First of all, just to avoid being snookered by a trick question, we should verify that these are really right triangles:
7² + 24² really is 25² , and 8² + 15² really is 17² , so we're OK there.
In the first one:
sin(one acute angle) = 7/25 = 0.28
the angle = sin⁻¹ (0.28) = 16.26°
the other acute angle = (90° - 16.26°) = 73.74°
In the second one:
sin(one acute angle) = 8/17 = 0.4706...
the angle = sin⁻¹ (0.4706...) = 28.07°
the other acute angle = (90° - 28.07°) = 61.93°
I'm sorry, but just now, I don't know how to do the
third triangle in the question.
Answer:
Hence average rate of change is greater for f(x) in (0,3).
Yes. f(x) is greater than g(x) in the interval (0,3)
Yes. g(3) <f(3)
Step-by-step explanation:
To find average rate of change of f and g in (0,3)
f(3)-f(0)/3 = (9-0)/3 =3
g(3) = -9-18 = -27
g(0) = 0
Rate of change in(0,3) of g(x) = -27/3 =-9
Hence average rate of change is greater for f(x) in (0,3)
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Both f and g have intercepts of y as 0
Hence both are equal.
3) Yes. f(x) is greater than g(x) in the interval (0,3)
Because g(x) <0 for all x in (0,3) while f(x) >0
4) g(3)= -9-18=-27 <f(3)
