Answer:
As the x-values go to negative infinity, the function’s values go to positive infinity.
Explanation:
if the ans choices are:
As the x-values go to negative infinity, the function’s values go to negative infinity.
As the x-values go to negative infinity, the function’s values go to positive infinity.
As the x-values go to positive infinity, the function’s values go to negative infinity.
As the x-values go to positive infinity, the function’s values go to zero.
the ans is the 2nd choice
Answer:
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Explanation:
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Answer:
a) v = +/- 0.323 m/s
b) x = -0.080134 m
c) v = +/- 1.004 m/s
Explanation:
Given:
a = - (0.1 + sin(x/b))
b = 0.8
v = 1 m/s @ x = 0
Find:
(a) the velocity of the particle when x = -1 m
(b) the position where the velocity is maximum
(c) the maximum velocity.
Solution:
- We will compute the velocity by integrating a by dt.
a = v*dv / dx = - (0.1 + sin(x/0.8))
- Separate variables:
v*dv = - (0.1 + sin(x/0.8)) . dx
-Integrate from v = 1 m/s @ x = 0:
0.5(v^2) = - (0.1x - 0.8cos(x/0.8)) - 0.8 + 0.5
0.5v^2 = 0.8cos(x/0.8) - 0.1x - 0.3
- Evaluate @ x = -1
0.5v^2 = 0.8 cos(-1/0.8) + 0.1 -0.3
v = sqrt (0.104516)
v = +/- 0.323 m/s
- v = v_max when a = 0:
-0.1 = sin(x/0.8)
x = -0.8*0.1002
x = -0.080134 m
- Hence,
v^2 = 1.6 cos(-0.080134/0.8) -0.6 -0.2*-0.080134
v = sqrt (0.504)
v = +/- 1.004 m/s
Answer:
P ( 2.5 < X < 7.5 ) = 0.7251
Explanation:
Given:
- The pmf for normal distribution for random variable x is given:
f(x)=0.178 exp(-0.100(x-4.51)^2)
Find:
the fraction of individuals demonstrating a response in the range of 2.5 to 7.5.
Solution:
- The random variable X follows a normal distribution with mean u = 4.51, and standard deviation s.d as follows:
s.d = sqrt ( 1 / 0.1*2)
s.d = sqrt(5) =2.236067
- Hence, the normal distribution is as follows:
X ~ N(4.51 , 2.236)
- Compute the Z-score values of the end points 2.5 and 7.5:
P ( (2.5 - 4.51) / 2.236 < Z < (7.5 - 4.51 ) / 2.236 )
P ( -0.898899327 < Z < 1.337168651 )
- Use the Z-Table for the probability required:
P ( 2.5 < X < 7.5 ) = P ( -0.898899327 < Z < 1.337168651 ) = 0.7251
