<transcript><audio_2>quickly warms up to 85 degrees Fahrenheit you're going to let H of T be the temperature X feet from the heater T minutes after the heater is turned on alright now before I go any further I'm</transcript><caption><image_3>The image is a screenshot of a math worksheet with a graph on the right side. The graph has a curved line that starts at the top and ends at the bottom. The x-axis of the graph is labeled as "t (minutes)" and the y-axis is labeled with the temperature. On the left side of the image, there is a question that reads "You are in a room 30 feet long with a heater at one end. In the morning the room is in 64 degrees F. You have on the heater, which quickly warm up to 85 degrees E. Let the temperature x feet from the heater. If the figure below shows the outside of the room, it shows that the temperature is 30 minutes after it was turned off. For example, the temperature in minutes is 60 minutes.</caption><transcript><audio_4>just going to take some notes H of X T this guy represents temperature in degrees Fahrenheit after the heat is</transcript><caption><image_5>The image shows a hand holding a pen and writing on a piece of paper. The paper appears to be a math worksheet with a graph paper on it. The graph paper has a grid-like pattern on it and there is a line graph on the right side of the paper. On the left side, there is text that reads "You are in a room 10 feet long with a heater at one end. In the morning the rooms in 64 degrees F. You turn on the balance, which quickly wows up to 85 degrees F, let it (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,</caption><caption><image_6>The image shows a hand holding a black pen and writing on a piece of paper. The paper appears to be a math worksheet with a graph on it. The graph is a line graph with a vertical axis and a horizontal axis. The x-axis of the graph is labeled "H(x) = 50" and the y-axis is labeled as "60". 

On the left side of the paper, there is a question written in black ink that reads "You are in a room 10 feet long with a heater at one end. In the morning the room is in 64 degrees F. You turn on the heater, which quickly warm up to 85 degrees F, let it be the temperature of a foot from the heater. How warm is in 10 feet from the heaters 5 minutes after it was turned on? 60 minutes. The figure below shows the constant diagrams for the heat.

At the bottom right corner of the image, there are two lines, one labeled "60" and another labeled "80".</caption><transcript><audio_7>turned on X is feet from the heater and it's a good idea when you're working with a variety of variables to write</transcript><video><caption><image_8>The image is a graph of a heat exchanger with a curved line graph on the right side. The graph is plotted on a graph paper with a white background. On the left side of the graph, there is a question written in black text that reads "You are in a room 30 feet long with a heater at one end. In the morning the room is in 64 degrees F. You turn on the heater, which quickly warm up to 85 degrees E. Let H(x,f) be the temperature in a foot from the heater. How warm is it at 10 feet from the heaters 5 minutes after it was turned on? The figure below shows the contour diagram for H2.</caption><caption><image_9>The image is a graph of a temperature graph with a curved line on the x-axis and a vertical axis on the y-axis. The graph is plotted on a white background and shows the temperature of a room in a room with a heat exchanger at one end. The temperature is in degrees F. The heat exchangers are shown on the left side of the graph, with the temperature on the right side and the temperature at the bottom. 

There is also a note on the top right corner of the image that reads "You are in the room 30 feet long with a heater at one point. In the morning the room in 64 degrees F, you turn on the heater, which is quickly warm up to 45 degrees. Let H(x^2) be the temperature x feet from the heater. How warm is it in 10 feet from thermostat 5 minutes after it was turned on? 20 minutes after I was turned."

On the bottom left corner, there is a question that asks the viewer to answer the question. The answer is written in black text.</caption><caption><image_10>The image is a screenshot of a page from a math worksheet. The page is divided into two sections. On the left side of the page, there is a graph with a curved line that starts at the top and ends at the bottom. The graph is labeled "t (minutes)". On the right side, there are two lines, one labeled "60" and the other labeled "50". The graph shows that the temperature of the room is at a constant temperature of 60 degrees Fahrenheit. 

There is also a note on the page that explains that the room in a room is 30 feet long with a heater at one end. The temperature is in degrees Fahrenheit and the temperature is at 60 degrees. The note also mentions that the heat from the heater is in minutes.

On the bottom right corner of the image, there appears to be a hand holding a pen, suggesting that the person is writing or drawing the graph.</caption><caption><image_11>The image shows a hand holding a black pen and writing on a piece of paper. The paper appears to be a math worksheet with a graph on it. The graph is a line graph with a curved line that starts at the top and ends at the bottom. The x-axis of the graph is labeled with the letters "H(x) =" and the y-axis is labeled as "60". The line is curved and has a point on the left side, indicating that it is a heat exchanger. On the right side of the paper, there is a text that reads "You are in a room 30 feet long with a heater at one end. In the morning the room is 64 degrees F. You turn on the heater, which quickly turns up to 5 degrees E. Let the temperature x feet from the heat exchangers. The figure below shows the contour diagram for it. How warm is it from the heater 5 minutes after it was turned on? 20 minutes after the heat is turned off.</caption></video><transcript><audio_12>down what they mean without them being in a bunch of words okay now the figure here's our figure that's our contour map shows the contour diagram for H how warm is it 10 feet from the heater five minutes afterwards</transcript><caption><image_13>The image is a screenshot of a page from a math textbook. The page is divided into two sections. On the left side, there is a graph with a line graph on the right side. The graph shows the temperature of a room in a room with a heater at one end and a temperature at the other end. The temperature of the room is 64 degrees F.

On the top left corner of the page, there are instructions on how to calculate the temperature in the room. The instructions are written in black text on a white background. 

The graph shows that the temperature is at a constant constant of 60 degrees F, with the temperature being at the top of the graph and the temperature below the temperature. There is also a note on the bottom right corner that reads "How warm is it in 10 feet from the heater 5 minutes after it was turned on?"

There is a hand pointing to the graph, indicating that the user is in the process of solving the equation.</caption><transcript><audio_14>turned on so they're looking for H of 10 feet from the heater so that's feet from heater is X five minutes after was turned on so that's T so that's the value that we want from the chart the second one says 20 minutes afterwards</transcript><transcript><audio_15>turned on now doesn't give you a feet but I'm going to assume it's the same because they haven't stated otherwise so it's going to be H of 10 20 those are the two things that we want H of 10 5 H</transcript> quickly warms up to 85 degrees Fahrenheit you're going to let H of T be the temperature X feet from the heater T minutes after the heater is turned on alright now before I go any further I'm just going to take some notes H of X T this guy represents temperature in degrees Fahrenheit after the heat is turned on X is feet from the heater and it's a good idea when you're working with a variety of variables to write down what they mean without them being in a bunch of words okay now the figure here's our figure that's our contour map shows the contour diagram for H how warm is it 10 feet from the heater five minutes afterwards turned on so they're looking for H of 10 feet from the heater so that's feet from heater is X five minutes after was turned on so that's T so that's the value that we want from the chart the second one says 20 minutes afterwards turned on now doesn't give you a feet but I'm going to assume it's the same because they haven't stated otherwise so it's going to be H of 10 20 those are the two things that we want H of 10 5 H
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