Question

Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.

equal to zero
less than 2
equal to 6
greater than 11

Answer 1

Answer: The correct option is (B) less than 2.

Step-by-step explanation: Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

Since the rate of change is constant and is equal to 6, so we must have

So, from equation (i), we have

Now, when Y = 11, then from equation (ii), we get

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.

Explanation:

Answer 2

Answer: The correct option is (B) less than 2.

Step-by-step explanation: Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

`Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}`

Since the rate of change is constant and is equal to 6, so we must have

`k=6.`

So, from equation (i), we have

`Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)`

Now, when Y = 11, then from equation (ii), we get

`Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=(11)/(6)<(12)/(6)=2\\\\\\\Rightarrow X<2.`

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.