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6 An observer at A in the diagram is watching a plane fly overhead, and he tilts his head so that he is always looking directly at the plane. The aircraft is flying at 650 km/h at an altitude of 1.5 km. Let O be the angle of elevation of the plane from the observer, and suppose that the distance from A to B, directly below the aircraft, is x km. show that a By writing x = b A 650 km/h 1-5 km B 3 2 tan 0 3 dx de 2 sin²0 Hence find the rate at which the observer's head is tilting when the angle of inclination to the plane is. Convert your answer from radians per hour to degrees per second, correct to the nearest degree. 100-metre-high cliff. The boat is travelling towards the cliff at a inging when the angle of depression is 15º? arest degree f

6 An observer at A in the diagram is watching a plane fly overhead, and he tilts his head so that he is always looking directly at the plane. The aircraft is flying at 650 km/h at an altitude of 1.5 km. Let O be the angle of elevation of the plane from the observer, and suppose that the distance from A to B, directly below the aircraft, is x km. show that a By writing x = b A 650 km/h 1-5 km B 3 2 tan 0 3 dx de 2 sin²0 Hence find the rate at which the observer's head is tilting when the angle of inclination to the plane is. Convert your answer from radians per hour to degrees per second, correct to the nearest degree. 100-metre-high cliff. The boat is travelling towards the cliff at a inging when the angle of depression is 15º? arest degree f

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do you solve the first question. Question 6a and b. Thanks.
20 a b 6 An observer at A in the diagram is watching a plane fly overhead, and he tilts his head so that he is always looking directly at the plane. The aircraft is flying at 650 km/h at an altitude of 1.5 km. Let @ be the angle of elevation of the plane from the observer, and suppose that the distance from A to B, directly below the aircraft, is x km. SC Review of related Tates show that By writing x = A 650 km/h X 1-5 km B 3 dx de 3 2 sin² 0 2 tan 0 Hence find the rate at which the observer's head is tilting when the angle of inclination to the plane is. Convert your answer from radians per hour to degrees per second, correct to the nearest degree. 7 A boat is observed from the top of a 100-metre-high cliff. The boat is travelling towards the cliff at a speed of 50 m/min. How fast is the angle of depression changing when the angle of depression is 15°? Convert your answer from radians per minute to degrees per minute, correct to the nearest degree. 8 The water trough in the diagram is in the shape of an isosceles right triangular prism, x metres long. It is found that during summer in a drought, the amount of water lost to evaporation each day in cm' is equal to 10% of the surface area in cm². a Find a formula for the volume V cm³ of water in the trough when the depth is h cm. b Show that the rate at which the depth of the water is changing is constant. The volume of a sphere is increasing at a rate numerically equal to its surface area at that instant. Show 407 FM
Transcribed Image Text:20 a b 6 An observer at A in the diagram is watching a plane fly overhead, and he tilts his head so that he is always looking directly at the plane. The aircraft is flying at 650 km/h at an altitude of 1.5 km. Let @ be the angle of elevation of the plane from the observer, and suppose that the distance from A to B, directly below the aircraft, is x km. SC Review of related Tates show that By writing x = A 650 km/h X 1-5 km B 3 dx de 3 2 sin² 0 2 tan 0 Hence find the rate at which the observer's head is tilting when the angle of inclination to the plane is. Convert your answer from radians per hour to degrees per second, correct to the nearest degree. 7 A boat is observed from the top of a 100-metre-high cliff. The boat is travelling towards the cliff at a speed of 50 m/min. How fast is the angle of depression changing when the angle of depression is 15°? Convert your answer from radians per minute to degrees per minute, correct to the nearest degree. 8 The water trough in the diagram is in the shape of an isosceles right triangular prism, x metres long. It is found that during summer in a drought, the amount of water lost to evaporation each day in cm' is equal to 10% of the surface area in cm². a Find a formula for the volume V cm³ of water in the trough when the depth is h cm. b Show that the rate at which the depth of the water is changing is constant. The volume of a sphere is increasing at a rate numerically equal to its surface area at that instant. Show 407 FM
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