Answer:
The length of rectangular is increasing at a rate 0.5714 meters per hour.
Step-by-step explanation:
We are given the following in the question:
Initial dimensions of rectangular box:
Length,l = 10 m
Width,w = 7 m
[tex]\dfrac{dA}{dt} = 8\text{ square meters per hour}\\\\\dfrac{dw}{dt} = 40\text{ centimeters per hour} =0.4\text{ meters per hour}[/tex]
We have to find the rate of increase of length.
Area of rectangle =
[tex]A = l\times w[/tex]
Differentiating we get,
[tex]\displaystyle\frac{dA}{dt} = \frac{dl}{dt}w + \frac{dw}{dt}l[/tex]
Putting values, we get,
[tex]8 = \dfrac{dl}{dt}(7) + (0.4)(10)\\\\\dfrac{dl}{dt}(7) = 8 -4\\\\\dfrac{dl}{dt} \approx 0.5714[/tex]
Thus, the length of rectangular is increasing at a rate 0.5714 meters per hour.
Answer: The length increase [tex]\frac{4}{7}[/tex] meter per hour.
Step-by-step explanation:
Given:
Length = l = 10 m
Width = w = 7 m
The area increases at a rate of 8 square meters per hour. So, [tex]\frac{dA}{dt}=8[/tex].
The width increases by 40 centimeters per hour = 0.4 meter per hour. So, [tex]\frac{dw}{dt}=0.4[/tex].
[tex]A=L*w\\\frac{dA}{dt}=\frac{dL}{dt}\cdot w+L\cdot\frac{dw}{dt}\\8=\frac{dL}{dt}\cdot7+10\left(0.4\right)\\8=7\frac{dL}{dt}+4\\\frac{dL}{dt}=\frac{4}{7}[/tex]
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