The parametric equations x = square root t, y= 3t - 4 for t in [ 0,4] define a plane curve

a) We kindly invite you to read the explanation and check the image attached below for further details.

b) The rectangular equation is .

Step-by-step explanation:

a) Let and for . We proceed to graph the expression with the help of a graphing tool. In this case, the tool Desmos is used and the result is presented below.

b) The rectangular equation for the curve is:

(1)

(2)

By applying (1) in (2), we get the following equation in rectangular form:

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