The cost and revenue functions of a product and givenm by `C(x)=2x+400` and `R(x)=6x+20` respectively,where x is the number of items produced by the manufacturer.How many items the manufacturer must sell to realise some profit?

The domain and range of a function f given by f(x)=3/x+1 are subsets of {-1/2,0,2/3,6/7,1} and {-5,0,4 1/2,5,5 1/2}respectively. List the elements of the function as ordered pairs.

Show that the function f : R_0 rarr R_0 defined by f(x)=1/x , where R_0 is the set of nonzero real numbers is bijective.

The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =kx^2/2, where k is the force constant of the oscillator. For k = 0.5 N ^-1 , the graph of V(x) versus x is shown in Fig. 6.12. Show that a particle of total energy 1 J moving under this potential must ‘turn back’ when it reaches x = ± 2 m.,br>

The amplitude of current in series LCR circuit connected to an AC frequency "omega" is given by i_m = v_m/(sqrt(R^2+(X_L-X_C)^2) Where X_L and X_C are inductive and capacitative reactances respectively and "v_m" is amplitude of voltage. Starting fron this equation show that sharpness of resonance in the circuit is equal to the quality factor of the circuit.

If x=a,y=b is the solution of the equations x-y=2 and x+y=4 then the values of a and b are respectively, a)3 and 1 b)-1 and -3 c)6 and 4 d)5 and 3

Two metals X and Y have work functions 2eV and 5eV respectively. Which metal will emit electrons, when it is irradiated with light of wavelength 400 nm and why?