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Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h. The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as F = V²/500 – V/4 + 14. On the basis of the above information, answer the following questions :
Given a curve y = 7x − x³ and x increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when x = 5 is :
A rectangular visiting card is to contain 24 sq.cm. of printed matter. The margins at the top and bottom of the card are to be 1 cm and the margins on the left and right are to be 1½ cm as shown below :
The surface area of a cube increases at the rate of 72 cm²/sec. Find the rate of change of its volume, when the edge of the cube measures 3 cm.
If the radius of a circle is increasing at the rate of 0.5 cm/s, then the rate of increase of its circumference is :
A sandbag is dropped from a balloon at a height of 60 metres. When the angle of elevation of the sun is 30°, the position of the sandbag is given by the equation y = 60 – 4.9 t², where y is the height of the sandbag above the ground and t is the time in seconds.
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