The price of a diamond is proportional to the square of its mass, which is measured in carats. A 6 carat diamond was broken into two parts and total price of the two pieces is $\frac{5}{8}$ th of the price of original diamond. The masses (in carat) of two pieces are
The price of a diamond is proportional to the square of its mass, which is measured in carats. A 6 carat diamond was broken into two parts and total price of the two pieces is $\frac{5}{8}$ th of the price of original diamond. The masses (in carat) of two pieces are
A3.5 and 2.5
B5 and 1
C4.5 and 1.5
D3.2 and 2.8
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Correct answer is: 4.5 and 1.5
Explanation:
Actual price of diamond = \( k \times 6^{2}\)
= 36k where k is constant of proportionately.
New price of diamond\(=kx^{2}_{1} + kx^{2}_{2}\)
\(= 36k \times \frac{5}{8} = k \left(x^{2}_{1} + x^{2}_{2}\right)\)
\(= \frac{45}{2} = x^{2}_{1}+x^{2}_{2}\)
\(= 22.5 = x^{2}_{1}+x^{2}_{2}\)
\(= \left(4.5\right)^{2}+ \left(1.5\right)^{2} = x^{2}_{1}+x^{2}_{2}\)
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