Question

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

Answer 1

(A).The expression for  C in terms of y is $C= 3.2\sqrt{y}$.

(B). The value of C at y=400 is 64.

Step-by-step explanation:

(A).The expression for  C in terms of y is  C=3.2√y.

(B). The value of C at y=400 is 64.

Given:

C is directly proportional to the square root of y.

C= 12.8  & y = 16.

To Find:

(A).The expression for  C in terms of y.

(B). The value of C at y=400

Formula Used:

This directly proportional relationship between r and t is written as $r \propto t$.

 the  sign used in middle is  known as the sign of proportionality.

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

Solution

As given-C is directly proportional to the square root of y.

The relation can be  represented with the proportionality sign  as mentioned below.

$C\propto\sqrt{y}$

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

$C= k \sqrt{y}$   -------- equation no.01.

As given- the value of  C is 12.8 and the value of y is 16.

Put these values in the above equation  no.01,

$12.8=k\sqrt{16}$

$12.8= 4k$

$k=\frac{12.8}{4} =3.2$

(A). Express C in terms of y.

Putting the value of k in equation no.01.

$C= 3.2\sqrt{y}$

(B). Find C when y = 400

Put the value of y =400 in the above expression

$C= 3.2\sqrt{y}$

 $C= 3.2\sqrt{400}$  

  $C= 3.2\times20$

   $C=64$  

Thus, (A).The expression for  C in terms of y is $C= 3.2\sqrt{y}$.

         (B). The value of C at y=400 is 64.

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Answer 2

A) C = 3.2$\mathsf{\sqrt{y}}$

B) C = 64

Step-by-step explanation:

Given that, C is directly proportional to the square root of y

➜ C ∝ $\mathsf{\sqrt{y}}$

➜ C = k$\mathsf{\sqrt{y}}$ ... ... (i), where k is an arbitrary constant

Putting C = 12.8, y = 16 in (i), we get

12.8 = k$\mathsf{\sqrt{16}}$

➜ 12.8 = k × 4

➜ k = 3.2

From (i), we have

C = 3.2$\mathsf{\sqrt{y}}$ ... ... (ii)

This is the required expression of C in terms of y.

When y = 400, from (ii), we get

C = 3.2 × $\mathsf{\sqrt{400}}$

➜ C = 3.2 × 20

➜ C = 64

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