An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Recognize that direct variation implies a relationship of the form t = k × g .
Use a data point from the table to determine the constant of proportionality, k .
Calculate k = \tFrac 18 10 = 1.8 .
Substitute k back into the equation to find the relationship: t = 1.8 g ​ .

Explanation

Understanding Direct Variation The problem states that the tip varies directly with the number of guests. This means there's a constant ratio between the tip amount and the number of guests. We need to find the equation that expresses this relationship.

Setting up the Equation Since the tip, t , varies directly with the number of guests, g , we can write the relationship as t = k × g , where k is the constant of proportionality.

Using a Data Point to Find k We can use any data point from the table to find the value of k . Let's use the first data point: when g = 10 , t = 18 . Substituting these values into the equation, we get: 18 = k × 10 .

Solving for k Now, solve for k by dividing both sides of the equation by 10: k = \tFrac 18 10 = 1.8 .

Finding the Equation Substitute the value of k back into the equation t = k × g to get the equation that represents the relationship between the tip and the number of guests: t = 1.8 g .


Examples
Direct variation is a concept used in many real-life scenarios. For example, the distance you travel at a constant speed varies directly with the time you travel. If you drive at 60 miles per hour, the distance you cover is 60 times the number of hours you drive. Similarly, the amount you earn at a fixed hourly rate varies directly with the number of hours you work. If you earn $15 per hour, your total earnings are 15 times the number of hours you work. Understanding direct variation helps in predicting outcomes in various proportional relationships.

Answered by GinnyAnswer | 2025-07-03

When a current of 15.0 A flows for 30 seconds, approximately 2.81 × 1 0 21 electrons pass through the device. This is calculated by first determining the total charge and then dividing by the charge of a single electron. Thus, 450 C of charge contains around 2.81 × 1 0 21 electrons.
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Answered by Anonymous | 2025-07-04