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computergeek123

  • 3 years ago

Agh! Somebody PLEASE help!!!! Joshua is creating a series of rectangles, one inside the other. The length of the first rectangle, Rectangle A, is five inches. Joshua dilates Rectangle A about its center by a scale factor of two to get Rectangle B. He repeats this process using the same scale factor till he gets a rectangle of length 80 inches. How many dilations did Joshua perform including the dilation of Rectangle A?

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  1. eseidl
    • 3 years ago
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    Well, first off, what will be the length of rectangle B?

  2. computergeek123
    • 3 years ago
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    10?

  3. eseidl
    • 3 years ago
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    Yeah, should be (unless I'm missing something)|dw:1343835098119:dw|

  4. eseidl
    • 3 years ago
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    So, \[l_{0}=5\]\[l_{1}=5*2\]Now we dilate this again,\[l_{2}=(5*2)*2=5*2^2\]seeing a pattern,\[l_{n}=5*2^n\]

  5. eseidl
    • 3 years ago
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    But, we want to know how many dilations, n, gives us a length of 80. \[5*2^n=80\]Can you take it from here?

  6. computergeek123
    • 3 years ago
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    What do I do next?

  7. eseidl
    • 3 years ago
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    solve for n

  8. computergeek123
    • 3 years ago
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    like how?

  9. eseidl
    • 3 years ago
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    First divide both sides by 5. You get:\[2^n=16\]What is n?

  10. eseidl
    • 3 years ago
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    Do you understand exponents? If n=1 \[2^1=2\]If n=2\[2^2=2*2=4\]etc...

  11. computergeek123
    • 3 years ago
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    Thanks

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