CPhill

25%  pay   $600 - $649

5%  pay   < $600

So....about  30% pay less than  $650 

ACB will be an inscribed angle......it it measures 70°, then the arc it intercepts (AB) has twice this measure = 140°

Then....the length of this minor arc is given by :

Arc Length  =  2 * pi * radius * (140 /360)  =

2 * pi * 18 *  ( 7/18)  =

2 * pi * 7   =

14 pi   units

Good Job, Guest  !!!!

85

The cylinder (and hemisphere) both have a radius of 6....so....the total volume =

Volume of a cylinder  with a radius of 6 and height of 12   +  Volume of a hemisphere with a radius of 6

So  we have

pi  [  r^2 * height of cylinder   +    (1/2)(4/3) r^3  ]  =

pi  [ 6^2 * 12  +  (2/3)*6^3 ]  =

pi [ 432  + 144 ]  =

pi  [ 576 ]  ≈   1809.6 in ^3

Since the tangent is negatie and the csc is positive....  " t "  must fall into the second quadrant

tan t  =  -5 / 1    =   5 / - 1 =   y / x

We need to find r   =  √  [ x^2 + y^2]  =  √ [ (-1)^2  + 5^2 ]  = √26

sin t  =  y / r  =  5 / √26  =   (5/26)√26

cos t  =  x / r  =  -1 / √26  =  -√26/26

csc t  =   r / y  =  √26 / 5

sec t   =  r / x =  √26 / - 1    =  -√26

cot t  =  x / y  =   -1/5

And there you go  !!!

84

Volume of cylinder  =   pi *8^2 * 16  =  1024 pi  in^3     (1)

Volume of cone  = (1/3) pi * 4^2 * height  =  16/3 pi * height    (2)

If they have equal volumes.....set (1) and (2) equal  and solve for the cone's height

1024 pi    =  (16/3) pi * height        divide out pi

1024  = (16/3) * height       multiply both sides by 3/16

1024 (3/16)  = height 

192  in  = height

So.....the cone is    192/16  =  12 times as high as the cylinder

80

The  oblique cylinder doesn't matter.....we can consider it to be just like a "normal" cylinder as far as solving for the radius...so we have...

Volume of cylinder  = pi * r^2 * height

36 pi  = pi * r^2 * 18       divide both sides by 18 pi

2 = r^2      take the square root of both sides

√2  = r  ≈ 1.4 in

79

x^6 - 2x^5 - x^3 - 7  -  (3x^6 - 3x^5 + 2x^2 - 5)

Distribute  the  " - '   across the terms in the parentheses

x^6 - 2x^5 - x^3 - 7 - 3x^6 + 3x^5 - 2x^2 + 5       combine like terms

x^6 -3x^6 - 2x^5 + 3x^5 - x^3 - 2x^2 - 7 + 5

-2x^6 + x^5 - x^3 - 2x^2 - 2

78.  Volume of prism  = Area of Base * Height  

The base is a square, so its area is  6^2  = 36 in^2

The height  is 10 in

So the volume is   36 * 10  =  360 in^3

Volume of cylinder = pi * (diameter/ 2)^2 * height  = pi * (10/2)^2 * 6  = pi * 5^2 * 6  =

150pi in^3  ≈ 471.23 in ^3

So.....the cylinder has the greater volume

Here's the first two , LF  :

https://web2.0calc.com/questions/please-help-asap-ty_5#r7

And here are the other  ones :

https://web2.0calc.com/questions/please-help-asap-tysm#r1

f(x)  = 2x  + 2[ x  ( 1 - x) ]^(1/2)

f'(x)   2x + 2 [ x - x^2]^(1/2)      take the derivative

f '(x) = 2 + [ x - x^2]^(-1/2) (1 - 2x)        set this to 0

2  = (2x - 1)  * [x - x^2]^(-1/2)

2 (x - x^2)^(1/2)  = 2x - 1        square both sides

4 (x - x^2)  =  4x^2 - 4x + 1

4x - 4x^2  = 4x^2 - 4x + 1     simplify as

8x^2 - 8x + 1  =  0

8 (x^2 - x + 1/8)  = 0

x^2 - x + 1/8  =  0

x^2 - x  + 1/4  =  -1/8 + 1/4

(x - 1/2)^2  = 1/8        take the square root of both sides

x - 1/2 =  ±√(1/8)

x  = ±√(1/8) + 1/2

The positive root  gives the  x value of the maximum as  √[1/8] + 1/2  ≈ .3004

And the max value  is  ≈ 2.41421