Answers to math review

Algebra, Trig, Geometry

  1. x= -32/13

    2. y = -17/13

  2. angle at upper right is 70 degrees

    3. angle at middle top is 20 degrees

    angle at middle bottom right is 70 degrees

  3. The shaded area is (5/12)(pi)(5 cm)^2, which is about 32.7 square centimeters

    4. The perimeter surrounding the shaded area is 5 cm + 5cm + (5/12)(2 pi 5cm), which is about 23.1 cm

  4. x= 6cm

sin (theta) = 8/10

cos (alpha) = 8/10

tan (alpha) = 6/8

Calculus

  1. 2000/3
  2.  

    3. or could write as

     

     

  3. To find velocity, differentiate each component once. To find acceleration, differentiate each component again.

 

 

 

 

The position vector, r(t), describes a circle as time goes on. (The tip of the vector rotates counterclockwise.)

When t =0, 2 pi t =0. When t = 1/4, 2 pi t = pi/2.

So at t =0, v = 6pi (j) and a = -12 pi^2 (i)

And at t = 1/4, v = -6pi (i) and a = -12 pi^2 (j)

If you find the position at t =1/4, you'll find it has gone one-fourth the way around the circle, so the period is one second.

NOTICE: the magnitude of the acceleration is exactly (velocity)^2/(radius).