Question

an hourglass is turned over with the top part filled with sand. after 3 minutes, there are 855 ml of sand in the top half. after 10 minutes, there are 750 ml of sand in the top half. which equation represents this situation

Answer 1

`y=-15x+900`

Explanation:

Let x be the number of minutes and y be the quantity of sand in the hour glass.

After 3 minutes,

Quantity of sand in the top half=855 ml

After 10 minutes , quantity of sand in the top half=750 ml

We have to find the equation which represents this situation.

Now, we get two points (3,855) and (10,750)

Slope formula :
`m=(y_2-y_1)/(x_2-x_1)`

By using slope formula

Slope =
`(750-855)/(10-3)=(-105)/(7)=-15`

The equation of a line with slope m passing through the point
`(x_1,y_1)`

`y-y_1=m(x-x_1)`

The equation of line with slope -15 and passing through the point (3,855) is give by

`y-855=-15(x-3)`

`y-855=-15x+45`

`y=-15x+45+855=-15x+900`

Hence, the equation represents this situation is given by

`y=-15x+900`

Answer 2

An hourglass is turned over with the top part filled with sand. after 3 minutes, there are 855 ml of sand in the top half. after 10 minutes, there are 750 ml of sand in the top half. This can be represents a two points ( 3, 855) and (10, 750) . using this to solve the slope m = (750-855)/(10-3) = -15. And using one point the equation is y = -15x + 900.