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

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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​

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:

 \Large \: \therefore \tt \: k =  \orange 2

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

Answer:

  • The constant of variation (k) is 64.

Solution:

  •  \:  \:  \:  \:  \:  \:  \:  \:  \:  \sf \: y =  \frac{k}{x}   \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \sf \: 4=  \frac{k}{16}  \\  \sf \: 4 \: (16) = k \\   \:  \:  \:  \:  nderline{ \boxed { \purple{ \tt \: 64}}} =  \sf k

 \Large \: \therefore \tt \: k =  \orange {64}

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

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:

  •  \:  \:  \:  \:  \:  \:  \:  \sf \:A = klw \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \sf \:72 = k \: (12)(2) \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \sf \: 72 = k \: (24) \\  \sf \:  \frac{72}{24}  = k \\  \sf \:  nderline{ \boxed{ \purple{ \sf \: 3}}} =  \sf k

 \Large \: \therefore \tt \: k =  \orange {3}

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