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Bunuel
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If x and y are positive and x^2 + y^2 = 100, then for which of the 05 Apr 2021, 01:00
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D
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59% (01:46) correct 41% (01:34) wrong based on 425 sessions

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If x and y are positive and \(x^2+y^2=100\), then for which of the following is the value of x + y greatest?

A. x = 10
B. x = 9
C. x = 8
D. x = 7
E. x = 6
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D
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Bunuel
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If x and y are positive and x^2 + y^2 = 100, then for which of the 13 Apr 2021, 00:00
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Bunuel
If x and y are positive and \(x^2+y^2=100\), then for which of the following is the value of x + y greatest?

A. x = 10
B. x = 9
C. x = 8
D. x = 7
E. x = 6
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\(x^2 + y^2 = 100\) --> \((x+y)^2-2xy=100\) --> \((x+y)^2=100+2xy\) --> \(x+y=\sqrt{100+2xy}\).

We need to maximize \(x+y\), thus we need to maximize \(\sqrt{100+2xy}\). To maximize \(\sqrt{100+2xy}\) we need to maximize \(xy\).

Now, for given sum of two numbers, their product is maximized when they are equal, hence from \(x^2 + y^2 = 100\) we'll have that \(x^2y^2\) (or which is the same xy) is maximized when \(x^2=y^2\).

In this case \(x^2 + x^2 = 100\) --> \(x=\sqrt{50}\approx{7}\).

Answer: D.

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Hope it helps.
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If x and y are positive and x^2 + y^2 = 100, then for which of the 05 Apr 2021, 06:25
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Given: \(x^2 + y^2 = 100\), x and y are positive.
Greatest value of x + y at x =?

A. x = 10, y = 0, x + y = 10
B. x = 9, y = \(\sqrt{19}\) \(\approx\) 4.36, x + y \(\approx\) 13.36
C. x = 8, y = 6, x + y = 14
D. x = 7, y = \(\sqrt{51}\) \(\approx\) 7.14, x + y \(\approx\) 14.14
D. x = 6, y = 8, x + y = 14

So, correct answer is option D.
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If x and y are positive and x^2 + y^2 = 100, then for which of the 05 Apr 2021, 07:38
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MarmikUpadhyay
Given: \(x^2 + y^2 = 100\), x and y are positive.
Greatest value of x + y at x =?

A. x = 10, y = 0, x + y = 10
B. x = 9, y = \(\sqrt{19}\) \(\approx\) 4.36, x + y \(\approx\) 13.36
C. x = 8, y = 6, x + y = 14
D. x = 7, y = \(\sqrt{51}\) \(\approx\) 7.14, x + y \(\approx\) 14.14
D. x = 6, y = 8, x + y = 14

So, correct answer is option D.
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How did you determine the square of a prime?

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If x and y are positive and x^2 + y^2 = 100, then for which of the 05 Apr 2021, 08:02
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CEdward
MarmikUpadhyay
Given: \(x^2 + y^2 = 100\), x and y are positive.
Greatest value of x + y at x =?

A. x = 10, y = 0, x + y = 10
B. x = 9, y = \(\sqrt{19}\) \(\approx\) 4.36, x + y \(\approx\) 13.36
C. x = 8, y = 6, x + y = 14
D. x = 7, y = \(\sqrt{51}\) \(\approx\) 7.14, x + y \(\approx\) 14.14
D. x = 6, y = 8, x + y = 14

So, correct answer is option D.

How did you determine the square of a prime?

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We don't need to determine any square roots

For A, x+y=10 (and y=0)
For C and E, x+y=14

To evaluate B:
The square root of 19 will be greater than 4 and less than 5.
So x+y must be less than 9+5=14

To evaluate D:
The square root of 51 will be greater than 7 and less than 8
So x+y must be greater than 7+7=14
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If x and y are positive and x^2 + y^2 = 100, then for which of the 25 Apr 2021, 02:44
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Bunuel
If x and y are positive and \(x^2+y^2=100\), then for which of the following is the value of x + y greatest?

A. x = 10
B. x = 9
C. x = 8
D. x = 7
E. x = 6
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A: \(10^2+0^2=100\). Invalid because both x and y are positive
B: \(9^2+(4.x)^2=100\). 13.x
C=E: \(8^2+6^2=100.\) 14
D: \(7^2+(7.x)^2=100\) 14.x

D
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If x and y are positive and x^2 + y^2 = 100, then for which of the 25 Apr 2021, 03:31
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Solution:

Observe the options

A- X=10 then y must be 0 (0 is neither positive nor negative)- Eliminate

B-x=9 then y must be √ 19 = b/w 4 and 5 => x+y is around 13 point some value (Consider option for comparison)

C-x=8 then y must be 6 => x +y = 14 (Eliminate b, c and e too because if x = 6 then y must be 8 giving same sum of 14)

Its a PS question and hence same sum will not represent a correct answer option

(option d)

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If x and y are positive and x^2 + y^2 = 100, then for which of the 16 Aug 2023, 08:57
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If x and y are positive and x2+y2=100 then for which of the following is the value of x + y greatest?

Let us take the options one by one,
A. x = 10=>y=0; x+y=10
B. x = 9=>y=(19)^0.5; x+y=13.35
C. x = 8=>y=6; x+y=14
D. x = 7=>y=(51)^0.5; x+y=14.14 Hence Maximum and answer
E. x = 6=>y=8; x+y=14
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If x and y are positive and x^2 + y^2 = 100, then for which of the 20 Oct 2023, 10:31
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this question can be solved as a geometry problem.

x²+y²=10² is a circle with center in (0,0) and radius 45 degrees

we want to maximize k = x+y , which is an line equation

the way to do it is by draw y=k-x and move it by vary k and check where is intercepts the circle so it maximizes k. this will happen when k is such that the line is tangent to the circle.

x=10cos(45°) = 5sqrt(2) ~ 5*1.4 = 7.

the closer option(therefore the option with the bigger k) is D
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If x and y are positive and x^2 + y^2 = 100, then for which of the 22 Nov 2024, 03:47
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