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IV. Find the value of k in each of the following. Show your solutions below.
1. y varies directly as x and y = 8 when x =4



2. y varies inversely as x, and x = 16 when y = 4



3. A varies jointly as l and w and whose A = 72 sq. cm when l = 12 cm and w = 2cm​

Sagot :

VARIATIONS

Directions: Find the value of k in each of the following. Show your solutions below.

1. y varies directly as x and y = 8 when x =4

Answer:

  • The constant of variation (k) is 2.

Solution:

  • [tex] \: \sf{y = kx} \\ \: \: \sf{8 = 4 \: k} \\ \sf{k = \frac{8}{4} } \\ \: \sf \: k = \underline{ \boxed { \purple{ \tt2}}}[/tex]

[tex] \Large \: \therefore \tt \: k = \orange 2[/tex]

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

2. y varies inversely as x, and x = 16 when y = 4

Answer:

  • The constant of variation (k) is 64.

Solution:

  • [tex] \: \: \: \: \: \: \: \: \: \sf \: y = \frac{k}{x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 4= \frac{k}{16} \\ \sf \: 4 \: (16) = k \\ \: \: \: \: \underline{ \boxed { \purple{ \tt \: 64}}} = \sf k[/tex]

[tex] \Large \: \therefore \tt \: k = \orange {64}[/tex]

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

3. A varies jointly as l and w and whose A = 72 sq. cm when l = 12 cm and w = 2cm

Answer:

  • The constant of variation (k) is 3.

Solution:

  • [tex] \: \: \: \: \: \: \: \sf \:A = klw \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \:72 = k \: (12)(2) \\ \: \: \: \: \: \: \: \: \: \: \sf \: 72 = k \: (24) \\ \sf \: \frac{72}{24} = k \\ \sf \: \underline{ \boxed{ \purple{ \sf \: 3}}} = \sf k[/tex]

[tex] \Large \: \therefore \tt \: k = \orange {3}[/tex]

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