1. A grain elevator has a hole in the bottom that is releasing grain at 40 cubic inches per second. How long, to the nearest tenth of a second, does it take to fill a 5 foot tall cylinder with a diameter of 32 inches, if every minute the rate the grain is released at increases by 20%? (Hint: not a simple exponential change problem)
2. (This is a multi-step problem) The radius of a cylinder can be found by taking the product of the zeroes of y=x^3+3x^2-4x-12 with the product of the number of 12 basic functions that increase from negative infinity to positive infinity. The height of the cylinder is found by the product of the following two complex numbers (4+2i) and (6-3i). Then please find the volume of that cylinder if each of these refer to inches. Tommy has made six congruent snowballs whose sum of their volumes equals the volume of the cylinder. If we then take the sum of the snowballs' circumferences we will have found the height of a cone. The radius of that cone is equal to the number of extrema in the function y=x^3+3x^2-4x-12 where this unit is in feet. What is the volume of this cone in cubic inches?
If anyone is good at math and knows what I'm doing wrong, I'd really appreciate any help I can get. We're allowed to ask other people for help on this (it's a take-home test thing) but nobody I ask will lend a hand. Thanks in advance!
What I think I know for problem one:
Volume of the cylinder ≈ 48254.86 in^3
Rate of 2400 cubic inches per minute
y = 2400^1.2x
According to my formula, they'd intersect at 4.2392 minutes.
I don't think I did those one right though because it explicitly says that it's not a simple exponential problem.
What I think I know for problem two:
The zeroes of y=x^3+3x^2-4x-12 are -3, -2, and 2. (-3)(-2)(2)= 12
There are 4 basic functions that increase from negative infinity to positive infinity.
So the radius of the cylinder is 12 + 4 = 16.
The height of the cylinder is 30.
The volume of the cylinder = (pi)(r^2)(h), so V=24127.43
I'm not sure if I did this part correctly, but to find the volume of one snowball I divided the volume of the cylinder by 6, then I divided that number by (4/3)(pi) because the volume of a sphere is (4/3)(pi)(r^3) and then took the cube root of that number to get 9.865. Then, the circumference of the sphere would be (2)(pi)(r) = 61.98*6 = 371.90 for the height of the cone.
The radius of the cone is 24 inches (2 extrema * 12).
If I'm correct, then the volume of the cone would be (pi)(r^2)(h/3) = 2.24×10^5 cubic inches.
Problem is, that doesn't sound right to me, so any help would be greatly appreciated.
2. (This is a multi-step problem) The radius of a cylinder can be found by taking the product of the zeroes of y=x^3+3x^2-4x-12 with the product of the number of 12 basic functions that increase from negative infinity to positive infinity. The height of the cylinder is found by the product of the following two complex numbers (4+2i) and (6-3i). Then please find the volume of that cylinder if each of these refer to inches. Tommy has made six congruent snowballs whose sum of their volumes equals the volume of the cylinder. If we then take the sum of the snowballs' circumferences we will have found the height of a cone. The radius of that cone is equal to the number of extrema in the function y=x^3+3x^2-4x-12 where this unit is in feet. What is the volume of this cone in cubic inches?
If anyone is good at math and knows what I'm doing wrong, I'd really appreciate any help I can get. We're allowed to ask other people for help on this (it's a take-home test thing) but nobody I ask will lend a hand. Thanks in advance!
What I think I know for problem one:
Volume of the cylinder ≈ 48254.86 in^3
Rate of 2400 cubic inches per minute
y = 2400^1.2x
According to my formula, they'd intersect at 4.2392 minutes.
I don't think I did those one right though because it explicitly says that it's not a simple exponential problem.
What I think I know for problem two:
The zeroes of y=x^3+3x^2-4x-12 are -3, -2, and 2. (-3)(-2)(2)= 12
There are 4 basic functions that increase from negative infinity to positive infinity.
So the radius of the cylinder is 12 + 4 = 16.
The height of the cylinder is 30.
The volume of the cylinder = (pi)(r^2)(h), so V=24127.43
I'm not sure if I did this part correctly, but to find the volume of one snowball I divided the volume of the cylinder by 6, then I divided that number by (4/3)(pi) because the volume of a sphere is (4/3)(pi)(r^3) and then took the cube root of that number to get 9.865. Then, the circumference of the sphere would be (2)(pi)(r) = 61.98*6 = 371.90 for the height of the cone.
The radius of the cone is 24 inches (2 extrema * 12).
If I'm correct, then the volume of the cone would be (pi)(r^2)(h/3) = 2.24×10^5 cubic inches.
Problem is, that doesn't sound right to me, so any help would be greatly appreciated.
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