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24.10.2019 •
Mathematics
How does f(x) = 3 ^x change over the interval x = 4 to x= 5
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Ответ:
f(x) = 3^x increases steadily on the interval [4,5].
Step-by-step explanation:
This exponential function f(x) = 3^x has a positive base (3) which is larger than 1. Thus, this function continues to increase as x increases, including the case where x increases from 4 to 5.
Ответ:
Part A
The expression in terms of 't' representing the number of radians Josh has swept since the ride started is 3·t rad
Part B
The time to complete one revolution is (2·π/3) minutes
Part C.
The function 'f' that determines Josh's height above the ground (in feet) in terms of 't' is, f(t) = 44·sin(3·t + π/2) + 50
Step-by-step explanation:
The radius of the Ferris wheel = 44 foot
The height of the Ferris wheel above the ground = 50 feet
The direction of rotation of the Ferris wheel = CCW
The angular speed of the Ferris wheel, ω = 3 radians per minute
The position from which Josh boards the Ferris wheel = 3-O'Clock
The number of minutes since the ride started started = t
Part A
The expression in terms of 't' to represent the number of radians Josh has swept since the ride started = ω × t = 3 × t rad = 3·t rad
Part B
One complete revolution = 2·π radians
The time to complete one revolution = 2·π/ω = 2·π/(3 rad/minute) = (2·π/3) minutes = ·π minutes ≈ 2.0943951 minutes
Part C.
The height, 'h', of the Ferris wheel is given by the following sinusoidal relation
f(t) = A·sin(B·t + C) + D
Where;
A = The amplitude = The radius of the Ferris wheel = 44 ft.
The period, T = (2·π/3) minute
B = 2·π/T = 3
t = The time in minutes
D = The Ferris wheel's height above ground = 50 ft.
C = The horizontal shift = π/2 (Josh boards the Ferris wheel at t = 3-O'Clock which is the midline, a rotation of π/2 from the lowermost end of the Ferris wheel)
Therefore the function that determines Josh's height above the ground (in feet) in terms of 't' is presented as follows;
f(t) = 44·sin(3·t + π/2) + 50