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26 May 2021, 02:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (02:13) correct
19%
(03:21)
wrong
based on 97
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The function f(x,y) is defined by the equation \(f(x,y)=x^3−5xy^2\). If \(f(10,m)=200\), then what is the value of \(f(20,2m)\)?
A. 200
B. 400
C. 800
D. 1200
E. 1600
A. 200
B. 400
C. 800
D. 1200
E. 1600
26 May 2021, 02:52
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Bunuel
\(f(x,y)=x^3−5xy^2\)
\(f(10,m)=10^3−50m^2\)
\(10^3−50m^2 = 200\)
\(50m^2 = 800\)
\(m = 4\)
\(f(20,2m)\) = \(f(20,8)\)
\(f(20,8)\) = \(20^3 - 5*20*64\) = 8000 - 6400= 1600 (E), IMO
26 May 2021, 04:53
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The Function f(x,y) is defined by the equation \(f(x,y)=x^3−5xy^2\)
\(f(10,m) = 200\) is given.
\(f(10,m)=10^3-5*10*m^2 = 200\)
\(1000-50m^2=200\)
\(50m^2=800\)
\(m^2=16\)
\(m=4. \)
Now, we are asked the value of f(20,2m) which is nothing but f(20,8)
\(f(20,8) = 20^3-5*20*8^2\)
= \(8000-6400\)
= \(1600\).
Hence the correct answer is Option E
\(f(10,m) = 200\) is given.
\(f(10,m)=10^3-5*10*m^2 = 200\)
\(1000-50m^2=200\)
\(50m^2=800\)
\(m^2=16\)
\(m=4. \)
Now, we are asked the value of f(20,2m) which is nothing but f(20,8)
\(f(20,8) = 20^3-5*20*8^2\)
= \(8000-6400\)
= \(1600\).
Hence the correct answer is Option E
