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anonymous

  • one year ago

The function m = F(a) = a/8 gives the distance in inches on a map between two points that are actually a miles apart. 1. Whats if F(50)? What does F(50) represent?

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  1. anonymous
    • one year ago
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    Is This Algebra 2?

  2. anonymous
    • one year ago
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    yep

  3. jim_thompson5910
    • one year ago
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    F(a) = a/8 F(50) = 50/8 ... replace each 'a' with 50 F(50) = ???

  4. anonymous
    • one year ago
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    6.25?

  5. jim_thompson5910
    • one year ago
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    yes

  6. jim_thompson5910
    • one year ago
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    `The function m = F(a) = a/8 gives the distance in inches on a map between two points that are actually a miles apart` so basically, whatever the value of 'a' is, the output F(a) tells us the distance on the paper map so in this case, a = 50 miles means F(a) = 6.25 inches 6.25 inches on the map corresponds to 50 miles in real life

  7. anonymous
    • one year ago
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    oh ok. and how about this?

  8. anonymous
    • one year ago
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    theres another part

  9. anonymous
    • one year ago
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    What are the units for the domain and range of the function? What is the domain and range for the function?

  10. anonymous
    • one year ago
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    Would the range be x> than the number?

  11. jim_thompson5910
    • one year ago
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    what are some possible values for 'a' ?

  12. anonymous
    • one year ago
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    50... 6.25...?

  13. jim_thompson5910
    • one year ago
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    a = 50 is one value, what's another?

  14. anonymous
    • one year ago
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    a = 8?

  15. jim_thompson5910
    • one year ago
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    sure, we could have some distance be 8 miles we could also have 2 miles, 1.5 miles, 99 miles basically any positive number or 0

  16. anonymous
    • one year ago
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    oh, really?

  17. anonymous
    • one year ago
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    so the domain is x>0

  18. anonymous
    • one year ago
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    Yeah He's right

  19. jim_thompson5910
    • one year ago
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    yeah \(\Large a \ge 0\)

  20. anonymous
    • one year ago
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    Oh yeah

  21. anonymous
    • one year ago
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    I forgot the equal to part... Do you think you could help me with two more parts?

  22. jim_thompson5910
    • one year ago
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    'a' is the input variable (not x this time) remember to underline the `>`

  23. anonymous
    • one year ago
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    Yeah I Believe The Domain Is X > 0

  24. anonymous
    • one year ago
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    Find the a in terms of m and lable this new function G. Tell what this function represents?

  25. anonymous
    • one year ago
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    would this be like a(m)?

  26. jim_thompson5910
    • one year ago
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    in terms of meters?

  27. anonymous
    • one year ago
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    i guess... It doesn't really say

  28. jim_thompson5910
    • one year ago
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    it seems like there's something missing but idk what

  29. anonymous
    • one year ago
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    It just says find a in terms of m and label this new function G. Tell what this function represents.

  30. jim_thompson5910
    • one year ago
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    maybe they just want you to convert to meters

  31. jim_thompson5910
    • one year ago
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    1 mile = 1609.34 meters (approximate)

  32. anonymous
    • one year ago
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    No, but I think it's just asking for a in terms of m. This is like functions and inverses

  33. jim_thompson5910
    • one year ago
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    1 mile = 1609.34 meters (approximate) a*1 mile = a*1609.34 meters .... Multiply both sides by a. a miles = 1609.34a meters

  34. anonymous
    • one year ago
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    I am so confused...

  35. anonymous
    • one year ago
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    I think (a)(m)

  36. anonymous
    • one year ago
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    Ok.. Let's try last part then. Determine if F and G are inverses

  37. anonymous
    • one year ago
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    But for that we need to find out what a is in terms of m.... :(

  38. jim_thompson5910
    • one year ago
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    yeah I'm not sure what they want for g(x)

  39. anonymous
    • one year ago
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    yeah... Ugh, this is so aggravating

  40. anonymous
    • one year ago
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    Let me see if I can figure it out, and If I still can't I'll call you back.. Ok..?

  41. jim_thompson5910
    • one year ago
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    alright

  42. anonymous
    • one year ago
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    Thank you for your help so far though!!

  43. jim_thompson5910
    • one year ago
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    no problem

  44. anonymous
    • one year ago
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    @Mertsj

  45. Mertsj
    • one year ago
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    You rang?

  46. anonymous
    • one year ago
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    Yes, thank you

  47. anonymous
    • one year ago
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    I just don't get this question... Do you mind leading me through it?

  48. Mertsj
    • one year ago
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    Not at all. You found that the f(50)=6.25, right?

  49. anonymous
    • one year ago
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    yes

  50. anonymous
    • one year ago
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    But from there, I just sorta lost it... I don't get the find a in terms of m thing

  51. Mertsj
    • one year ago
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    Notice that the problem says that the function gives the distance in inches on a map.

  52. anonymous
    • one year ago
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    ok, I didn't think that was really important

  53. Mertsj
    • one year ago
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    So 6.25 is the distance in inches on a map. Big deal you say.

  54. anonymous
    • one year ago
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    Ok. I get that much but then I don't

  55. Mertsj
    • one year ago
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    And you have a point however, the second part of the question wants an explanation of the significance of 6.25 inches.

  56. anonymous
    • one year ago
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    Oh ok. Isn't the significance of it, the fact that you need it to be able to find G

  57. Mertsj
    • one year ago
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    And the problem tells us that as well when it says that 6.25 inches is the distance on the map of two cities that are "a" miles apart and "a" in our problem is 50 because our function is f(a)=a/8 and we found f(50).

  58. anonymous
    • one year ago
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    Like, isn't the 6.25 the value of a? Or have I mistaken this entire thing....?

  59. anonymous
    • one year ago
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    So what can I do to find the domain and range?

  60. Mertsj
    • one year ago
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    So we might say here is a map:|dw:1443834662965:dw|

  61. anonymous
    • one year ago
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    Oh ok. So 50 is a? correct?

  62. Mertsj
    • one year ago
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    yes

  63. anonymous
    • one year ago
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    Ok, and would that be the range...?

  64. Mertsj
    • one year ago
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    50 miles takes 6.25 inches on the map.

  65. anonymous
    • one year ago
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    ok

  66. Mertsj
    • one year ago
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    So if a is a number of miles on a map, then a would have to be some positive number, would it not?

  67. anonymous
    • one year ago
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    Yes. so the range would be any number greater than or equal to zero?

  68. Mertsj
    • one year ago
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    And that is the domain: the positive real numbers. Similarly, if you divide a positive real number by 8 you get a positive real number so the range is also the set of positive real numbers.

  69. anonymous
    • one year ago
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    Oh ok. And how can I find the range?

  70. Mertsj
    • one year ago
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    Did you read my previous post? Similarly, if you divide a positive real number by 8 you get a positive real number so the range is also the set of positive real numbers.

  71. Mertsj
    • one year ago
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    We would not include 0. Why would we want to represent 0 miles on a map?

  72. anonymous
    • one year ago
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    So the range would be x>0

  73. Mertsj
    • one year ago
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    yes

  74. anonymous
    • one year ago
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    Oh ok. So the domain is x=>0 and the range is x>0

  75. Mertsj
    • one year ago
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    Did you notice what I said about representing 0 miles on a map?

  76. anonymous
    • one year ago
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    What is the difference between the "units for the domain and range" and "what is teh domain and range"

  77. anonymous
    • one year ago
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    *the

  78. Mertsj
    • one year ago
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    "a" represents the members of the domain. According to the problem those numbers represent MILES between cities. f(a) represents the members of the range. According to the problem those numbers represent INCHES on the map.

  79. anonymous
    • one year ago
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    Oh that's what the units represent? Correct?

  80. Mertsj
    • one year ago
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    The units ARE miles and inches.

  81. anonymous
    • one year ago
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    Oh wait. To find a in terms of m, would I set it up like this? 50=f(6.25)=6.25/8

  82. Mertsj
    • one year ago
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    No. a is the number of miles. Would it be easier for you to use x and y?

  83. anonymous
    • one year ago
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    yes please.. all these variables give me a headache.

  84. Mertsj
    • one year ago
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    Or maybe m for miles and i for inches. We would say that inches = miles/8

  85. Mertsj
    • one year ago
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    Or i = m/8

  86. anonymous
    • one year ago
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    Ok, so 6.25=50/8

  87. Mertsj
    • one year ago
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    If we want miles in terms of inches we would say miles = 8(inches)

  88. anonymous
    • one year ago
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    so 50=8

  89. anonymous
    • one year ago
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    since 50 is the miles?

  90. Mertsj
    • one year ago
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    See? inches= miles divided by 8 and miles = inches times 8

  91. anonymous
    • one year ago
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    so 6.26=50/8 and 50=6.26/8

  92. Mertsj
    • one year ago
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    But your problem uses "a" for miles and f(a) for inches

  93. Mertsj
    • one year ago
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    6.25 = 50/8 and 50 = 8(6.25)

  94. anonymous
    • one year ago
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    oh right

  95. Mertsj
    • one year ago
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    f(a)= a/8 and a = 8(f(a))

  96. anonymous
    • one year ago
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    Oh ok. would that be the function?

  97. anonymous
    • one year ago
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    Where is the m though?

  98. Mertsj
    • one year ago
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    m = f(a) so you can replace f(a) with m

  99. Mertsj
    • one year ago
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    m=a/8 and a = 8m

  100. anonymous
    • one year ago
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    ok, and that would still be the same thing?

  101. Mertsj
    • one year ago
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    Yes. In math if two quantities are equal, you can replace one with the other.

  102. anonymous
    • one year ago
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    Oh cool, thanks! and are they both inverses? F and G? I would think so because inverses must both be equal to x, right?

  103. Mertsj
    • one year ago
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    I don't know where you are getting G.

  104. Mertsj
    • one year ago
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    I don't see it anywhere in the problem you posted.

  105. anonymous
    • one year ago
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    Well the new function must be named G. At least that's what the problem tells me.

  106. anonymous
    • one year ago
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    Find a in terms of m and label this new function G

  107. Mertsj
    • one year ago
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    Perhaps you should post the entire problem

  108. anonymous
    • one year ago
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    I did. Its a bit farther up. Like in pieces. I am sorry

  109. anonymous
    • one year ago
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    This is what it says. The function m=f(a) = a/8 give the distance in inches on a map between two points that are actually a miles apart. What is f(50)? What does F(50) represent? What are the units for the domain and range of the new function? What is the domain and range of the new function? Find a in terms of m and lable this new function G. Tell what this function represents. Determine if F and G are inverses

  110. Mertsj
    • one year ago
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    So a in terms of m is a=8m and the problem said to label this g. So we have g(m)=8m

  111. anonymous
    • one year ago
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    Oooh. Oh wow, that is what I had originally but I erased it because I thought it was wrong... And this would represent the number of miles, right?

  112. Mertsj
    • one year ago
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    yes.

  113. anonymous
    • one year ago
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    Ok, and how about the whole inverse thing?

  114. anonymous
    • one year ago
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    I-am spus , ce tot vorbești ? Acest lucru pare complet ... nu contează . Voi taci acum .

  115. Mertsj
    • one year ago
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    If you replace the variable in the function f with x you will get f(x)=x/8. If you replace the variable in the function g with x you will get g(x)=8x. According to the definition of inverse functions, you would get the same thing if they were inverses. We don't get the same thing so they are not inverse functions.

  116. anonymous
    • one year ago
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    I am sorry @SweetBeat but I am afraid we don't understand your question...

  117. anonymous
    • one year ago
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    and oh ok

  118. anonymous
    • one year ago
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    Oh, right they both have to be the same thing right?

  119. Mertsj
    • one year ago
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    @SweetBeat Neither of us know the language you are posting in so we find it very distracting and that is why I keep deleting your posts.

  120. anonymous
    • one year ago
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    Oh ok. I was wondering who was doing that.

  121. Mertsj
    • one year ago
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    Yes. The way to find an inverse function is to interchange the variables.

  122. anonymous
    • one year ago
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    Thank you so much @Mertsj for all of your help!! i understand this much better now!!!

  123. Mertsj
    • one year ago
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    So the inverse of m= a/8 is a = m/8

  124. anonymous
    • one year ago
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    Thank you, than you *bows in a grateful manner*

  125. anonymous
    • one year ago
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    Oh yeah you just switch them

  126. Mertsj
    • one year ago
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    you're very welcome. Good luck.

  127. anonymous
    • one year ago
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    One more question... I apologize. But the domain and range would be the x>0 (domain in miles) and x=>0 (range in inches) right? @Mertsj

  128. anonymous
    • one year ago
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    I just got confused on that one part

  129. Mertsj
    • one year ago
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    Yes. Very good but typically we use y for range. You might want to use a for domain and m for range since those are the variables used in your problem.

  130. anonymous
    • one year ago
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    Ok. Thank you!

  131. Mertsj
    • one year ago
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    yw

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