus, we can write the equation:
Fraction of sensors upgraded per unit =
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It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers
Answer:
Step-by-step explanation:
The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:
Rectangle 1 (top base):
Rectangle 2 (bottom base):
Trapezoids 1 and 2 (lateral):
Rectangles 3 and 4 (lateral):
Thus the total surface area is equal to