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Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.

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Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of
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12 Apr 2017, 04:25

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Top Contributor

Bunuel wrote:

If (x + 2)² = 9 and (y + 3)² = 25, then what is the maximum value of x/y?

(A) 1/8 (B) 1/2 (C) 5/8 (D) 5/2 (E) 10/3

(x + 2)² = 9 We have (something)² = 9 So, EITHER something = 3 OR something = -3 In other words, EITHER x + 2= 3 OR x + 2 = -3 If x + 2= 3. then x = 1 If x + 2= -3. then x = -5

(y + 3)² = 25 We have (something)² = 25 So, EITHER something = 5 OR something = -5 In other words, EITHER y + 3= 5 OR y + 3 = -5 If y + 3= 5, then y = 2 If y + 3= -5, then y = -8

We want to MAXIMIZE the value of x/y If the x-value and y-value have OPPOSITE signs, x/y will be NEGATIVE If the x-value and y-value have the SAME sign, x/y will be POSITIVE So, need the x-value and y-value have the SAME sign

Try #1 x/y = 1/2

Try #2 x/y = (-5)/(-8) = 5/8

Since 5/8 is greater than 1/2, the correct answer is C

Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of
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19 Apr 2017, 14:56

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Bunuel wrote:

If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of x/y?

(A) 1/8 (B) 1/2 (C) 5/8 (D) 5/2 (E) 10/3

Let’s determine values for x and y.

(x + 2)^2 = 9

√(x + 2)^2 = √9

|x + 2| = 3

We need to determine the value of x when (x + 2) is positive and when (x + 2) is negative.

x + 2 = 3

x = 1

OR

-(x + 2) = 3

-x - 2 = 3

-x = 5

x = -5

So x = 1 or x = -5.

In a similar fashion, we determine the value of y.

(y + 3)^2 = 25

√(y + 3)^2 =√25

|y + 3| = 5

We need to determine the value of y when (y + 3) is positive and when (y + 3) is negative.

y + 3 = 5

y = 2

OR

-(y + 3) = 5

-y - 3 = 5

-y = 8

y = -8

y = 2 or y = -8

We can maximize the value of x/y if x and y are both positive or if x and y are both negative. If x and y are both positive, then x/y = 1/2. If x and y are both negative, then x/y = -5/-8 = 5/8. Since 5/8 > 1/2, the maximum value of x/y is 5/8.

Answer: C
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