Question

23. If 2x + 3y + 4 = 0 and v(x) = 6 then v (y) is
(a)8/3
(c) -9
my 9
(d) 6​

Answer 1

$\displaystyle \sf V(y) = \frac{8}{3}$

Given :

2x + 3y + 4 = 0 and V(x) = 6

To find :

The value of V(y) is

(a) 8/3

(b) - 9

(c) 9

(d) 6

Concept :

Var(ax + b) = V(ax + b) = a²Var(x) = a²V(x)

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that , 2x + 3y + 4 = 0 and V(x) = 6

Step 2 of 2 :

Find the value of V(y)

$\displaystyle \sf 2x + 3y + 4 = 0$

$\displaystyle \sf{ \implies }3y = - 2x - 4$

$\displaystyle \sf{ \implies }V(3y) = V( - 2x - 4)$

$\displaystyle \sf{ \implies } {3}^{2} V(y) = {( - 2)}^{2} V( x )$

$\displaystyle \sf{ \implies } 9 V(y) = 4 V( x )$

$\displaystyle \sf{ \implies } V(y) = \frac{4}{9} V( x )$

$\displaystyle \sf{ \implies } V(y) = \frac{4}{9} \times 6$

$\displaystyle \sf{ \implies } V(y) = \frac{8}{3}$

Hence the correct option is (a) 8/3

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