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There is 1 in. of water in a pool. The water level is increasing at 0.75 in./min . Which linear equation represents the total depth of the water, in inches, after x minutes?


A. 1+y=0.75x

B. y=0.75x+1

C. y=0.75x

D. x=0.75y

Respuesta :

I think it is B. y=0.75x+1. I think that 1 in. of water in a pool is the y-intercept.
aachen

Answer:

B. [tex]y=0.75x+1[/tex]

Step-by-step explanation:

Initial level of pool, [tex]y_i=1 \ inch.[/tex]

The rate of increase in level of water, [tex]\dfrac{dy}{dt}=0.75\ inch/min.[/tex]

Now, to find relation between depth  and time .

From above equation, [tex]dy=0.75\ dt[/tex].

Now at time = 0 min depth is 1 inch and at any time t=x min and depth=y inch.

Therefore, [tex]\int\limits^y_1 \, dy=0.75\int\limits^x_0 \, dt[/tex].

Integrating both sides,

We get [tex]y|_1^y=0.75\ t|_0^x[/tex]

[tex]y-1=0.75x[/tex]

[tex]y=0.75x+1[/tex]

Therefore , correct answer is B.

Hence, it is the required solution.

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