Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius.
Ah, I see we're entering the chilly world of temperature and time. Quite the cool equation you've got there! So, if I understand correctly, we're trying to figure out how the temperature changes over time when we have ice around a bowl of water. Well, let's break it down!
First, we have the equation: D = -75t + 22. Let's break it down further. The variable D represents the temperature of the water in degrees Celsius, and t represents the time measured in minutes.
Now, if you're wondering why we have a negative coefficient multiplying t, think of it like this: The negative sign is like a chilly ice cube cooling down our equation. As time passes, the temperature decreases since the ice is doing its cooling magic. So, the larger t gets, the smaller the temperature becomes. Brrr, winter is coming!
But what about the +22 at the end? Well, think of it as the starting temperature before the ice therapy begins. It's like a warm little hug to the water before the ice cools it down. How nice!
So, by using this equation, you can calculate the temperature at a given time. Just plug in the value of t, and the equation will give you the corresponding temperature.
Hope that clears things up and brings a little laughter to your ice-cold equation! Stay cool!
To answer a question related to the given equation D = -75t + 22, we need to know the specific question you have in mind. However, let's go over some possible questions and how you can use the equation to find the answers.
1. What is the temperature after a certain amount of time?
To find the temperature after a certain amount of time, you need to substitute the desired time value (t) into the equation and solve for D. For example, if you want to know the temperature after 10 minutes, you would substitute t = 10 into the equation to get:
D = -75(10) + 22
D = -750 + 22
D = -728
So, the temperature after 10 minutes is -728 degrees Celsius.
2. How much does the temperature change in a given time period?
To find the change in temperature over a particular time period, you need to calculate the difference between the temperatures at the start and end of that period. For example, to find the change in temperature over 20 minutes, you would substitute t = 20 and t = 0 (the starting time) into the equation and calculate the difference:
D₁ = -75(20) + 22
D₁ = -1500 + 22
D₁ = -1478
D₀ = -75(0) + 22
D₀ = 22
Change in temperature = D₁ - D₀
Change in temperature = -1478 - 22
Change in temperature = -1500
So, the temperature drops by 1500 degrees Celsius over the 20-minute period.
3. How long does it take for the temperature to reach a certain value?
To find the time it takes for the temperature to reach a specified value, you need to rearrange the equation to solve for t. For example, if you want to find when the temperature reaches -500 degrees Celsius, you would rearrange the equation as follows:
D = -75t + 22
-500 = -75t + 22
Next, you would solve the equation for t:
-75t = -500 - 22
-75t = -522
t = (-522) / (-75)
t ≈ 6.96
Therefore, it takes approximately 6.96 minutes for the temperature to reach -500 degrees Celsius.
Remember that these examples are just possible questions you can ask about the equation. If you have a different question, please provide more details, and I'll be happy to help you further!
To lower the temperature, ice is placed around a bowl of water, and the relationship between time and temperature is represented by the equation D = -75t + 22. Here's a step-by-step breakdown of how this equation works:
1. D represents the temperature, measured in degrees Celsius.
2. t represents the time, measured in minutes.
3. The equation D = -75t + 22 is a linear equation and follows the form y = mx + b, where m is the slope and b is the y-intercept.
4. In this equation, -75 represents the slope and indicates that for every increase of 1 in the time (t), the temperature (D) will decrease by 75 degrees Celsius.
5. The +22 in the equation represents the intercept, which is the temperature at time zero, or the starting temperature before any ice is placed.
6. The negative sign (-) in front of 75 indicates that the temperature is decreasing over time, as would be expected when ice is used to lower the temperature of the water.
So, when using this equation, you can substitute the time value (t) to find the corresponding temperature (D) at that time.