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3 years ago

Columbia Records unveiled the LP (a vinyl record) in the Waldorf Astoria on June 18, 1948,

Mathematics

1 answer:

snow_tiger [21]3 years ago

8 0

Answer:

Difference in volume between the 10 inch diameter and the 12 inch diameter vinyl records = 3.872 in³

Step-by-step explanation:

Both of the vinyl records will each be modelled as a cylinder

Volume of a cylinder = πr²h

For the 12 inches diameter records.

r = (12/2) = 6 inches

h = thickness = 0.112 inches

Volume = π × (6²) × 0.112 = 12.672 in³

For the 10 inches diameter records

r = (10/2) = 5 inches

h = thickness = 0.112 inches

Volume = π × (5²) × 0.112 = 8.8 in³

Difference in volume between the two vinyl records = 12.672 - 8.8 = 3.872 in³

Hope this Helps!!!

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Find the value of n, correct to 4 significant figures.

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Answer:

6.708

Step-by-step explanation:

Y varies directly as the square of x (Given)

$\implies y\:\alpha \:x^2$ ......(1)

Y varies inversely as the square root of z (Given)
$\implies y\:\alpha\: \frac{1}{\sqrt z}$ ......(2)

Combining (1) & (2), we find:

$y\:\alpha \:\frac{x^2}{\sqrt z}$

$\implies y=\frac{kx^2}{\sqrt z}$ (Where k is constant of proportionality).....(3)

Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.

$2=\frac{k(3)^2}{\sqrt 4}$

$\implies 2=\frac{k(9)}{2}$

$\implies k =\frac{4}{9}$

Plugging the value of k in (3), we find:

$y=\frac{4x^2}{9\sqrt z}$ ....(4)

Next, in equation (4), plug y = 5, x = n and z = 16 and obtain the value of n by solving it.

$5=\frac{4(n)^2}{9\sqrt {16}}$

$\implies 5=\frac{4(n)^2}{9(4)}$

$\implies 5=\frac{(n)^2}{9}$

$\implies 5(9)=(n)^2$

$\implies 45=(n)^2$

$\implies n=\sqrt{45}$

$\implies n=6.70820393$

$\implies n\approx 6.708$

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