CPhill

3w * (-w)  =

3w * (-1w)  =

3 * -1 *  w * w  =

-3w^2

4 - 2a < 3a-1       add 1, 2a   to both sides

5 < 5a             divide both sides by 5

1 < a

 lim        tan5x

x->0      e^(2x) -1     use L'Hospital's Rule

 lim        5sec^2(5x)   =    5secx^2(0)   =   5*1  =  5

x->0      2e^(2x)                 2e^(2*0)          2 *1     2

Lateral surface area  = pi * radius * slant height

50  = pi * 5 * slant height    divide both sides by 5 pi

50 / [5 pi] =  10/pi cm = slant height ≈ 3.183 cm

V_cone  =  pi * r^2 * h

314.16 = pi * (5)^2 * h

314.16 = 25pi * h       divide both sides by 25pi

[ 314.16 ] / [ 25 pi]  =  h ≈ 4 cm

sinθ=   y/ r = a / 1 = a

cosθ =  x / r

And

1 - sin^2 θ  =  1 - a^2  = cos^2 θ

So

cos θ  =  ± √ [ 1 - a^2 ]

And since  tanθ<0   = sinθ / cosθ = a / cosθ and a > 0.....this angle is in the second quadrant.....so the cosine is negative

So

cos θ  =   - √ [ 1 - a^2 ]

Try this, Jessica :  http://www.purplemath.com/modules/radicals.htm

480g / 30  = 16g per unit

Total units  = 30 + 31  = 61

61 x 16g   =  976g

2x+y+3z = -12    (1)

3x-2y-z = 3          (2)

-x+5y+2z = -3    (3)

Multiply equation 3 by 2 add to equation 1

11y + 7z  = -18     (4)

Multiply equation 3 by 3 add to equation 2

13y + 5z  = -6       (5)

Multiply equation 4 by  -5

-55y - 35z  = 90   (6)

Multiply equation 5 by  7

91y  + 35z  = -42    (7)

Add (6)  and (7)

36y  = 48     →    y  = 48/36   = 4/3

And using (4)    .....11(4/3) + 7z  = -18   →   -54/3  - 44/3 = 7z  →  z  =  -98/21  = - 14/3

And using (3)    .....-x+5(4/3)+2(-14/3) = -3   →  x  =  20/3 - 28/3 + 9/3  =  1/3

So  {x, y, z }  =  { 1/3, 4/3, - 14/3 }