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kogti [31]
3 years ago
11

Which ordered pair (x, y) is the solution to the given system of linear equations?

Mathematics
1 answer:
anygoal [31]3 years ago
4 0

Answer:

(-1,0)

Step-by-step explanation:

3(-1)+3(0)=-3

-3+0=-3

-3=-3

-2(-1)+(0)=2

2+0=2

2=2

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Reika [66]

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}}

7 0
3 years ago
I need help on my math
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5 0
3 years ago
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Jada walks up to a tank of water that can hold up to 10 gallons when it is activated a dream empty water from the tank at a cons
professor190 [17]

Correct question:

Jada walks up to a tank that can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water. At what rate is the amount of water in the tank changing? use a signed number, and include the unit of measurement in your answer.

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Step-by-step explanation:

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After 3 minute,

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4 years ago
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