Get expert advice and community support for all your questions on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
To determine the most logical interpretation of the equation [tex]\(C(20) = 700\)[/tex] given the cost function [tex]\(C(L) = 300 + 20L\)[/tex], let's go through the steps to understand what this function represents and how the given values fit into it.
1. Understand the given cost function:
[tex]\[ C(L) = 300 + 20L \][/tex]
This equation states that the cost [tex]\(C\)[/tex] for installing a sewer pipe consists of a fixed cost of [tex]$300 plus an additional $[/tex]20 for each foot of the pipe. Here,
- [tex]\(300\)[/tex] is the fixed cost.
- [tex]\(20L\)[/tex] is the variable cost that depends on the length [tex]\(L\)[/tex] of the pipe in feet.
2. Interpret the given value:
- The equation [tex]\(C(20) = 700\)[/tex] involves substituting [tex]\(L = 20\)[/tex] feet into the cost function.
3. Substitute [tex]\(L = 20\)[/tex] into the cost function:
[tex]\[ C(20) = 300 + 20 \times 20 \][/tex]
4. Calculate the cost:
[tex]\[ C(20) = 300 + 400 = 700 \][/tex]
This calculation confirms that for [tex]\(L = 20\)[/tex] feet, the cost is $700.
5. Interpret the calculated result:
The calculated cost [tex]\(700\)[/tex] corresponds to installing a pipe that is [tex]\(20\)[/tex] feet long.
Given the options, let's examine which matches our interpretation:
- (A) The cost to install a 700-foot sewer pipe is 20 dollars.
- This is incorrect because it misinterprets both the cost and the length in the context of the cost function.
- (B) 20 times the cost of a typical pipe is equivalent to 700 dollars.
- This is incorrect because it does not directly relate to the cost function given or to the interpretation of the calculated result.
- (C) The cost to install a 20-foot-long sewer pipe is 700 dollars.
- This is correct because it directly matches the interpretation of our calculated result.
Therefore, the most logical interpretation of the equation [tex]\(C(20) = 700\)[/tex] is:
[tex]\[ \boxed{\text{(C) The cost to install a 20-foot-long sewer pipe is 700 dollars.}} \][/tex]
1. Understand the given cost function:
[tex]\[ C(L) = 300 + 20L \][/tex]
This equation states that the cost [tex]\(C\)[/tex] for installing a sewer pipe consists of a fixed cost of [tex]$300 plus an additional $[/tex]20 for each foot of the pipe. Here,
- [tex]\(300\)[/tex] is the fixed cost.
- [tex]\(20L\)[/tex] is the variable cost that depends on the length [tex]\(L\)[/tex] of the pipe in feet.
2. Interpret the given value:
- The equation [tex]\(C(20) = 700\)[/tex] involves substituting [tex]\(L = 20\)[/tex] feet into the cost function.
3. Substitute [tex]\(L = 20\)[/tex] into the cost function:
[tex]\[ C(20) = 300 + 20 \times 20 \][/tex]
4. Calculate the cost:
[tex]\[ C(20) = 300 + 400 = 700 \][/tex]
This calculation confirms that for [tex]\(L = 20\)[/tex] feet, the cost is $700.
5. Interpret the calculated result:
The calculated cost [tex]\(700\)[/tex] corresponds to installing a pipe that is [tex]\(20\)[/tex] feet long.
Given the options, let's examine which matches our interpretation:
- (A) The cost to install a 700-foot sewer pipe is 20 dollars.
- This is incorrect because it misinterprets both the cost and the length in the context of the cost function.
- (B) 20 times the cost of a typical pipe is equivalent to 700 dollars.
- This is incorrect because it does not directly relate to the cost function given or to the interpretation of the calculated result.
- (C) The cost to install a 20-foot-long sewer pipe is 700 dollars.
- This is correct because it directly matches the interpretation of our calculated result.
Therefore, the most logical interpretation of the equation [tex]\(C(20) = 700\)[/tex] is:
[tex]\[ \boxed{\text{(C) The cost to install a 20-foot-long sewer pipe is 700 dollars.}} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.