alot of stated problemos

[B3ndythumbs]

Ya i've been putting off posting these, so here come alot...

27. A stack of five identical plates is 8 cm tall and a stack of 9 is 13 cm tall. What would be the heigh of a stack of 4 if all plates nest within ea other?
ANS - 6.75 cm

28. The great pyramid of Khufu was constructed in 2589 BC with 481.4 ft as a height. Due to weathering, in 2004 AD its height was 449 ft. Assuming a linear decrease, when is the year which the height will be 440 ft?
ANS - 3279 AD

37. A hoola hoop is 36 inch in mean diameter and 1 in diameter in cross section. What is the volume?
ANS - 88.8 cubic in

36. Aspect ratio of US flag is 10:19. If a large flag has stripes at the bottom running 30 ft, what is shortest acceptable flagpole if the flag comes no close than 15 ft to the ground?
ANS - 30.8 ft

57. Icing is drizzled on top of a 9-in diameter cake. It is poured on the center at a rate of 1 cup/min and icing thickness is constant. If the icing on the cake is spreading radially at .5 in/s when it reaches the edge, what is the icing thickness?
ANS - .0170 in

27. What is the percent difference in distance to the horizon from a 5 ft tall person standing on ground and the same person on a 50-ft tall platform?
ANS - 232%

46. A 6-ft tall person occupies a volume of 3.85 cubic ft. What is the volume occupied by a 100-ft tall person statue? I think it should be 17800 cubic ft? ANS - 4630 ft.

Percent difference is always 2nd value minus 1st value, then divide by 1st value right? Is percent error the same or different?

46. A company makes all their saucepans using .03 in thick sheet metal. If an empty 2 qt saucepan weighs 2.7 lb, how much does a filled 4 qt saucepan weigh?
ANS - 12.6 lb

27. What is the roaming area of a goat on a 20 ft leash tied to the corner of a shed 8 ft by 12 ft?
ANS - 1110 sq. ft.

Thanx for all the help!

[AuSmith]

27. The height of a stack of [unparseable or potentially dangerous latex formula] plates is the height of one plate plus the height of [unparseable or potentially dangerous latex formula] gaps.

We can tell the height of a gap is [unparseable or potentially dangerous latex formula] in. So the height of [unparseable or potentially dangerous latex formula] plates is [unparseable or potentially dangerous latex formula] plates minus a gap. [unparseable or potentially dangerous latex formula] in.

28. From [unparseable or potentially dangerous latex formula] BC to [unparseable or potentially dangerous latex formula] AD is [unparseable or potentially dangerous latex formula] years. And there was a decrease of [unparseable or potentially dangerous latex formula] ft. With the linear assumption, we have that the pyramid is falling at [unparseable or potentially dangerous latex formula] ft./yr. We want how long it will take to fall [unparseable or potentially dangerous latex formula] more feet. [unparseable or potentially dangerous latex formula], which occurs around October of the year [unparseable or potentially dangerous latex formula].

37. If there were any one easy answer, it would be to find the circumference of the [unparseable or potentially dangerous latex formula] inch radius and multiply by the volume of the cross section. [unparseable or potentially dangerous latex formula] cu. in. Here is why that works...

You can estimate the area of the circular cross section to as close as you want to by slicing it into many rectangles with the centers of the rectangles directly above the center of the circle. Hence, you can estimate the volume to as close as you want by rotating those cross sections.

For any washer (what you get when you rotate a rectangle by a large radius) with mean radius of [unparseable or potentially dangerous latex formula], we see the volume is

[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]

So, you can sum all those little washers up (integrate) and you see that the quick solution was indeed valid.

36. The bottom of the flag is longer than how far up the pole it runs. So, it takes up [unparseable or potentially dangerous latex formula] of the pole. [unparseable or potentially dangerous latex formula] ft.

57. It spreads at [unparseable or potentially dangerous latex formula] in/s, taking [unparseable or potentially dangerous latex formula] seconds to cover a [unparseable or potentially dangerous latex formula] in. radius. After [unparseable or potentially dangerous latex formula] seconds, you have [unparseable or potentially dangerous latex formula]. This is equally spread over [unparseable or potentially dangerous latex formula] sq. in. [unparseable or potentially dangerous latex formula] in. Did I forget a [unparseable or potentially dangerous latex formula] somewhere?

[AuSmith]

27. I guess we're now expected to remember the radius of the earth? ...[unparseable or potentially dangerous latex formula] miles. You can form a right triangle where the three points are your head, the furthest point you can see on the horizon, and the center of the earth.

You get that the distance to the horizon is

[unparseable or potentially dangerous latex formula] mi.

If you're standing on a [unparseable or potentially dangerous latex formula] ft. platform, this becomes

[unparseable or potentially dangerous latex formula]

Yes,

[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]

Percent error is [unparseable or potentially dangerous latex formula]

46. The [unparseable or potentially dangerous latex formula] ft tall person is [unparseable or potentially dangerous latex formula] times taller, thicker, and wider. So, we have [unparseable or potentially dangerous latex formula] times more volume. I get what you got.

46. Since the thickness stays the same, the weight increases as fast as the surface area. If it asked for an empty [unparseable or potentially dangerous latex formula] qt saucepan, I would say [unparseable or potentially dangerous latex formula]. Now, it really bothers me that it doesn't say what it's filled with... how ludicrous! Given that a gallon of water is [unparseable or potentially dangerous latex formula] lbs, you get [unparseable or potentially dangerous latex formula]. Disgusting. I can't believe it.

27. The goat definitely has three quarters of the full circle [unparseable or potentially dangerous latex formula]. Then, you have [unparseable or potentially dangerous latex formula] ft quarter circle on the [unparseable or potentially dangerous latex formula] ft. side and a [unparseable or potentially dangerous latex formula] ft. quarter circle on the [unparseable or potentially dangerous latex formula] ft. side.

[unparseable or potentially dangerous latex formula] sq. ft.

[B3ndythumbs]

LOL wow, thanx so much!!!

57. Uhh, its 231 cu. in in a gal. :P

[AuSmith]

Haha, I guess I used [unparseable or potentially dangerous latex formula] and wrote [unparseable or potentially dangerous latex formula].