3.34 transform the following vectors into cylindrical coordinates and then evaluate them at the indicated points: (a) a = ˆx(x + y) at p1 = (1, 2, 3) (b) b = ˆx(y − x) + ˆy(x − y) at p2 = (1, 0, 2) ∗ (c) c = ˆxy2/(x2 + y2) − ˆyx2/(x2 + y2) + ˆz4 at p3 = (1,−1, 2) (d) d = ˆr sin θ + ˆ θθ cos θ + ˆ φφcos2 φ at p4 = (2, π/2, π/4) ∗ (e) e = ˆr cos φ + ˆ θθ sin φ + ˆ φφsin2 θ at p5 = (3, π/2, π)

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi

it is 10.6 according to my calculations