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12345Plotting graphs

Solutions to the exercises

Exercise 1
a

V = 10 π r 2

b

Enter Y1=10πX^2. Use the table to determine where r gives a volume closest to 1000 cm3. You will find r 5 . 6 cm.

c

V = 2 π r 3

d

The volume of the tin can is: 500 cm3. Make a table corresponding to: Y1=2πX^3. You will find r 4 . 3 cm.

Exercise 2
a

K = 200 + 0 . 04 a

b

I = 0 . 10 a

c

Use the table to find the first value of a for which K < I . You will find a = 3334

Exercise 3
a

Enter: Y1=250-0.5X^2 with window settings: 0 x 500 and 0 y 40000 .

b

Enter: Y1=0.04+200/X with window settings: 0 x 100 and 0 y 100 .

c

Enter: Y1=60/(30+0.5X) with window settings: 0 x 500 and 0 y 3 .

Exercise 4
a

12.83 euros

b

G T K = 100 q + 0 . 1 q

c

v.a.: q = 0

d

When the value of q becomes very large, so does the value of G T K become very large.

Exercise 5
a

l and b represent the length and the width of the printed part of the poster, given in cm. 1 m2 = 10000 cm2. The size of the poster is ( l + 25 ) ( b + 20 ) = 10000 .

b

b + 20 = 10000 ( l + 25 ) and therefore b = 10000 ( l + 25 ) - 20 .
GR: Y1=10000/(X+25)-20 with window settings: 0 x 500 and 0 y 400 .

c

When l = 0 , it follows that b = 380 and when b = 0 , it follows that l = 475 . In conclusion 0 l 475 and 0 b 380 .

d

In the table you can find that b = l when l 77 . 5 cm.
The dimensions of the poster will become 97.5 by 102.5 cm.

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