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C is directly proportional to the square root of y.
When C = 12.8, y = 16.
(a) Express C in terms of y.
(b) Find C when y = 400

Sagot :

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Answer:

  • Explained and Given Below.

Explanation:

C ∝ √y

C = k√y

If C = 12.8, y = 16

12.8 = k√16

12.8 = k(4)

k = 3.2

So the expression:

C = 3.2√y

solve for C when y = 400

C  = 3.2(√400)

C = 3.2(20)

C = 64

The expression for C in terms of y where C is directly proportional to the square root of y is C=3.2√y and the value of C at y=400 is 64.

What is directly proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

C is directly proportional to the square root of y. Thus, the relation can be represented with the proportionality sign as,

[tex]C\propto \sqrt{y}[/tex]

Let k is the proportionality constant. Thus, the equation can be rewritten as,

[tex]C=k \sqrt{y}[/tex]

Here, the value of  C is 12.8 and the value of y is 16. Put these values in the above equation as,

[tex]12.8=k \times\sqrt{16}\\12.8=k \times4\\k=\dfrac{12.8}{4}\\k=3.2[/tex]

Thus, the value of constant is 3.2.

  • (a) Express C in terms of y.

The value of constant is 3.2. Thus, the expression for C in terms of y is given as,

[tex]C=3.2\sqrt{y}[/tex]

  • (b) Find C when y = 400

Put the value of y =400 in the above expression.

[tex]C=3.2\sqrt{400}\\C=3.2\times20\\C=64[/tex]

Thus, the expression for C in terms of y where C is directly proportional to the square root of y is C=3.2√y and the value of C at y=400 is 64.

Learn more about directly proportional relationship here:

https://brainly.com/question/13082482

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