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Dmitriy789 [7]
3 years ago
6

A chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying capacity of 564,000 gallons. Ta

nk cars with three different carrying capacities are​ available: 6,000 ​gallons,12,000 gallons, and 24,000 gallons. How many of each type of tank car should be​ leased?
Let x1 be the number of cars with a 6,000 gallon​ capacity, x2 be the number of cars with a 12,000 gallon​ capacity, and x3 be the number of cars with a 24,000 gallon capacity. Select the correct choice below and fill in the answer boxes within your choice.
Mathematics
1 answer:
yan [13]3 years ago
3 0

You forgot to give the choices so I will solve the problem in detail step-by-step explanation and then you can select the correct choice and fill in the answer boxes within your choice correctly.

Given the criteria stated in the problem, we can obtain the  following linear system:

\left \{ {{x_{1} + x_{2} + x_{3}  = 28} \atop {6000x_{1} + 12000x_{2}  + 24000x_{3} =564000}} \right.

The corresponding augmented matrix is

\left[\begin{array}{ccc|c}1&1&1&28\\6000&12000&24000&564000\end{array}\right]

\left[\begin{array}{ccc|c}1&1&1&28\\6000&12000&24000&564000\end{array}\right]  \frac{1}{6000} R_{1}→ R_{2}\left[\begin{array}{ccc|c}1&1&1&28\\1&2&4&94\end{array}\right] R_{2} +(-1)R_{1}

→R_{2} \left[\begin{array}{ccc|c}1&1&1&28\\0&1&3&66\end{array}\right]  R_{1} +(-1)R_{2}→R_{1} \left[\begin{array}{ccc|c}1&0&-2&-38\\0&1&3&66\end{array}\right]

The linear system corresponding to the reduced form is

\left \{ {{x_{1} -2x_{3} =-38} \atop {x_{2}+3x_{3}  =66}} \right.

Since x_{3} is the free variable, we let x_{3} =t, where t is any real number. Then the general solution can be written as follows:

\left \{ \begin{array}{ccc}x_{1} =&-38&+2t\\x_{2} =&66&-3t\\x_{3} =&t\end{array}\right

where t is any real number.

However, the definitions of x_{1},x_{2} and x_{3} imply that the solutions must be non-negative integers.  Therefore, we need to derive the possible range of values of t such that the general solution make sense for this problem:

\left \{ \begin{array}{ccc}-38&+2t&\geq 0\\66&-3t&\geq 0\\t&&\geq 0\end{array}\right

Solving the inequalities, we finally obtain all the relevant solutions  to the linear system:

\left \{ \begin{array}{ccc}x_{1} =&-38&+2t\\x_{2} =&66&-3t\\x_{3} =&t\end{array}\right

where t is any integer such that 19 \leq t \leq 22.

Thus, you just need to apply the above solution to the choices given to you and fill in the answer boxes correctly.

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On another map the distance between saugerties and kingston is 2 inches. Whar would tge distance from saugerties to catskill be
Mariana [72]

The question is incomplete. The map is attached as a photo and here is the complete question:

a. What is the actual distance between Saugerties and

Kingston? ___________________________

b. Catskill is 15 miles from Saugerties. What would the

distance on the map be? ___________________________

c. On another map, the distance between Saugerties and

Kingston is 2 inches. What would the distance from Saugerties to

Catskill be on this map? __________________

Since you have asked the answer for part (c) only, here is the answer:

Answer:

<u>The distance from Saugerties to Catskill would be </u><u>3 inches</u><u> on this map.</u>

Step-by-step explanation:

On the given map, the distance between Saugerties and Kingston is 4 inches and the scale is <u>1 inch = 2.5 miles.</u>

To calculate the actual distance in miles between Saugerties and Kingston, consider the given scale:

1 inch ---------- 2.5 miles

4 inches ------ x miles

Cross multiplying:

1x = 2.5 x 4

x = 10 miles

The actual distance between Saugerties and Kingston is 10 miles.

On another map, the distance between Saugerties and Kingston is 2 inches. Which means the scale is 2 inches = 10 miles. So 1 inch = 10/2 = 5 miles

The scale on the other map is 1 inch = 5 miles.

Catskill is 15 miles from Saugerties (given in the previous part). So on the map:

1 inch -------- 5 miles

y inch ------- 15 miles

Cross multiplying:

15 = 5y

y = 15/5

<u>y = 3 inches.</u>

The distance from Saugerties to Catskill would be 3 inches on this map.

7 0
3 years ago
Order the following list of numbers from least to greatest <br>V35, 5.7, 17/3, 5.83<br>​
irina1246 [14]

Answer:  

17/3, 5.7, 5.83, √35.

Step-by-step explanation:

√35, 5.7, 17/3, 5.83

√35 = 5.916

5.7 = 5.700

17/3 =  5.667

5.83 = 5.830.

So the answer is  17/3, 5.7, 5.83, √35.

​

8 0
3 years ago
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KonstantinChe [14]


The rise is the vertical distance between the two points, which is the difference between their y-coordinates. That makes the rise y2 − y1. The run between these two points is the difference in the x-coordinates, or x2 − x1.
8 0
3 years ago
Which situation can be represented by the inequality? x&lt;90 A. A refrigerator weighs more than 90 kg. B.There are 90 children
stellarik [79]
The inequality is:  x < 90 ( or x is less than 90 ).
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Answer B is represented by: x = 90.
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C ) A kiddie pool holds under 90 L of water.

6 0
3 years ago
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To make a perfect square, we must know that 22/2 = 11. In this case:

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