Projectile Motion An object is propelled upward at an angle θ , 45 ∘ < θ < 90 ∘ , to the horizontal with an initial velocity v 0 feet per second from the base of a plane that makes an angle of 45 ∘ with the horizontal. See the illustration. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function R ( θ ) = v 0 2 2 16 cos θ ( sin θ − cos θ ) Show that R ( θ ) = v 0 2 2 32 [ s i n ( 2 θ ) − c o s ( 2 θ ) − 1 ] In calculus, you will be asked to find the angle θ that maximizes R by solving the equation sin ( 2 θ ) + cos ( 2 θ ) = 0 solve the equation for θ . What is the maximum distance R if v 0 =32 feet per second? Graph R = R ( θ ) , 45 ∘ ≤ θ ≤ 90 ∘ , and find the angle θ that maximizes the distance R . Also find the maximum distance. Use v 0 = 32 feet per second. Compare the results with the answers found in parts (b) and (c).
Projectile Motion An object is propelled upward at an angle θ , 45 ∘ < θ < 90 ∘ , to the horizontal with an initial velocity v 0 feet per second from the base of a plane that makes an angle of 45 ∘ with the horizontal. See the illustration. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function R ( θ ) = v 0 2 2 16 cos θ ( sin θ − cos θ ) Show that R ( θ ) = v 0 2 2 32 [ s i n ( 2 θ ) − c o s ( 2 θ ) − 1 ] In calculus, you will be asked to find the angle θ that maximizes R by solving the equation sin ( 2 θ ) + cos ( 2 θ ) = 0 solve the equation for θ . What is the maximum distance R if v 0 =32 feet per second? Graph R = R ( θ ) , 45 ∘ ≤ θ ≤ 90 ∘ , and find the angle θ that maximizes the distance R . Also find the maximum distance. Use v 0 = 32 feet per second. Compare the results with the answers found in parts (b) and (c).
Solution Summary: The author illustrates how an object is propelled upward at an angle of 45, to the horizontal with an initial velocity of v 0 feet per second.
Projectile Motion An object is propelled upward at an angle
, to the horizontal with an initial velocity
feet per second from the base of a plane that makes an angle of
with the horizontal. See the illustration. If air resistance is ignored, the distance
that it travels up the inclined plane is given by the function
Show that
In calculus, you will be asked to find the angle
that maximizes
by solving the equation
solve the equation for
.
What is the maximum distance
if
feet per second?
Graph
, and find the angle
that maximizes the distance
. Also find the maximum distance. Use
feet per second. Compare the results with the answers found in parts (b) and (c).
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
PLEASE SHOW ME THE RIGHT ANSWER/SOLUTION
SHOW ME ALL THE NEDDED STEP
13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
DO NOT GIVE THE WRONG ANSWER
SHOW ME ALL THE NEEDED STEPS
11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
Chapter 7 Solutions
Mylab Math With Pearson Etext -- Standalone Access Card -- For Precalculus (11th Edition)
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