Given: An airplane is flying horizontally at a constant height of 1000 meters above a fixed radar station. At a certain instant, the angle of elevation θ at the station is π/4 radians and decreasing at a rate of 0.1 rad/sec. Problem: What is the speed of the aircraft at this moment?

Q: The displacement (in centimeters) of a particle s moving back and forth along a straight line is…

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Q: The displacement from equilibrium of an object in harmonic motion on the end of a spring is given…

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Q: on the graph of f(x) = 4 sin (7 pi(x)), points P and Q are at consecutive lowest and highest points…

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Q: Suppose that the displacement d (in meters) of an object at timet (in seconds) satisfies Harmonic…

A: we have to find maximum displacement and period of given function. the solution is following

Q: A man walks along a straight path at a speed of 6 ft/s. A searchlight is located on the ground 24 ft…

A: NOTE: Refresh your page if you can't see any equations. . for the right angle triangle, use the tan…

Q: Question 18 ▼ Two cars are moving towards an intersection. One car is 150 meters north of the…

A: To solve this problem, we have to establish a geometric relationship between the cars and using…

Q: Question 11 If y = sin?t + tant, x=- In(-cost) - e inr, find the value of y' when t=. 4

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Q: The curves 71 (t) =(- 4t, ť, – 2t) and 7,(t) = (sin( – 3t), sin(3t), t – T) intersect at the origin.…

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Q: Rocket Elevation angle - 3000 ft- Camera Launching pad 12. For the camera and rocket in the above…

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Q: Lemi the Ant is eagerly watching a pink flower falling straight down towards a point on the ground…

A: The horizontal distance from lemi = 75 cm  The angle of elevation decreasing at the rate dθdt=-120…

Q: The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal 25cm wide.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 6. In the triangle shown, if 0 increases at a constant rate of 3 radians per minute, at what rate is…

A: Given:             θ increases at a constant rate of 3 radians per minute               i.e.,…

Q: A woman at a point A on the shore of a circular lake with radius 4 mi wants to arrive at the point C…

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Q: Consider the triangle shown below. If 0 increases at a constant rate of 2 radians per minute, at…

A: We can use application of derivative in order to solve the given problem.

Q: 11. The position of a particle as it moves horizontally is described by the given equation S=sint -…

A: Here, the displacement function is given by: s=sin t-cos t, 0≤t≤2π Now, to find the maximum and…

Q: 1. The velocity of a plane is modeled by v(t) = –1+ cos (+ 3 sin (), measured in miles per minute,…

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Q: sin A cos A 3 4. Determine the solutions to the equation - for 0 < A < 2n accurate to two decimal…

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Q: The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 +40…

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Q: A small frictionless cart, attached to the wall by a spring, is pulled 10 cm from its rest position…

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Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: The displacement (in centimeters) of a particle s moving back and forth along a straight line is…

A: Displacement function is given by We need to find average velocity during each given time period.

Q: Water traveling along a straight portion of a river normally flows fastest in the middle, and the…

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Q: A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back…

A: Instantaneous velocity is given by vt=dstdt, where s(t) is the displacement.

Q: A child wanders slowly down a circular staircase from the top of a tower. With x, y, z in feet and…

A: Given data is: x=10cost,  y=10sint,  and z=70-5t

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift‑off point.…

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Q: A tracking camera, located 1200 ft from the point of launching, follows a vertically ascending…

A: We need to find the rate at which balloon is rising in the air. This means we need to find dh/dt

Q: Question 1: A wind turbine has blades that turn at a rate of  15 revolutions per minute.  If each…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: pumps capable of delivering 100 hp to an agricultural applicati ated in a present economy study. The…

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Q: "The formula specifies the position of a point P that is moving harmonically on a vertical axis,…

A: The formula specifies the position of a point P that is moving harmonically on a vertical axis is…

Q: A dart is thrown upward with an initial velocity of 64 ft/s at an angle of elevation of 56°.…

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Q: Between two telephone poles that are 40 feet apart, there is a wire suspended in the shape of a…

A: we have to find slope of the curve and where the wire meets tha left pole

Q: EXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the…

A: x/6 = tanA x= 6 tanA dx/dt = (6) sec^2A (dA/dt) dA/dt = (1/6)cos^2A dx/dt dA/dt = (4/6)  cos^2A

Q: A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides…

A: Let AP=10 metres and BQ=9 metres be two vertical walls. Then, AB=a, AR=x and RB=a-x. Let ∠PRA=θ1 and…

Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: A dart is thrown upward with an initial velocity of 67 ft/s at an angle of elevation of 59°.…

A: Given that A dart is thrown upward with an initial velocity of 67 ft/s at an angle of elevation of…

Q: On a morning of a day when the sun will pass directly overhead, the shadow of a 64-ft building on…

A: Given: On a morning of a day when the sun will pass directly overhead the shadow of a 64-ft building…

Q: After exercising for a few minutes, a person has a respiratory cycle for which the velocity of…

A: 1Here,   v = 1.7 sinπt5a Full respiration cycle will be from sin(0) to sin 2π          ie   sin0 =…

Q: The displacement (in centimeters) of a particle s moving back and forth along a straight line is…

A:

Q: (a) A plane is traveling due east and passes over a radar station. When the plane is directly over…

A: using trigonometric identity

Q: The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal 25cm wide.…

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Q: Consider the following problem: A6 meter long ladder leans against a wall when the bottom of the…

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Q: A ship leaves port traveling southwest at a rate of 12 mi&gt;hr. At noon, the ship reaches its…

A: Let θ be the angle between the radar station and the ship at time t

Q: An aqueduct has water flowing through it, supplying a nearby village. Recent surveys of the duct…

A: Solve

Q: The displacement of a particle on a vibrating string is given by the equation s(t) = 11 + sin(11nt)…

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Q: 4. The vertical position, h, in metres, of a Ferris wheel is modeled using the function h(t) = 10…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Consider a triangle where two sides have fixed lengths 14 cm and 16 cm. Suppose the two sides are…

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Q: 3 feet per second, how tast is A 10-foot ladder rests against a wall. If the top of the ladder…

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Q: 1. Suppose that a bunny is running at a rate of 3 ft per second when r = 4. How fast is the angle 0…

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Q: Verify the identity by transforming the left-hand side into the right hand side.…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: A 13-centimeter pendulum moves according to the equation 0 = 0.17 cos(2t), where 0 is the angular…

A: Given that θ=0.17cos(2t)θ'=0.17-sin(2t)ddt(2t) [chain rule]θ'=0.17-sin(2t)(2)θ'=-0.34sin(2t)