Solved on Oct 23, 2023

Find the equation for water level $L$ receding at 0.5 ft/day when initial level is 34 ft. Determine how many days until level reaches 26 ft.

STEP 1

Assumptions1. The initial water level of the river is34 feet. . The water level is receding at a constant rate of0.5 foot per day.
3. We are asked to find the number of days it will take for the water level to reach26 feet.

STEP 2

We can model the water level of the river as a linear equation, where the slope represents the rate of change (receding rate) and the y-intercept represents the initial water level. The equation can be written as $= Initial\, level - Receding\, rate \\times days$

STEP 3

Now, plug in the given values for the initial level and receding rate to get the equation for the water level after d days.
$=34 -0.5d$

STEP 4

To find out when the water level will be26 feet, we can set L equal to26 in our equation and solve for d.
$26 =34 -0.d$

STEP 5

Rearrange the equation to isolate d on one side.
$0.5d =34 -26$

STEP 6

Calculate the right side of the equation.
$0.5d =8$

STEP 7

Finally, divide both sides of the equation by0.5 to solve for d.
$d = /0.5$

STEP 8

Calculate the number of days.
$d =8 /0.5 =16$ So, it will take16 days for the water level to reach26 feet.

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Find the equation for water level $L$ receding at 0.5 ft/day when initial level is 34 ft. Determine how many days until level reaches 26 ft.

STEP 1

Assumptions1. The initial water level of the river is34 feet. . The water level is receding at a constant rate of0.5 foot per day.
3. We are asked to find the number of days it will take for the water level to reach26 feet.

STEP 2

We can model the water level of the river as a linear equation, where the slope represents the rate of change (receding rate) and the y-intercept represents the initial water level. The equation can be written as $= Initial\, level - Receding\, rate \\times days$

STEP 3

Now, plug in the given values for the initial level and receding rate to get the equation for the water level after d days.
$=34 -0.5d$

STEP 4

To find out when the water level will be26 feet, we can set L equal to26 in our equation and solve for d.
$26 =34 -0.d$

STEP 5

Rearrange the equation to isolate d on one side.
$0.5d =34 -26$

STEP 6

Calculate the right side of the equation.
$0.5d =8$

STEP 7

Finally, divide both sides of the equation by0.5 to solve for d.
$d = /0.5$

STEP 8

Calculate the number of days.
$d =8 /0.5 =16$ So, it will take16 days for the water level to reach26 feet.

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Find the equation for water level LLL receding at 0.5 ft/day when initial level is 34 ft. Determine how many days until level reaches 26 ft.

STEP 1

Assumptions1. The initial water level of the river is34 feet. . The water level is receding at a constant rate of0.5 foot per day.3. We are asked to find the number of days it will take for the water level to reach26 feet.

STEP 2

STEP 3

Now, plug in the given values for the initial level and receding rate to get the equation for the water level after d days.=34−0.5d =34 -0.5d=34−0.5d

STEP 4

To find out when the water level will be26 feet, we can set L equal to26 in our equation and solve for d.26=34−0.d26 =34 -0.d26=34−0.d

STEP 5

Rearrange the equation to isolate d on one side.0.5d=34−260.5d =34 -260.5d=34−26

STEP 6

Calculate the right side of the equation.0.5d=80.5d =80.5d=8

STEP 7

Finally, divide both sides of the equation by0.5 to solve for d.d=/0.5d = /0.5d=/0.5

STEP 8

Calculate the number of days.d=8/0.5=16d =8 /0.5 =16d=8/0.5=16So, it will take16 days for the water level to reach26 feet.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the equation for water level $L$ receding at 0.5 ft/day when initial level is 34 ft. Determine how many days until level reaches 26 ft.

Assumptions1. The initial water level of the river is34 feet. . The water level is receding at a constant rate of0.5 foot per day.
3. We are asked to find the number of days it will take for the water level to reach26 feet.

Now, plug in the given values for the initial level and receding rate to get the equation for the water level after d days.
$=34 -0.5d$

To find out when the water level will be26 feet, we can set L equal to26 in our equation and solve for d.
$26 =34 -0.d$

Rearrange the equation to isolate d on one side.
$0.5d =34 -26$

Calculate the right side of the equation.
$0.5d =8$

Finally, divide both sides of the equation by0.5 to solve for d.
$d = /0.5$

Calculate the number of days.
$d =8 /0.5 =16$ So, it will take16 days for the water level to reach26 feet.