+0  
 
0
196
16
avatar+273 

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

LaughingFace  Apr 25, 2018
 #1
avatar
+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
 #2
avatar+273 
+2

thanks!! 

LaughingFace  Apr 25, 2018
 #3
avatar+88897 
+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

 

 

cool cool cool

CPhill  Apr 25, 2018
 #4
avatar+88897 
+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

 

 

cool cool cool

CPhill  Apr 25, 2018
 #5
avatar+88897 
+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

 

cool cool cool

CPhill  Apr 25, 2018
 #6
avatar+9552 
+3

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

laugh

Omi67  Apr 25, 2018
 #7
avatar+88897 
+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

 

 

cool cool cool

CPhill  Apr 25, 2018
 #8
avatar+88897 
+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

 

 

cool cool cool

CPhill  Apr 25, 2018
 #9
avatar+1770 
+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
avatar+88897 
+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  !!!!

 

 

cool cool cool

CPhill  Apr 25, 2018
 #11
avatar+2190 
+3

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

TheXSquaredFactor  Apr 25, 2018
 #12
avatar+88897 
+2

OK....I'm out-voted....LOL!!!!!

 

 

cool cool cool

CPhill  Apr 25, 2018
 #13
avatar+273 
+2

LOL regardless, thanks for all the help!!!!

LaughingFace  Apr 25, 2018
 #14
avatar+3035 
+2

81. (5x)^1/2=square root of 5x, which is \(\sqrt5x, B\)

tertre  Apr 25, 2018
 #15
avatar+273 
+2

Thanks so much! 

LaughingFace  Apr 25, 2018
 #16
avatar+3035 
+1

No problem, here anytime! smileysmiley

tertre  Apr 26, 2018

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