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The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.
- a)5 cm/s
- b)6 cm/s
- c)2 cm/s
- d)1 cm/s
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The length of the rectangle is changing at a rate of 4 cm/s and the ar...
Let the length be l, width be b and the area be A.
The Area is given by A=lb
Given that, dl/dt =4cm/s and dA/dt =8 cm/s
Substituting in the above equation, we get
Given that, l=4 cm and b=1 cm
The Area is given by A=lb
Given that, dl/dt =4cm/s and dA/dt =8 cm/s
Substituting in the above equation, we get
Given that, l=4 cm and b=1 cm
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The length of the rectangle is changing at a rate of 4 cm/s and the ar...
To find the rate of change of width, we need to use the formula for the area of a rectangle: A = length * width. We are given that the length is changing at a rate of 4 cm/s and the area is changing at a rate of 8 cm/s. We are also given the values of length and width at a particular point in time, which are 4 cm and 1 cm respectively.
Let's denote the rate of change of width as dw/dt (where t represents time). We can express the area as a function of time using the given values:
A = length * width
A = 4 cm * 1 cm
A = 4 cm^2
Now, we can differentiate both sides of the equation with respect to time (t):
dA/dt = (d(length)/dt) * width + length * (d(width)/dt)
Given that dA/dt = 8 cm/s, d(length)/dt = 4 cm/s, length = 4 cm, and width = 1 cm, we can substitute these values into the equation:
8 cm/s = 4 cm/s * 1 cm + 4 cm * (d(width)/dt)
Simplifying the equation, we have:
8 cm/s = 4 cm/s + 4 cm * (d(width)/dt)
Rearranging the terms, we get:
4 cm/s = 4 cm * (d(width)/dt)
Now, we can solve for (d(width)/dt):
(d(width)/dt) = (4 cm/s) / (4 cm)
(d(width)/dt) = 1 cm/s
Therefore, the rate of change of width is 1 cm/s. Option D is the correct answer.
Let's denote the rate of change of width as dw/dt (where t represents time). We can express the area as a function of time using the given values:
A = length * width
A = 4 cm * 1 cm
A = 4 cm^2
Now, we can differentiate both sides of the equation with respect to time (t):
dA/dt = (d(length)/dt) * width + length * (d(width)/dt)
Given that dA/dt = 8 cm/s, d(length)/dt = 4 cm/s, length = 4 cm, and width = 1 cm, we can substitute these values into the equation:
8 cm/s = 4 cm/s * 1 cm + 4 cm * (d(width)/dt)
Simplifying the equation, we have:
8 cm/s = 4 cm/s + 4 cm * (d(width)/dt)
Rearranging the terms, we get:
4 cm/s = 4 cm * (d(width)/dt)
Now, we can solve for (d(width)/dt):
(d(width)/dt) = (4 cm/s) / (4 cm)
(d(width)/dt) = 1 cm/s
Therefore, the rate of change of width is 1 cm/s. Option D is the correct answer.
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The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer?
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The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer?.
The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer?.
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The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.a)5 cm/sb)6 cm/sc)2 cm/sd)1 cm/sCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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