What is the answer to 6 2/7 * 2 1/ 10

Mathematics

2 answers:

mixas84 [53]4 years ago

4 0

Answer:

13.2

Step-by-step explanation:

Grace [21]4 years ago

4 0

Answer: 13 1/5

Step-by-step explanation:

1) We convert the fractions into mixed numbers. That gives you 44/7 * 21/10.

2) We multiply straight across. That gives you 924/70

3) We recalculate them to make it a proper fraction. That would give you the answer.

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In cylindrical coordinates, the equations of the surfaces become

$z = 4 - 4r^2 \\\\ z = (r^2)^2 - 1 = r^4 - 1$

These surfaces intersect on the cylinder of radius 1 with cross sections parallel to the x,y-plane:

$4 - 4r^2 = r^4 - 1 \\\\ \implies r^4 + 4r^2 - 5 = (r-1)(r+1)(r^2+5) = 0 \\\\ \implies r=1$

Then in cylindrical coordinates, the volume of the space bounded by these surfaces is

$\displaystyle \int_0^{2\pi}\int_0^1\int_{r^4-1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^1 \int_{r^4 - 1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr \\\\ = \pi \int_0^1 (4-4r^2)^2 - (r^4-1)^2 \,\mathrm dr \\\\ = \pi \int_0^1 (15-32r^2+18r^4-r^8)\,\mathrm dr = \boxed{\frac{352\pi}{45}}$