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valentina_108 [34]
3 years ago
9

A stretched spring has a length of 12 inches when a weight of 2 lbs is attached to the spring. The same spring has a length of 1

8 inches when a weight of 5 lbs is attached to the spring. What is the length of the spring when no weights are attached?
Mathematics
1 answer:
Advocard [28]3 years ago
8 0
The way I figured this one out was saying that if it takes 2lbs to stretch it to 12 inches and 5lbs to stretch to 18 inches that means that 3 additional pounds = 6 inches. Therefore, each additional pound is 2 inches. We know already that with 2 lbs it was 12 inches in length and we can also say that 2 lbs = 4 inches. So subtract 4 from 12 and you end up with the answer of 8 inches. 
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(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per
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The question is incomplete. Below is the complete question:

A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11

mm and the overall height is 18 mm.

(a) Find the volume of the pill in cubic millimeters. Round to the nearest cubic

millimeter.

(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per

cubic millimeter? Round to the nearest tenth of a cubic millimeter.

Answer:

a. 603 cubic millimetre

b. 1.7 mg/mm^3

Step-by-step explanation:

The since the pill has the shape of a cylinder and 2 hemispheres at both ends of the cylinder, if we are to calculate the volume, we will need the formula for calculating the volume of a cylinder and the volume of a hemisphere:

a. The volume of a cylinder = π×r^2×h and the volume of a hemisphere = 2×π×r^3.

The total height of the pill is 18mm but that of the cylinder specifically is 11cm, so 18 - 11 = 7mm.

This becomes the combined radius of the two hemispheres. We will now split it into 2:

7/2 = 3.5mm

This becomes the radius of each of the 2 hemispheres and will be used for calculating their respective volumes. The cylinder too will share same radius with the spheres (3.5mm). Let us take π as 3.14

Volume of the pill is then:

V =[2× (2/3 × π×r^3)] + π×r^2×h

V = [2×[(2/3) × 3.14 × 3.5^3]] + 3.14 × (3.5^2) × 11

[2 × (89.752)] + 423.115

179.504 + 423.115

= 602.619

= 603mm^3 (nearest cubic millimetre)

b. In order to find out how much vitamin C the pill will contain per cubic millimetre if it is to contain 1000mg of vitamin C, we will simply divide 1,000mg by the already calculated volume:

= 1000/63

= 1.658

= 1.7 mg/mm^3 (nearest tenth)

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3 years ago
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