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11 Feb 2022, 04:15
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C
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Question Stats:
87% (01:23) correct
13%
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based on 194
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For all positive numbers x, Δx is defined as the cube root of x, and ∇x is defined as the square root of x. If ∇(Δk)=m^2 , then k =
A. m^(12/5)
B. m^6
C. m^12
D. m^36
E. m^64
A. m^(12/5)
B. m^6
C. m^12
D. m^36
E. m^64
kungfury42
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11 Feb 2022, 23:33
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Given ∇(Δk)=m^2
Using ∇ as square root function, and Δ as cube root function, we get
(Square root of (Cube root of K)) = M²
Squaring both sides
(Cube root of K) = M⁴
Cubing both sides
K = M¹²
Hence, our answer is option C.
Posted from my mobile device
Using ∇ as square root function, and Δ as cube root function, we get
(Square root of (Cube root of K)) = M²
Squaring both sides
(Cube root of K) = M⁴
Cubing both sides
K = M¹²
Hence, our answer is option C.
Posted from my mobile device
08 Aug 2022, 00:47
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Given that Δx = cube root of x, and ∇x = square root of x and ∇(Δk) = \(m^2\) and we need to find the value of k
Δx = cube root of x = \(x^{(\frac{1}{3})}\) and
∇x = square root of x = \(x^{(\frac{1}{2})}\)
Lets start by finding the value of Δk
To find Δk we need to compare what is after Δ in Δk and Δx
=> We need to substitute x with k in Δx = \(x^{(\frac{1}{3})}\) to get the value of Δk
=> Δk = \(k^{(\frac{1}{3})}\)
=> ∇(Δk) = ∇(\(k^{(\frac{1}{3})}\))
Similarly, ∇(\(k^{(\frac{1}{3})}\)) = \(k^{(\frac{1}{3})})^{(\frac{1}{2})}\) = \((k^{(\frac{1}{3}) * (\frac{1}{2})}\) = \(k^{(\frac{1}{6})}\)
=> ∇(Δk) = \(k^{(\frac{1}{6})}\) = \(m^2\) (given)
Raising both the sides to the power of 6 we get
\(( k^{(\frac{1}{6})}) ^ 6\) = \((m^2)^6\) = \((m^{2*6})\)
=> k = \(m^{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
Δx = cube root of x = \(x^{(\frac{1}{3})}\) and
∇x = square root of x = \(x^{(\frac{1}{2})}\)
Lets start by finding the value of Δk
To find Δk we need to compare what is after Δ in Δk and Δx
=> We need to substitute x with k in Δx = \(x^{(\frac{1}{3})}\) to get the value of Δk
=> Δk = \(k^{(\frac{1}{3})}\)
=> ∇(Δk) = ∇(\(k^{(\frac{1}{3})}\))
Similarly, ∇(\(k^{(\frac{1}{3})}\)) = \(k^{(\frac{1}{3})})^{(\frac{1}{2})}\) = \((k^{(\frac{1}{3}) * (\frac{1}{2})}\) = \(k^{(\frac{1}{6})}\)
=> ∇(Δk) = \(k^{(\frac{1}{6})}\) = \(m^2\) (given)
Raising both the sides to the power of 6 we get
\(( k^{(\frac{1}{6})}) ^ 6\) = \((m^2)^6\) = \((m^{2*6})\)
=> k = \(m^{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
