Two adjacent angles form a complementary relationship. One angle is twelve more than twice the other angle. Draw a picture to re
present the situation. Then solve for each unknown angle measure.
1 answer:
Answer:
The angles are 26 and 64
Step-by-step explanation:
When two angles are complementary, what this means is that the add up to 90 degrees
Now, let’s say one of the angles is x, the other angle is 12 more than twice it; mathematically that would be 2x + 12
Since they add up to be 90, we have
x + 2x + 12 = 90
3x + 12 = 90
3x = 90-12
3x = 78
x = 78/3
x = 26
The other angle is 2x + 12 = 2(26) + 12 = 52 + 12 = 64
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Answer:
S(t) = a.sin (b.t) + d
a = -1.5, b = (2π/365), d = 3.47
S(t) = -1.5 sin (2πt/365) + 3.47
Step-by-step explanation:
Complete Question is presented in the attached image to this solution.
- Dingane has been observing a certain stock for the last few years and he sees that it can be modeled as a function S(t) of time t (in days) using a sinusoidal expression of the form
S(t) = a.sin(b.t) + d.
On day t = 0, the stock is at its average value of $3.47 per share, but 91.25 days later, its value is down to its minimum of $1.97.
Find S(t). t should be in radians.
S(t) =
Solution
S(t) = a.sin(b.t) + d.
At t = 0, S(t) = $3.47
S(0) = a.sin(b×0) + d = a.sin 0 + d = 3.47
Sin 0 = 0,
S(t=0) = d = 3.47.
At t = 91.25 days, S(t) = $1.97
But, it is given that T has to be in radians, for t to be in radians, the constant b has to convert t in days to radians.
Hence, b = (2π/365)
S(91.25) = 1.97 = a.sin(b×91.25) + d
d = 3.47 from the first expression
S(t = 91.25) = a.sin (91.25b) + 3.47 = 1.97
1.97 = a.sin (2π×91.25/365) + 3.47
1.97 = a sin (0.5π) + 3.47
Sin 0.5π = 1
1.97 = a + 3.47
a = -1.5
Hence,
S(t) = a.sin (b.t) + d
a = -1.5, b = (2π/365), d = 3.47
S(t) = -1.5 sin (2πt/365) + 3.47
Hope this Helps!!!
