problems using proportionality

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling.

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling.

t a d

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling.

t a d

When running a mile, one runs a distance 1.6 times less. The time running is proportional. It is 1.6 times less.

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling.

t a d

When running a mile, one runs a distance 1.6 times less. The time running is proportional. It is 1.6 times less.

4____ = 2.51.6

A bronze copy is made out ofexactly the same material and inexactly the same proportionsas the the NYC Statue of Liberty but reduces its volume from the NYC volume of 4000 m3 to 2 m3. The original mass is 3 x 107 kg. What is the mass of the new copy?

Jardin du Luxembourg

each MK82 bomb has 89 kg lbs TNT and delivers 4.1 x 105 kJ

Vietnam 1965

To one significant figure,how much energy does the new bunker buster deliver?

proportionality relations II

What is formula relating volume of a cube to the length of theside of the cube? We call the length of a side of cube 2r.

What is formula relating volume of a sphere to the length of theradius of sphere? We call the radius of a sphere r.

2r

r2r

What is the proportionalityrelation between V and r?

To one significant figurewhat is proportionality constant?

2r

r

What is the proportionalityrelation between V and r?

To one significant figurewhat is proportionality constant?

2r

V a r3

proportionality constant = 8

2r

r2r

V a r3

proportionality constant ≈ 4

Volume of sphere and cube have exactly the same proportionality relation. Only proportionality constant is different.

Vgreat pyramid = 1⅔ r3 Egyptian great pyramids often havesimilar proportions. The width is approximately 8/5 times theheight.

What is the proportionality relation between volume and r?

What is the proportionality constant?

V a r3

2r

r2r If

shapeis fixed

then, nomatter what

the shape, volumealways proportional

to a length cubed.