Question

7 Mark for Review \( 4 x^{2} \) In a certain factory, assume that the number of workers is constant. The number of minutes \( N \) that it takes to make a single unit of a product and the number of units \( U \) of the product that are made per day satisfy the relationship \( U=\frac{k}{N} \), where \( k \) is a constant. Which of the following best describes the relationship between the rate of change, with respect to time \( t \), of \( U \) and the rate of change, with respect to time \( t \), of \( N \) ? (A) \( \frac{d U}{d t}=\frac{k}{\left(\frac{d N}{d t}\right)} \) (B) \( \frac{d U}{d t}=\frac{-k}{\left(\frac{d N}{d t}\right)} \) (C) \( \frac{d U}{d t}=\frac{k}{N^{2}}\left(\frac{d N}{d t}\right) \) (D) \( \frac{d U}{d t}=\frac{-k}{N^{2}}\left(\frac{d N}{d t}\right) \)

          7 Mark for Review
\( 4 x^{2} \)

In a certain factory, assume that the number of workers is constant. The number of minutes \( N \) that it takes to make a single unit of a product and the number of units \( U \) of the product that are made per day satisfy the relationship \( U=\frac{k}{N} \), where \( k \) is a constant. Which of the following best describes the relationship between the rate of change, with respect to time \( t \), of \( U \) and the rate of change, with respect to time \( t \), of \( N \) ?
(A) \( \frac{d U}{d t}=\frac{k}{\left(\frac{d N}{d t}\right)} \)
(B) \( \frac{d U}{d t}=\frac{-k}{\left(\frac{d N}{d t}\right)} \)
(C) \( \frac{d U}{d t}=\frac{k}{N^{2}}\left(\frac{d N}{d t}\right) \)
(D) \( \frac{d U}{d t}=\frac{-k}{N^{2}}\left(\frac{d N}{d t}\right) \)

7 Mark for Review
4 x^2

In a certain factory, assume that the number of workers is constant. The number of minutes N that it takes to make a single unit of a product and the number of units U of the product that are made per day satisfy the relationship U=(k)/(N), where k is a constant. Which of the following best describes the relationship between the rate of change, with respect to time t, of U and the rate of change, with respect to time t, of N ?
(A) (d U)/(d t)=(k)/(((d N)/(d t)))
(B) (d U)/(d t)=(-k)/(((d N)/(d t)))
(C) (d U)/(d t)=(k)/(N^2)((d N)/(d t))
(D) (d U)/(d t)=(-k)/(N^2)((d N)/(d t))

Added by Paul H.

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