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The Jemperature over a 10-hour period is given by T(t) = "(2 + 91+ 32 Ia) Find the average temperature [b) Find the minimum temperalure [c) Find the maximum te...

Question

The Jemperature over a 10-hour period is given by T(t) = "(2 + 91+ 32 Ia) Find the average temperature [b) Find the minimum temperalure [c) Find the maximum temperature la) The average temperature is degrees (Type an integer or & decimal Round to one decimal place as needed )

The Jemperature over a 10-hour period is given by T(t) = "(2 + 91+ 32 Ia) Find the average temperature [b) Find the minimum temperalure [c) Find the maximum temperature la) The average temperature is degrees (Type an integer or & decimal Round to one decimal place as needed )



Answers

The table below gives the average monthly temperatures in degrees Fahrenheit for a certain area.
Find the mean and median for the following.
a. The maximum temperature
b. The minimum temperature

We are going to do problem number 93 discussion. We have to find ah given things like highest and lowest average. Okay. Now from the given expression, the expression is T of Acts This is equals two 23.65 Sign by by six. Multiplied two. X managed to five by three. This is added to 51.75 This is uh function. Okay, mm. The average monthly temperature with respect to X. Okay, so here X is the month. No, in first part it is hushed that what will be the high established monthly temperature. So when this function is going to be highest, this whole function is going to be highest and this sign function is going to be one. This complete part is going to be one. Then only we will have the highest monthly temperature. So when the sign function is going to be one, so we will be having 23.65 multiplied to one plus 51 175 Okay, this will give us the highest average temperature. So let us just tried done by turning this too. So that is 23.6, Wife, 23.65 plus 51.75 This is equal to 23.65 plus 51.75 So this is equal to 75.4. So 75.4 degree Fahrenheit is the highest temperature. Now, in be part we have to find its lowest average monthly temperature. So when when it is going to be lowest, when this sine function is going to be minus one. Okay, so this is the lowest temperature will be 23.65 Multiplied two minus one plus 51.75 So let us see how much it is. There is minus of 23.65 This is added to 51.75 This is 28. I want one degree friday night, this is average monthly temperature launched, monthly temperature. Okay, now let us do the C part in C part. It is. What is the distance between the highest and lowest? So if you see the graph of sine function, it is generally like this. Okay, so this is the highest in this is the lowest in the difference between this is half of its total time period. Okay, so let me just find the time period in this case is by by success uh multiplied to act. So period in this case that will be equal to pi divided by five by six. So piper get cancel out and period in this case is killed manus. The period in this case is 12 months. No, as period is 12 months of the gap between highest and lowest is half of the period, so half of the period is 12 by two, so that is six months. So six months will be the answer in this case. So that's some. Thank you.

Mhm Hi there in this problem. We're looking at a quadratic function. All right. We have a problem graft here. And what our function is representing is the temperature at a particular time in the day in degrees Fahrenheit. Uh So that's the output of our function. The input of our function is time and specifically the number of hours after six a.m. So, we're gonna look at some key feature of this graph and the main one is when does our we can look at this Y intercept right here. And what this is indicating this this zero kamas 59.3 is saying that at six a.m. When this function started, when it starts recording its data, our temperatures about 59 3°. All right. Our vertex up at the top here Is communicating that 6.7 hours after six ham our temperature hits quite warm, 90.86°. About 91°. All right. So if we're looking at six hours past six a.m. This is getting us to 12 and we might even want to look at here. 0.7 14. We're gonna multiply that by 60 for 60 minutes. All right. We're going to get At 1242. Right, We reached the hottest temperature of 90 pointless round this to one decimal boys, degrees Fahrenheit? Yeah. Okay. All right.

Mhm. The point of precipitation is plotted in the ground. Next we need to compute a. D. C. M. D. We know that the highest precipitation as 6.1 and know it precipitation is 0.2 hence day. Is there a roid that is 6.1 Class .2 or 2? Make a few calls straight points 15 and a echoes 6.1 Miners, 3.15 vehicles, 2.95. And also we know that the period is 12. Hence the because two parts over 12, which equals hi over six. And for C. We know that the highest precipitation. Yes, on january and has hi over six times one plus C. Show rico pie or group since the sine function reaches its maximum or pioneer to. And then we know that C equals pi anniversary. So the function P. T. It calls 2.95 times Sine hi over 16. Yes pi over three Charles 3.15. And its graph has also plotted in the picture.

So we have an equation for excuse me for a temperature and in Augusta Georgia, I believe it is and that the temperature is equal to or y is equal to 17 times the co sign Of, high over six times the temperature. Or excuse me the time. And then uh for the month and uh -7 pi over six And that is plus 75. Mhm. And let's just take a peek and see if they use those variables, yep, they use the same once they did, it is t up t and so temperature in terms of time and again, we know that january is considered to be one. And so we wanted to graph that and I grabbed it knowing that we wanted to go from time of one Two time of 25. So I put that in for my ex and just had a new tick marks every five, Which that was important. And then I know that the middle of the graph is at 75 and if I add on 17, I'm going to be up to 92. So I went up to as high as 100 And if I subtract 17 away I'm down to 58. So I went as low as 50. So my window looked like this and then I grafted on my calculator and the graph looked kind of like this like so accept, it will look more sinuous little than mine does. And then we wanted to know what the temperature was for april and for december in april is when X is four, in december is when X is 12. So when I was on my graph, I hit second calculate and I went to value and I type in for my X equals four and it tells me that that temperature will end up being at 75 degrees would be the average temperature Did the same thing for 12. And I find that the average temperature is going to end up being 60.3°.. Now, Graphically, we want to find when with the temperature will be. And let's see it said, I believe below 67, or lower which months? And so if we go back and we type in For Y Some to 67, So for Y said to just type in 67 and then grab that will find that your calculator will graph this nice lines. And if you will even have it in color and we can see these months along here and we could trace along we could do an intercept. But you want to find what these months are, what these months are and what these months are. And so if I just do a quick, do an intersect Mode on the calculator and have first curved second curve and then just move my cursor over. Or I can actually even just type in around one and that's going to get me to this point. And I find out that this point is that about months three and likewise do the same thing for the next one and type in the intersect and first curved second curve and then move the cursor till I get over here. We're close to, it doesn't have to be right there at that point And we see that that's going to take place at about this is at 10.9, 10.9. So we're going to have the 11th month and then if we add on a period, the period is 12. So if I add on 12 to this, this is going to be 15 at on 12 to this and we're going to be at 20 two point, that's a nine. And so if we want to know what months during that time frame, we're going to end up having the month 123 And here we're going to have the months 11, 12, 11, 12 And then we'll go back to January and so on. But these are the months in which we're going to end up having the temperature below 67 during year, during January, February March, and also in November and December.


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