Question

A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 35 degrees. At what rate is the distance from the plane to the radar station increasing 4 minutes later?

The distance is increasing at ________________________ km/min.

**Hint:** The law of cosines for a triangle is

*c*2=*a*2+*b*2−2*a**b*cos(*θ*)

where *θ*

is the angle between the sides of length a and b.

Answer #1

A plane flying with a constant speed of 9 km/min passes over a
ground radar station at an altitude of 6 km and climbs at an angle
of 25 degrees. At what rate is the distance from the plane to the
radar station increasing 5 minutes later?
Hint: The law of cosines for a triangle is
c^2=(a^2)+(b^2)−2abcos(θ)
where ? is the angle between the sides of length a and b

At a given moment, a plane passes directly above a radar station
at an altitude of 6 km and the plane's speed is 800 km/h. Let θ be
the angle that the line through the radar station and the plane
makes with the horizontal. How fast is θ changing 24 min after the
plane passes over the radar station?

A plane flying horizontally at an altitude of 1 mi and a speed
of 480 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 4 mi away from the station. (Round your answer to the nearest
whole number.)

A plane flying horizontally at an altitude of 1 mi and a speed
of 470 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 2 mi away from the station. (Round your answer to the nearest
whole number.)
mi/h

A plane flying horizontally at an altitude of 2 mi and a speed
of 540 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 4 mi away from the station. (Round your answer to the nearest
whole number.)
mi/h

A plane flies horizontally at an altitude of 6 km and passes
directly over a tracking telescope on the ground. When the angle of
elevation is π/4, this angle is decreasing at a rate of π/4
rad/min. How fast is the plane traveling at that time?

A plane flying horizontally at an altitude of 5 mi and a speed
of 470 mi/h passes directly
over a radar station. Find the rate at which the distance from
the plane to the station is increasing
when it is 7 mi away from the station. For full credit I expect
to see a well-labeled picture. Show all
work. Round your final answer to the nearest whole number. Do
not round intermediate values.
Include units of measure in your answer.

1.A conical tank has height 3 m and radius 2 m at the top. Water
flows in at a rate of 1.5 m3/min. How fast is the water
level rising when it is 1.1 m from the bottom of the tank? (Round
your answer to three decimal places.)
2.At a given moment, a plane passes directly above a radar
station at an altitude of 6 km. The plane's speed is 900 km/h. How
fast is the distance between the plane...

1.Let θ (in radians) be an acute angle in a right triangle and
let x and y, respectively, be the lengths of the sides adjacent to
and opposite θ. Suppose also that x and y vary with time. At a
certain instant x=1 units and is increasing at 9 unit/s, while y=7
and is decreasing at 19 units/s. How fast is θ changing at that
instant?
2.An airplane in Australia is flying at a constant altitude of 2
miles and...

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