+273 I need help with all, but any help is great help!!! Thanks in advance! 
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)
+129852 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
+129852 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
+129852 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
+129852 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
+129852 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
+2448 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)
+129852 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 !!!!
+2446 This is not truly significant anymore, but, to me, it looks as if the diameter is 6 inches.
