A poster is to have a total area of 125 cm2. There is a margin round the edges of 6 cm at the top and 4 cm at the sides and bottom where nothing is printed. What width should the poster be in order to have the largest printed area?

The correct answer is 15 cm.

Step-by-step explanation:

Let the width of the required poster be a cm.

We need to have a 6 cm margin at the top and a 4 cm margin at the bottom. Thus total margin combining top and bottom is 10 cm.

Similarly total margin combining both the sides is (4+4=) 8 cm.

So the required printing area of the poster is given by {( a-10 ) × ( a - 8) }

This area is equal to 125 as per as the given problem.

∴ (a - 10) × (a - 8) = 125

⇒ - 18 a +80 -125 =0

⇒ - 18 a -45 = 0

⇒ (a-15) (a-3) = 0

By law of trichotomy the possible values of a are 15 and 3.

But a=3 is absurd as a 4.

Thus the required answer is 15 cm.

dV(t)/dt = kV(t)

Step-by-step explanation:

Since the rate of change of the car’s value in dollars per year dV(t)/dt is proportional to the car’s value V(t), ten

dV(t)/dt ∝ V(t)

dV(t)/dt = kV(t)