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A steam plant burns two types of coal: anthracite (A) and bituminous (B). For each ton of A burned, the plant produces 27.6 million Btu of heat, 3100 grams (g) of sulfur dioxide, and 250 g of particulate matter (solid-particle pollutants). For each ton of B burned, the plant produces 30.2 million Btu, 6400 g of sulfur dioxide, and 360 g of particulate matter.a. How much heat does the steam plant produce when it burns $x_{1}$ tons of $\mathrm{A}$ and $x_{2}$ tons of $\mathrm{B}$ ?b. Suppose the output of the steam plant is described by a vector that lists the amounts of heat, sulfur dioxide, and particulate matter. Express this output as a linear combination of two vectors, assuming that the plant burns $x_{1}$ tons of $\mathrm{A}$ and $x_{2}$ tons of $\mathrm{B}$ .c. $[\mathbf{M}]$ Over a certain time period, the steam plant produced 162 million Btu of heat, $23,610$ g of sulfur dioxide, and 1623 $\mathrm{g}$ of particulate matter. Determine how many tons of each type of coal the steam plant must have burned. Include a vector equation as part of your solution.

$x 1 = 3.9$ tons of nathracite conl nold $x 2 = 1.8$ tons of hituminous coal.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Missouri State University

McMaster University

Idaho State University

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in discussion that, given is there is a steam plant they advanced to type of poll is interested and B is luminous for each ton off a burn, the plant produced 7 27.6 million BTU off heat, okay, and 3100 g off sulfur dioxide and 2 50 g off particular matter way can say that he is the particular matter and the same in Batum Ina's. It will give on the values, uh, 30.2 million video off heat and 6400 g off sulfur dioxide and 3 60 g off particular matter P or politan. Okay, so the question is, how much heat does the steam plant produce when it wants Excellent Turn off e plus export Enough. Be so simple. This will be excellent on off a an expert on or be so excellent and is Onley heat. The question given is only here, So this will be 27.6 Class X two on the heat from the bottom Ina's Is this 30 point to and that will be the final product million btu off heat. So this will be the answer off. Caution A. Okay, now the ocean be the same as question A. In the question be it is asked about all the heat, the sulfur dioxide and the bulletin matter. Okay. And that. So I will read the question. Be first, uh, in the output. Supposed the heat cell photo oxidant particular. Enter particular matter. All three are present. Then we have to write this output as a linear combination of factor. Okay, so this will be simple X one A plus. XTO be and excellent. It will be 27.6, heat 3100 sulfur dioxide and 2 50 particular matter plus x two and B is 13.2. Video off million video off heat 6400 s auto on to 60 off particular matter. And that will be questo. Total amount produced in the steam plant. Okay, so this will be over. Answer of question be. And the cautions see, is the next part off portion be in the caution? See, the given is the given Is the total production off this equation? So this equation is 27.6 30. 100 2. 50 plus x two, 30.2, 6400 to 60 and total amount that is produced is given as 1 62 million VT! Off heat 23.610 is 23 1000. 6 months. Zero is sulfur and 16 to 3 is particular matters. So we have to find X one and x two hair. So for this, we will put in these in the metrics. Okay? And this will be like this. 27.6, 3100 to 15. Okay. And 30.2, 6400 to 60. And the result will be 1 62 to 3610 on 16 to 3. So when we reduce this metrics until we find the values of X one next to we will get in the final one. Zito 3.9 and 11.8 on 000 So from Disick wish thesis metrics, we can say the value off X one is hair and extra is hair. So excellent equals two 3.9 and x two equals two, 1.8. It means excellent equals two equals 23.9 ton off turn off entry side A and X two equals two, 1.8 tons off. Bit ominous be. This will be our final answer. Thank you

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