Answers:
Domain = [-3, 3]
Range = [-1, 2]
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Explanation:
The domain is the set of all allowed x inputs. Visually, the left-most point is when x = -3, so -3 is the smallest allowed x input. We have a closed circle at this endpoint, so this endpoint x value is included. In contrast, if you had an open circle, then you would exclude the endpoint.
Similarly, we have a closed endpoint at the other side as well when x = 3. This is the largest allowed x value. The domain is the set of x values such that meaning x is between -3 and 3, including both endpoints. This translates to the interval notation of [-3, 3]. The square brackets say "include the endpoint".
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The range is the set of possible y outputs of a function. The lowest the function goes is when y = -1, and the highest is when y = 2. We include both endpoints. The range as a compound inequality is which converts to the interval notation of [-1, 2]
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Answer:
x ≈ 4.2
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(72°) = b/x = 13/x
x = 13/tan(72°) ≈ 4.223956
Rounded to the nearest tenth, x ≈ 4.2.
<u>Solution-</u>
The profit function given in the question,
Where,
x = the number of houses built in a year
We can calculate y-intercept by putting x=0, so
y-intercept is -1673, i.e when x=0 or the number of houses built is 0, their profit is -1673. Actually it is not the profit, but loss. So if they don't build any house, they will lose $1673
We can calculate x-intercept or zeros by putting y=0, so
Calculating the zeros by graphing calculator, they are as follows,
x-intercept shows that they need to built at least 15 (as number house can not be fraction) houses, in order to start profiting. Even though they start profiting after building 2 houses, but then the profit starts decreasing and reaches 0 again and so does happen after building 11th house. (It might happen due to the other costs and investments used for building the houses ). But after finally building 15th house they start profiting.
Call the point of attachment at the top of the building point T. (Angle T = 25°) The angle N = 180° -32° -25° = 123°. The Law of Sines tells you the relationship ...
... TM/sin(N) = MN/sin(T)
... MN = TM·sin(T)/sin(N) = (200 ft)·sin(25°)/sin(123°)
... MN ≈ 100.8 ft