PLZ HELPP 1) Which polar equation represents an ellipse?

Question

1) Which polar equation represents an ellipse?

a)

b)

c)

d)

2) Two forces act on an object. The first force has a magnitude of 400 newtons and acts at an angle of 30° as measured from the horizontal. The second force has a magnitude of 280 newtons and acts at an angle of 135° as measured from the horizontal. Determine the vector v that represents the resultant force

a) v=(200-140√2)i + (200√3+140√2)j

b) v=(200+140√2)i + (200√3+140√2)j

c) v=(200√3+140√2)i + (200+140√2)j

d) v=(200√3 - 140√20i +(200+140√2)j

3) For v=-3i+6j, find unit vector u in the direction of v

a) u=-i+j

b) u= -1/3i + 2/3j

c) u=-√5/5 i + 2√5/5J

d) u= -√3/3 i +2√3/ 3 j

4) Which of the following is a point on the plane curve defined by the parametric equations?

x = 4t

y=12t^2+4t-1

a) (4,7)

b) (4,207)

c) (-2,4)

d) (-2,0)

Answer 1

2) Break the force into x and y components.

F1x = 400*cos(30)*i F1y = 400*sin(30)*j

F2x = 280*cos(135)*i F2y = 280*sin(135)*j

The Resulting force will be F = (400*cos(30)+280*cos(135))*i + (400*sin(30)+280*sin(135))*j I'll let you simplify

3) the magnitude |v| = √(-3)²+(6)² = √45 = 3*√5

u = (1/(3*√5))* (-3*i + 6*j) = (-3/(3*√5))*i + (6/(3*√5))*j . I'll let you simplify

4) You have to plug in different values.

if x = 4, 4t = 4 or t=1

Plug in t=1 to y=12t^2+4t-1. Does y = 7 or 207 for t = 1?

if x = -2, 4t = -2 or t = -1/2

Plug t = -1/2 ro y=12t^2+4t-1 Does y = 4 or 0 for t = -1/2?

I'll let you figure this out?

1) Try this one on your own. If you need further help, let me know.