Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition
5th Edition
ISBN: 9780133311617
Author: Prentice Hall
Publisher: Prentice Hall
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The number of hours of daylight each day for a particular city can be modeled using the sinusoidal function s(m)=5sin(2π/12m−π/2)+13 , where s is the number of hours of sunlight per day, and m represents the month of the year, with m=1 corresponding to January, m=2 corresponding to February, etc.
What is the number of hours of daylight in the longest day of the year?
A.8 hours
B. 13 hours
C.18 Hours
D.24 hours
The height above the ground of a rider on a Ferris wheel can be modeled by the sinusoidal function
h=6sin(1.05t−1.57)+8ℎ=6sin(1.05t-1.57)+8
where hℎ is the height of the rider above the ground, in metres, and t is the time, in minutes, after the ride starts.
When the rider is at least 11.5 m above the ground, she can see the rodeo grounds. During each rotation of the Ferris wheel, the length of time that the rider can see the rodeo grounds, to the nearest tenth of a minute, is min.
The position function of a particle is given by ?(?) , where t is measured issecond and s is measured in metres.
a) Find the velocity and acceleration functions.
b) When does the particle change direction?c) What is the velocity at ? = 3 seconds? Is the particle moving away or towards its starting position?
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- #6arrow_forwardA particle moves along a line so that at time t, its position is 8 = 4 sin 4t. a. When does the particle change direction? b. What is the particle's maximum velocity? c. What is the particle's minimum distance from the origin? What is its maximum distance from the origin?arrow_forwardThe motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =arrow_forward
- 1. A particle moves along the x-axis so that its velocity at any given time is = 2t - 3 and x (0) = 3. v(t) = a.) Find the equation for position of the particle as a function of t, x(t). b.) Find the position of the particle at t = 3. c.) At what values of t does the particle change direction? d.) Where is the particle when the position is a minimum?arrow_forwardA particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the equation below. If the velocity of the particle is 6 m/sec at time t = 3 sec, then the velocity of the particle in m/sec at time t = 7 sec is?arrow_forwardV(t) An object moves with velocity function v (t) = sin(t) during the time interval [0; π]. The next two questions refer to this object. Aarrow_forward
- b. An object moves along a straight line with acceleration given by a(t) = - cos(t), and s(0) = 1, and v(0) = 0. Find the maximum distance the object travels from zero, and find its maximum speed. Describe the motion of the object.arrow_forwardAs your heart beats, it fills with blood and then pushes the blood out to the body, and then fills with blood again, completing the cycle. The volume of blood in the heart, V(t), measured in ml over time, t in seconds can be modeled by the sinusoidal function: V(t)= a cos( s(t) + c a) If the maximum volume of blood in the heart is 140 mL and the minimum volume of blood is 70 mL, determine the values of a and c in the model above and state the completed sinusoidal function (fill the values for a and c into the model). Show your work. Assume that the cycle begins with maximum volume of blood at t = 0 sec. b) Determine the period of the model. Leave the final answers in an exact form, in simplified terms. Make sure to include the appropriate units. Show all necessary work. (Exact form means no decimals) c) Sketch a graph showing one cycle of the volume of blood in the heart over time. Assume the horizontal line drawn in the grid below represents the axis of the curve (midline). Show the…arrow_forward
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