F(x) = 3x2 g(x) = 3 - 2x
1 answer:
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Answer:
a) The sinusoidal equation is;
The function is h = -24·cos[π(t )] + 24
The sketch of one full revolution is attached
b) The height of the nail at 0.8 seconds is 43.42 cm
Step-by-step explanation:
The sinusoidal equation that models the nails height can be given as follows;
y = A·cos[B(x - C)]+D
A = The amplitude = Half maximum height = 48/2 = 24 cm
The period = 2·π/B = Time to complete one oscillation = 2 seconds
∴ B = 2·π/2 = π
x = t = Time
C = The horizontal shift
D = the vertical shift = 24 cm
y = The height of the nail = h
We have;
h = -24·cos[π(t - C)] + 24
At t = 0, h = 0, therefore, we have;
0 = -24·cos[π(0 - C)] + 24
24·cos[π(0 - C)] = 24
∴ cos[π(0 - C)] = 24/24 = 1
π(0 - C) = 0
C = 0
The function is h = -24·cos[π(t )] + 24
b) The height of the nail at 0.8 seconds is given as follows;
h = -24×cos[π(0.8)] + 24 =
h = 19.42 + 24 = 43.42 cm.
Answer: a) 11.26% and b) 50.23%
Step-by-step explanation:
Number of graduates donated to a political campaign n(A) = 91
Number of graduates donated to assist medical research n(B) = 76
Number of graduated to help preserve the environment n(C) = 131
Number of graduated donated to all n(A∩B∩C) = 27
Number of graduates donated to none = 24
Number of graduated donated to political campaign and to medical research n(A∩B) = 32
Number of graduates donated to medical research and to preserve the environment n(B∩C) = 48
Number of graduates donated to a political campaign and to preserve the environment n(C∩A) = 56
Now,
n(U)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C) -n(C∩A)+n(A∩B∩C)+n(none)
So, What percent of the college graduates donated to none of the three listed causes?
Percentage would be
(b) What percent of the college graduates donated to exactly one of the three listed causes?
Exactly one = 91+76+131-2(32-56-48)+3(27)=107
Percentage would be
Hence, a) 11.26% and b) 50.23%