Chau will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.19 per mile driven. The second plan has an initial fee of $57 and costs an additional $0.15 per mile driven.

175 Miles has to be driven to do the plans cost the same.

Step-by-step explanation:

Assume The Chau Drive Y miles .

We Have Given Two Plans ,

Now,Put First Plan=Second Plan (When Both Plans Cost The Same)

50$ + 0.19$ × Y = 57$ + 0.15$ × Y

0.04$ × Y = 7  ⇔  Y = 175 Miles

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this