Question

question 5 of 20
you may not use your calculator for this question.
which of the following could be the units for \\(\frac{dy}{dx}\\) if \\(y\\) is the surface area of a tumor and \\(x\\) is the radius of the tumor?
\\(\bigcirc\\) a. millimeters per centimeter
\\(\bigcirc\\) b. meters per radian
\\(\bigcirc\\) c. square millimeters per millimeter
\\(\bigcirc\\) d. meters per second
\\(\bigcirc\\) e. gallons per hour

Explanation:

Step1: Determine units of y and x

y is surface area, so its unit is area (e.g., square millimeters, square meters). x is radius, so its unit is length (e.g., millimeters, meters).

Step2: Analyze units of dy/dx

The derivative \(\frac{dy}{dx}\) has units of (units of y) / (units of x). So (area unit) / (length unit). For example, square millimeters / millimeter.

Step3: Evaluate options

• A: Length / Length (mm/cm) – incorrect.
• B: Length / Angle (m/radian) – incorrect.
• C: Square millimeters / millimeter – matches (area/length) – correct.
• D: Length / Time (m/s) – incorrect.
• E: Volume / Time (gallons/hour) – incorrect.

Answer:

C. Square millimeters per millimeter