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The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.

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(i) Perimeter , P = 2(x+y) (ii) A = x⋅ y ∴ When x = 8 cm and y = 6 cm, Hence, the area of the rectangle is increasing at the rate of 2 cm2/min.
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(i) Perimeter , P = 2(x+y)

(ii) A = x y

When x = 8 cm and y = 6 cm, 

Hence, the area of the rectangle is increasing at the rate of 2 cm2/min.

 

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(a) -2 (b) 2
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Since the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, we have: and (a) The perimeter (P) of a rectangle is given by, P = 2(x + y) Hence, the perimeter is decreasing at the rate of 2 cm/min. (b) The area (A) of a rectangle is given...
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Since the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, we have:

and

(a) The perimeter (P) of a rectangle is given by,

P = 2(x + y)

Hence, the perimeter is decreasing at the rate of 2 cm/min.

(b) The area (A) of a rectangle is given by,

A = x y

When x = 8 cm and y = 6 cm,

Hence, the area of the rectangle is increasing at the rate of 2 cm2/min.

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Total teaching experiences is 26 year's of 11 and 12

Perimeter of rectangle =2(x+y) dp/dt= 2( dx/dt +dy/dt =2×(-5+4)=-2 area of rectangle =x×y dA/dt=xdy/dt+ ydx/dt=8×4+-5×6=2
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Perimeter of rectangle =2(x+y)                                     dp/dt= 2( dx/dt +dy/dt =2×(-5+4)=-2                          area of rectangle =x×y                                                  dA/dt=xdy/dt+ ydx/dt=8×4+-5×6=2

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