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.
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.
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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Question
How do you solve question 7. Thank you.
Transcribed Image Text:Z tan U
u
Z SI U
b 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 cm³ 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.
=
X
9 The volume of a sphere is increasing at a rate numerically equal to its surface area at that instant. Show
dr
that
dt
1.
I
10 A point moves anticlockwise around the circle x² + y²
= 1 at a uniform speed of 2 m/s.
a Find an expression for the rate of change of its x-coordinate in terms of x, when the point is above the
x-axis. (The units on the axes are metres.)
onswer to part a to find the rate of change of the x-coordinate as it crosses the y-axis at
heen obvious without this formula?
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