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Write and apply a model for direct variatio EXAMPLE 2 Meteorology Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diagram shows a hailstone at two different times during its formation.

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EXAMPLE 2. Write and apply a model for direct variation. Meteorology. Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diagram shows a hailstone at two different times during its formation. EXAMPLE 2. - PowerPoint PPT Presentation

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Page 1: Write and apply a model for direct variation

Write and apply a model for direct variation

EXAMPLE 2

Meteorology

Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diagram shows a hailstone at two different times during its formation.

Page 2: Write and apply a model for direct variation

Write and apply a model for direct variation

EXAMPLE 2

a. Write an equation that gives the hailstone’s diameter d (in inches) after t minutes if you assume the diameter varies directly with the time the hailstone takes to form.

b. Using your equation from part (a), predict the diameter of the hailstone after 20 minutes.

Page 3: Write and apply a model for direct variation

Write and apply a model for direct variation

EXAMPLE 2

SOLUTION

a. Use the given values of t and d to find the constantof variation.

Write direct variation equation.d = at

0.75 = a(12) Substitute 0.75 for d and 12 for t.

0.0625 = a Solve for a.

An equation that relates t and d is d = 0.0625t.

b. After t = 20 minutes, the predicted diameter of the hailstone is d = 0.0625(20) = 1.25 inches.

Page 4: Write and apply a model for direct variation

Use ratios to identify direct variation

EXAMPLE 3

Sharks

Great white sharks have triangular teeth. The table below gives the length of a side of a tooth and the body length for each of six great white sharks. Tell whether tooth length and body length show direct variation. If so, write an equation that relates the quantities.

Page 5: Write and apply a model for direct variation

Use ratios to identify direct variation

EXAMPLE 3

Tooth length, t (cm)

1.8 2.4 2.9 3.6 4.7 5.8

Body length, b (cm)

215 290 350 430 565 695

SOLUTION

Find the ratio of the body length b to the tooth length t for each shark.

Page 6: Write and apply a model for direct variation

Use ratios to identify direct variation

EXAMPLE 3

215 1.8

119 290 2.4

121

430 3.6

119 565 4.7

120 695 5.8

120

350 2.9

121=

ANSWER

Because the ratios are approximately equal, the data show direct variation. An equation relating tooth length and body length is = 120, or b = 120t.b

t

Page 7: Write and apply a model for direct variation

GUIDED PRACTICE for Examples 2 and 3

5. What If? In Example 2, suppose that a hailstone forming in a cloud has a radius of 0.6 inch. Predict how long it has been forming.

ANSWER

Hailstone has been forming for about 19.2 minutes.

Page 8: Write and apply a model for direct variation

GUIDED PRACTICE for Examples 2 and 3

Sharks

In Example 3, the respective body masses m (in kilograms) of the great white sharks are 80, 220, 375, 730, 1690, and 3195. Tell whether tooth length and body mass show direct variation. If so, write an equation that relates the quantities.

6.

ANSWER

not a direct variation.


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