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Answer:
The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Step-by-step explanation:
Dimensions of the rectangle
Height = 5cm
Rate of base = 3/2 cm/min
Area = 60cm^2
We know the area of a rectangle of given by = base* Height
b*h = 60
b*5 = 60
b = 12cm
Applying Pythagoras theorem while drawing a diagonal to the rectangle
so our diagonal will be 13cm
Upon differentiating the area of the rectangle we get
b*h = A=60cm^2
using the chain rule of differentiation
h*db/dt + b*dh/dt = 0
b*dh/dt = -h*db/dt
12*dh/dt = -5*3/2
dh/dt = -5/8 cm//min
so the height of the rectangle is decreasing at the rate of -5/8cm/min
now we have all the measurements we need
b = 12 , db/dt = 3/2cm/min
h = 5 , dh/dt = -5/8 cm/min
Upon differentiating we get
2b*db/dt + 2h*dh/dt = 2D*dD/dt
b*db/dt + h*dh/dt = D*dD/dt
12*3/2 + 5*(-5/8) = 13*dD/dt
18 -25/8 = 13*dD/dt
= 13*dD/dt
dD/dt =
Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Part A
Purchase Value of Anna's Car in 2015 = $36,000
Depreciated Value of Anna's Car in 2017 = $25,000
We know that the value of the car is depreciating linearly.
From the above data, we can see that the value of the car has reduced by $36,000-$25,000 = $11,000 over 2 years.
⇒ Per year the value has been depreciated by
⇒ Per year the value has been depreciated by $5,500
So if the value of a car in 2015 is V₀ then value of the car after t years can be determined by the below function:
V (t) = V₀ - (t*5,500), where t indicates the years passed since 2015
OR V (t) = 36,000 - (t*5,500), where t indicates the years passed since 2015
Part B
Suggested value of Anna's car for trade in option in 2018 = $15,000
In 2018, 3 years would have been passed since 2015. Using the value of t = 3 in the function determined in Part A:
V(3) = V₀ - (3*5,500)
⇒ V(3) = 36,000 - (16,500)
⇒ V(3) = $19,000
From the above calculations, we can see that the value of the car in 2018 should be $19,000, however the suggested value for trade in is indicated as $15,000 which is lower than what the value of the car should be. Hence, basis linear depreciation, the $15,000 value is not fair for the car in 2018.