Assignment 12a

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course mth 163

6/25 11am

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Question: `q001. Note that this assignment has 3 questions

If we know that y = k x^2, then if (x2/x1) = 7, what is (y2/y1)?

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Your solution:

If (x2/x1) = 7, then y2/y1 = (x2/x1) ^2 which means y2/y1 = 7^2 = 49, so

confidence rating #$&*: 2

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Given Solution:

If y2 = k x2^2 and y1 = k x1^2, then y2 / y1 = (k x2^2) / ( k x1^2). Since k / k = 1 this is the same as

y2 / y1 = x2^2 / x1^2, which is the same as

y2 / y1 = (x2 / x1)^2.

In words this tells us if y to is proportional to the square of x, then the ratio of y2 to y1 is the same as the square of the ratio of x2 to x1.

Now if (x2 / x1) = 7, we see that y2 / y1 = (x2 / x1)^2 = 7^2 = 49.

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Self-critique (if necessary): I did not know what to do with the k in the equation, but I see the pattern of what to do now.

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Self-critique rating: 3

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Question: `q002. If we know that y = k x^3, then if (x2/x1) = 7, what is (y2/y1)?

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Your solution:

y2 = kx2^3 and y1 = kx1^3 so y2/y1 = (kx2^3 / kx1^3) the k/k = 1

y2/y1 = x2^3 / x1^3 is equal to y2/y1 = (x2/x1) ^3 which is 7^3 = 343

confidence rating #$&*: 3

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Given Solution:

If y2 = k x2^3 and y1 = k x1^3, then y2 / y1 = (k x2^3) / ( k x1^3). Since k / k = 1 this is the same as

y2 / y1 = x2^3 / x1^3, which is the same as

y2 / y1 = (x2 / x1)^3.

In words this tells us if y to is proportional to the cube of x, then the ratio of y2 to y1 is the same as the cube of the ratio of x2 to x1.

Now if (x2 / x1) = 7, we see that y2 / y1 = (x2 / x1)^3 = 7^3 = 343.

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Self-critique (if necessary):

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Self-critique rating:

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Question: `q003. If we know that y = k x^-2, then if (x2/x1) = 64, what is (y2/y1)?

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Your solution:

y2 = kx2^-2, y1 = kx1^-2, then y2/y1 = (kx2^-2 / kx1^-2), so k/k = 1

y2/y1 = (x2/x1) ^-2, then y2/y1 = (1/64) ^2 = .00024414

confidence rating #$&*: 3

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Given Solution:

If y2 = k x2^-2 and y1 = k x1^-2, then y2 / y1 = (k x2^-2) / ( k x1^-2). Since k / k = 1 this is the same as

y2 / y1 = x2^-2 / x1^-2, which is the same as

y2 / y1 = (x2 / x1)^-2, which is the same as

1 / (x2 / x1)^2, which gives us

(x1 / x2)^2.

So if y = k x^-2, then (y2 / y1) = (x1 / x2)^2.(

In words this tells us if y to is inversely proportional to the square of x, then the ratio of y2 to y1 is the same as the square of the ratio of x1 to x2 (note that this is a reciprocal ratio).

Now if (x2 / x1) = 64, we see that y2 / y1 = (x1 / x2)^2 = (1/64)^2 = 1/ 4096.

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Self-critique (if necessary):

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&#Very good responses. Let me know if you have questions. &#