A bike travels 4 miles in half an hour, what is its speed?

please help me ill do anything! Collecting and Analyzing Data There are two types of observations: qualitative and quantitative.

OverLord2011 [107]

It depends on how you want to format your data table, as you can create as many columns or rows as you wish, but the important thing is, to display your quantitative data suitably and in the most simple manner. The main reason why data tables are even used, is to simplify and represent the data in an easy to interpret and access form. If your data table has two columns, then the left side would likely be the manipulated variable, or also known as the independent, and the right side would be the responding or dependent variable. To determine which is which, just look at your data and see which one is manipulated (changed) in order to make the other one "respond" or react to the changes (responding variable). In your case it seems that you do have two units, therefore two "sets" of data, so make sure you know which is which. Also, when you put it into your data table, ensure that you put your units in the top labeling row, so you won't have to rewrite (m 3) for every row of data. After that, it should be fairly easy to input your data and such into the table.

6 0

3 years ago

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the o

julsineya [31]

Answer:

1) $k=-\frac{1}{46}\approx -0.02$

2) $\textit{Limiting value} = 24$

3) $T(10)\approx \frac{494611944}{6436343}\approx 76.8$

Explanation:

First of all note that

$T_s=24$ is the surroundings temperature, the temperature of the room where the cup of coffee is. Then, the differential equation is:

$\frac{dT}{dt}=k(T-24)$

Also, note that all units are in degrees celsius and minutes. Then, we don't have to convert units. Let's not write units explicitly from now on.

Explanation

1) We have that

$\textit{rate of cooling}=\frac{dT}{dt}=1,\quad T=70$

at some point - the exact time at which this is true doesn't really play any role because the equation doesn't have t on the right hand side. Then, from the equation we get

$1=-(70-24)=46k\Rightarrow k=-\frac{1}{46}\approx -0.02$

The minus comes from considering the temperature must decrease. With this value we can write the equation more explicitely:

$\frac{dT}{dt}=-\frac{1}{46}(T-24)$

2) The coffee is cooling off as time goes by, and it won't get any cooler than 24 degrees celsius because that's the temperature of the room. Then, in the long run, the temperature of the coffee is 24 degrees celsius.

3) Remember that Euler's method consists of using an initial exact measurement to predict what will happen in the future, approximately. There is a formula to make those predictions an it depends on the time step they gave us. Let's compute things first and then I tell you the equations we used.

In this case we know that we start with a 90 degrees celsius cup of coffee, or, in terms of math,

$T(0)=90$

Then, we can predict:

$T(2)\approx 90+2\left[-\frac{1}{46}(90-24)\right]=\frac{2004}{23}\approx 87.1$

Let's use fractions so we don't lose accuracy from now. With this number we can make an approximation of the temperature after 2 more seconds:

$T(4)\approx \frac{2004}{23}+2\left[-\frac{1}{46}\left(\frac{2004}{23}-24\right)\right]=\frac{44640}{529}\approx 84.4$

and then

$T(6)\approx \frac{44640}{529}+2\left[-\frac{1}{46}\left(\frac{44640}{529}-24\right)\right]=\frac{994776}{12167}\approx 81.8$

and then

$T(8)\approx \frac{994776}{12167}+2\left[-\frac{1}{46}\left(\frac{994776}{12167}-24\right)\right]=\frac{22177080}{279841}\approx 79.2$

and finally, the number we wanted to find:

$T(10)\approx \frac{22177080}{279841}+2\left[-\frac{1}{46}\left(\frac{22177080}{279841}-24\right)\right]=\frac{494611944}{6436343}\approx 76.8$

I hope you noticed the pattern to compute the next prediction:

$\textit{next prediction} = \textit{previous one (or exact value if it's the first step)}\\+ h\ast(\textit{right hand side of the differential equation at the previous one})$