Question

Martha conducted an experiment in which she dropped marbles into a beaker that contained somewater. As each marble was added, the water level in the beaker was recorded in a table. Note: eachmarble was identical in size and material as the next. Unfortunately, she spilled water on her datatable and the water dissolved all her information except for two data points: (5 marbles, 22milliliters) and (12 marbles, 50 milliliters). Using what is left of the data, answer the following questions A) How much did the water rise each time a marble was added to the beaker? How do youknow?B) What was the height of the water in the beaker before Martha started adding marbles? How do you know?C) Write an equation Martha can use to predict the height of the water if she knows how many marbles have been added

Answer 1

To find the rise in water level for each marble, subtract the initial water level from the final water level. The initial water level can be inferred by analyzing the rise in water level. Martha can predict the water height based on the number of marbles added using the equation: Water height = (number of marbles added * rise in water level per marble) + initial water level.

Step-by-step explanation:

How much did the water rise each time a marble was added to the beaker? How do you know?

To find out how much the water rose each time a marble was added, we can subtract the initial water level from the final water level when each marble was added. Using the given data, we can calculate the rise in water level as follows:

For the first data point, the rise in water level was 22 mL - 0 mL = 22 mL.
For the second data point, the rise in water level was 50 mL - 22 mL = 28 mL.

Therefore, the water rose by 22 mL and 28 mL when adding the 5th and 12th marble, respectively.

What was the height of the water in the beaker before Martha started adding marbles? How do you know?

To determine the height of the water in the beaker before Martha started adding marbles, we need to find the initial water level. Since the given data doesn't provide this information directly, we can infer it by finding the rise in water level for each marble. From the calculations in the previous question, we found that the water rose by 22 mL and 28 mL for the 5th and 12th marble, respectively. Therefore, the initial water level would be 0 mL - 22 mL - 28 mL = -50 mL (below the zero mark of the beaker).

Write an equation Martha can use to predict the height of the water if she knows how many marbles have been added

To predict the height of the water in the beaker based on the number of marbles added, Martha can use the equation:

Water height = (number of marbles added * rise in water level per marble) + initial water level

Using the given data, we know that the rise in water level per marble is 28 mL. Assuming the initial water level is -50 mL, the equation can be simplified to:

Water height = (number of marbles added * 28 mL) - 50 mL

Answer 2

Given:

The height of the water in the beaker is 22 millimeters when there are 5 marbles.

The height of the water in the beaker is 50 millimeters when there are 12 marbles.

A)

Required:

We need to find the amount of water that rises each time when the marble was added to the beaker.

Step-by-step explanation:

The difference between the 5 marbles and 12 marbles is 12-5 =7 marbles.

The difference between the height 22mm and 50 mm is 50-22 =28 mm.

Divide 28mm by 7 to find the amount of water that rises each time when the marble was added to the beaker.

`The\text{ amount of water rise each time marble was added to the beaker =}(28)/(7)`
`The\text{ amount of water rise each time marble was added to the beaker =4 mm}`

Answer:

`The\text{ amount of water rise each time marble was added to the beaker =4 mm}`

B)

Required:

We need to find the height of the water in the beaker before Martha started adding marbles.

Step-by-step explanation:

Multiply 5 by 4 to find the amount of water that rises after adding 5 marbles.

`5*4=20mm`

Subtract 20 mm from 22 mm to find the height of the water in the beaker before Martha started adding marbles

`22-20=2mm`

Answer:

The height of the water in the beaker is 2 mm before Martha started adding marbles.

C)

Required:

The initial height of the water in the beaker is 2mm.

The height rises 4 mm each time adding a marble.

Let x be the number of marble added to the water.

Let y be the height of the water in the beaker after adding x number of marbles.

The equation Martha can use to predict the height of the water if she knows how many marbles have been added is

`y=4x+2`

Answer:

`y=4x+2`