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c=(4b)/(root(3)(d))
The formula gives the capsize screening value, 
c, for a sailboat with a beam 
b feet long and that displaces 
d pounds of water. Higher capsize screening values suggest that a sailboat is more stable. Which of the following equations correctly gives the displacement in terms of the capsize screening value and the beam length?
Choose 1 answer:
(A) 
d=((4b)^(3))/(c)
(B) 
d=(c^(3))/(4b)
(c) 
d=((4b)/(c))^(3)
(D) 
d=((c)/(4b))^(3)

c=4bd3 c=\frac{4 b}{\sqrt[3]{d}} \newlineThe formula gives the capsize screening value, c c , for a sailboat with a beam b b feet long and that displaces d d pounds of water. Higher capsize screening values suggest that a sailboat is more stable. Which of the following equations correctly gives the displacement in terms of the capsize screening value and the beam length?\newlineChoose 11 answer:\newline(A) d=(4b)3c d=\frac{(4 b)^{3}}{c} \newline(B) d=c34b d=\frac{c^{3}}{4 b} \newline(C) d=(4bc)3 d=\left(\frac{4 b}{c}\right)^{3} \newline(D) d=(c4b)3 d=\left(\frac{c}{4 b}\right)^{3}

Full solution

Q. c=4bd3 c=\frac{4 b}{\sqrt[3]{d}} \newlineThe formula gives the capsize screening value, c c , for a sailboat with a beam b b feet long and that displaces d d pounds of water. Higher capsize screening values suggest that a sailboat is more stable. Which of the following equations correctly gives the displacement in terms of the capsize screening value and the beam length?\newlineChoose 11 answer:\newline(A) d=(4b)3c d=\frac{(4 b)^{3}}{c} \newline(B) d=c34b d=\frac{c^{3}}{4 b} \newline(C) d=(4bc)3 d=\left(\frac{4 b}{c}\right)^{3} \newline(D) d=(c4b)3 d=\left(\frac{c}{4 b}\right)^{3}
  1. Given formula isolation: The original formula is given by c=4bd3c = \frac{4b}{\sqrt[3]{d}}. We want to solve for dd in terms of cc and bb.
  2. Multiplication and isolation: First, we isolate the term with dd on one side by multiplying both sides of the equation by (d3)(\sqrt[3]{d}). This gives us c(d3)=4bc \cdot (\sqrt[3]{d}) = 4b.
  3. Division by cc: Next, we divide both sides of the equation by cc to get d3\sqrt[3]{d} = 4bc\frac{4b}{c}.
  4. Eliminating cube root: To solve for dd, we need to get rid of the cube root. We do this by raising both sides of the equation to the power of 33, which gives us d=(4bc)3d = \left(\frac{4b}{c}\right)^3.
  5. Comparison with options: Now we compare the result with the given options. The correct equation that matches our result is (C) d=(4bc)3d = \left(\frac{4b}{c}\right)^3.

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