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answer the question correctly for good luck

If ‘c’ is directly proportional to‘d’ and c = 24 when d = 4

Find an equation connecting ‘c’ and ‘d’

Find ‘c’ when d = 8

Find ‘d’ when c = 54

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Answer:

  • The equation connecting c and d is: c = kd
  • The value of c when d=8 is: 48
  • The value of d when c=54 is: 9

Step-by-step explanation:

Proportion can be defined as the effect of changing one quantity on the other.

Given that

‘c’ is directly proportional to‘d’

It can mathematically be written as:

c∝d

A constant is introduced in the equation when the proportionality symbol will be removed. The constant is called constant of proportionality

[tex]c =kd[/tex]

Given that

c = 24 when d = 4

Putting the values

[tex]24 = k(4)\\k = \frac{24}{4}\\k = 6[/tex]

Putting the value of k

[tex]c = 6d[/tex]

Putting d = 8

[tex]c = 6(8) = 48[/tex]

Putting c = 54

[tex]54 = 6d\\d = \frac{54}{6}\\d = 9[/tex]

Hence,

  • The equation connecting c and d is: c = kd
  • The value of c when d=8 is: 48
  • The value of d when c=54 is: 9

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