The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S are functions of the mileage m, C(m) =0.4 m +50 and S(m) = 0.03 m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003x^(2)+15x+4000 . Find the marginal cost when 17 units are produced.

A body travels uniformly a distance of (13.8 pm 0.2)m in a time (4.0 pm 0.3)s . Determine velocity of the body within error limits.

A flywheel of moment of inertia 5.0 kg m^2 is rotated at a speed of 60 rad/s. Because of the friction at the axle, it comes to rest in 5.0 minutes. Find a. The average torque of the friction. B. the total work done by the friction and c. the angular momentum of the wheel 1 minute before it stops rotating.

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. T he total energy of the satellite in terms of g_0 ,the value of acceleration due to gravity at the earth 's surface ,is

The distance travelled by a particle in time t is given by s=(2.5m/s^2)t^2 . Find a. the average speed of the particle during the time 0 to 5.0 s, and b. the instantaneous speed at t=5.0 is

A straight metal wire crosses a magnetic field of flux 4 m Wb in a time 0.4 s. Find the magnitude of the emf induced in the wire.

The heat is flowing through a rod of length 50 cm and area of cross-section 5cm². Its ends are respectively at 25°C and 125°C. The coefficient of thermal conductivity of the material of the rod is 0.092 kcal / m×s×°C. The temperature gradient in the rod is

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s and the amplitude is 0.5 cm. (a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x= 50 cm has reached its maximum displacement.