Question

The side x of a rectangle is increasing at a rate of 2 cm/s
while its side y is decreasing

at a rate of 1 cm/s.

(a) Find how fast the perimeter P of the rectangle is changing when
x = 4 cm and

y = 3 cm.

(b) Find how fast the area A of the rectangle is changing when x =
4 cm and y = 3

cm.

(c) Find how fast the length l of diagonal of the rectangle is
changing when x = 4

cm and y = 3 cm.

Answer #1

a. Each side of a square is increasing at a rate of 2 cm/s. At
what rate is the area of the square increasing when the area of the
square is 49 cm2? cm2/s
b. The length of a rectangle is increasing at a rate of 4 cm/s
and its width is increasing at a rate of 5 cm/s. When the length is
7 cm and the width is 5 cm, how fast is the area of the rectangle
increasing?

The length of a rectangle is increasing at a rate of 5 cm/s and
its width is increasing at a rate of 4 cm/s. When the length is 15
cm and the width is 6 cm, how fast is the area of the rectangle
increasing?

The length of a rectangle is increasing at a rate of 8 cm/s and
its width is increasing at a rate of 9 cm/s. When the length is 9
cm and the width is 5 cm, how fast is the area of the rectangle
increasing?

1. Find y' if sin y + 2x^4 = e^x + 4y + xy^3
2. The width of a rectangle is decreasing at a rate of 3
cm/sec.ind its area is increasing at a rate of 40 cm?/sec. How fast
is the length of the rectangle changing when its length is 4 cm and
its width is 7 cm ?

The radius of a circular cylinder is increasing at rate of 3
cm/s while the height is decreasing at a rate of 4 cm/s.
a.) How fast is the surface area of the cylinder changing when
the radius is 11 cm and the height is 7 cm? (use A =2 pi r2 +2 pi
rh )
b.) Based on your work and answer from part (a),is the surface
area increasing or decreasing at the same moment in time? How do...

One side of a triangle is increasing at a rate of 9 cm/s and a
second side is decreasing at a rate of 7 cm/s. If the area of the
triangle remains constant, at what rate does the angle between the
sides change when the first side is 22 cm long, the second side is
31 cm, and the angle is π/3? (Round your answer to three
decimal places.)

each side of a cube is increasing at a rate of 4 cm/s at what
rate is the surface area of the cube increasing when the surface
area of the cube is 486 cm^2

The height of a triangle is decreasing at a rate of 1 cm/min
while its area is increasing at a rate of 2 cm^2/min.
(a) What is the base of the triangle when its height is 10 cm
and its area is 100 cm^2?
(b) At what rate is the base of the triangle changing when its
height is 10 cm and its area is 100cm^2?

The
altitude of a triangle is increasing at a rate of 2.5 cm/min
while the area the triangle is increasing at a rate of 2.5 cm² per
minute. At what rate is the base of the triangle changing when the
altitude is 8.5 cm and the area is 94 cm² ?

The altitude (height) of a triangle is increasing at a rate of 1
cm/min while the area of the triangle is increasing at a rate of 2
square cm per min. At what rate is the base of the triangle
changing when the altitude is 10 cm and the area is 100 square
cm?

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