Prove that: `t a n 70^0=t a n 20^0+2t a n 50^0dot`

The value of (tan70^(0)-tan20^(0))/(tan50^(0)) =

Prove that sum_(r=0)^n 3^r nCundersetr = 4^n .

Prove that the area of the triangle whose vertices are (t,t -2), (t + 2 , t + 2), and (t + 3, t ) is independent of t.

The position of a particle is given by r=3.0thati+2.0t^(2)hatj+5.0hatk where t is in seconds and the coefficients have the proper units for r to be in matres. (a) Find v (t) and a(t) of the particle . (b) Find the magnitude and direction of v (t) at t=1.0 s.

The position of an object moving along x-axis is given by x=a+bt^(2) where a = 8.5 m, b = 2.5 m s^(-2) and t is measured in seconds. What is its velocity at t = 0 s and t = 2.0 s. What is the average velocity between t = 2.0 s and t = 4.0 s ?

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

The position of a particle is given by r=3.0thati-2.0t^(2)hatj+4.0hatkm where t is in seconds and the coefficients have proper units for r to be in metres . (a) Find the v and a of the particle ? (b) What is the magnitude and direction of velocity of the particle at t=2.0s ?

Let A=[(0,1),(0,0) ] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .