Mathematics, 25.11.2019 15:31 amy290

0. 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.
(c) another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of
vitamin c per cubic millimeter. how much less vitamin c does this second pill contain, rounded to the
nearest milligram, than the one pictured?

Answers: 1

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Answers

Answer from: aredwolf2017

Part a) The volume of the pill is $603\ mm^{3}$

Part b) $1.7\frac{mg}{mm^{3}}$

Part c) $215\ mg$

Step-by-step explanation:

Part a) Find the volume of the pill in cubic millimeters

we know that

The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)

$V=\frac{4}{3}\pi r^{3} +\pi r^{2}h$

we have

$r= (18-11)/2=3.5\ mm$

$h=11\ mm$

assume

$\pi =3.14$

substitute

$V=\frac{4}{3}(3.14)(3.5)^{3} +(3.14)(3.5)^{2}(11)$

$V=603\ mm^{3}$

Part 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?

Divide 1,000 milligrams by the volume

$1,000/603=1.7\frac{mg}{mm^{3}}$

Part c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the

nearest milligram, than the one pictured?

step 1

Find the volume of the sphere

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=10/2=5\ mm$ ----> the radius is half the diameter

assume

$\pi =3.14$

substitute

$V=\frac{4}{3}(3.14)(5)^{3}$

$V=523.33\ mm^{3}$

step 2

Multiply the volume by 1.5 milligrams of vitamin C per cubic millimeter

$523.33*1.5=785\ mg$

step 3

Find the difference

$1,000-785=215\ mg$

Answer from: Quest

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

Answer from: Quest

2nd one in the first row is correct

Me on this i’m so tired and i can’t sleep until my progress is at 80 and this is the end of my year

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0. a pill has the shape of a cylinder with a hemisphere at each end. the height of the cylindrical p...