I need help with all, but any help is great help!!! Thanks in advance!

LaughingFace Apr 25, 2018

#1**+3 **

83)

Volume of cube = S^3, where S = one side

V = 16^3 =4,096 mm^3 - volume of the cube

Volume of square pyramid =S^2 x h/3, where S=side, h=height

V =S^2 x h/3

4,096 =16^2 x h/3

4,096 = 256 x h/3 Divide both sides by 256

16 = h/3 Cross multiply

h = 48 mm - Height of the pyramid

48 / 16 = **3x - higher is the square pyramid than the cube.**

**81)**

The answer is "B"

79)

Simplify the following:

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

-(3 x^6 - 3 x^5 + 2 x^2 - 5) = -3 x^6 + 3 x^5 - 2 x^2 + 5:

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

Grouping like terms, x^6 - 3 x^6 + 3 x^5 - 2 x^5 - x^3 - 2 x^2 - 7 + 5 = (x^6 - 3 x^6) + (-2 x^5 + 3 x^5) - x^3 - 2 x^2 + (-7 + 5):

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

x^6 - 3 x^6 = -2 x^6:

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

3 x^5 - 2 x^5 = x^5:

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

5 - 7 = -2:

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

Factor -1 out of -2 x^6 + x^5 - x^3 - 2 x^2 - 2:

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

Guest Apr 25, 2018

#3**+3 **

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

CPhill Apr 25, 2018

#4**+3 **

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

CPhill Apr 25, 2018

#5**+3 **

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

CPhill Apr 25, 2018

#7**+3 **

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

CPhill Apr 25, 2018

#8**+2 **

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

CPhill Apr 25, 2018

#9**+2 **

This is what I did to get 85)

Volume of Hemisphere: \((2/3) \Pi r^3=(2/3)\Pi 3^3=56.5486677 \)

Volume of cylinder is \(\Pi r^2h=\Pi 3^2*12=339.29 \)

339.29+56.5486677=395.8 in.^3 (rounded to the nearest tenth)

RainbowPanda Apr 25, 2018

#10**+1 **

RainbowPanda has assumed a radius of 3...I assumed a radius of 6......from the pic...I can't actually tell if the "6" is the radius or the diameter.....

Anyway......you have an answer for each assumption !!!!

Thanks, RP !!!!

CPhill
Apr 25, 2018

#11**+3 **

This is not truly significant anymore, but, to me, it looks as if the **diameter** is 6 inches.

TheXSquaredFactor
Apr 25, 2018