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computergeek123
 2 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?
computergeek123
 2 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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eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1Well, first off, what will be the length of rectangle B?

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, should be (unless I'm missing something)dw:1343835098119:dw

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1So, \[l_{0}=5\]\[l_{1}=5*2\]Now we dilate this again,\[l_{2}=(5*2)*2=5*2^2\]seeing a pattern,\[l_{n}=5*2^n\]

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1But, we want to know how many dilations, n, gives us a length of 80. \[5*2^n=80\]Can you take it from here?

computergeek123
 2 years ago
Best ResponseYou've already chosen the best response.0What do I do next?

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1First divide both sides by 5. You get:\[2^n=16\]What is n?

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.1Do you understand exponents? If n=1 \[2^1=2\]If n=2\[2^2=2*2=4\]etc...
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