Mathematics, 20.09.2019 06:00 naseersaad

Cylindrical coordinates? hi,
i am having problems with a homework question,
i am asked to sketch the solid by the given inequalities.
0 < = theta < = pi/2 and r < = z < = 2
how do i find r?
if possible guide me to the answer instead of giving it to me. i need to know this stuff.
in advance for any .

Answers: 1

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$0\le\theta\le\dfrac\pi2$ tells you that $x\ge0$ and $y\ge0$ .

Recalling that in cylindrical coordinates, $r^2=x^2+y^2\implies r=\sqrt{x^2+y^2}$ , we then know that $0\le\sqrt{x^2+y^2}\le z$ , and so we're confined to the first octant (where each of x,y,z

are non-negative).

The upper limit of $z\le2$ tells us that the region is bounded above by the plane z=2

, which is parallel to the

plane.

Meanwhile, the lower limit of $z=r=\sqrt{x^2+y^2}$ can be visualized by first squaring both sides:

$z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2$

If you're not already familiar with what this equation represents, we can approach it piecemeal. At one extreme, when x=y=0

, we have $z=\sqrt{0^2+0^2}=0$ , so the region has a "vertex" at the origin.

When z=2

, we have the Cartesian equation 4=x^2+y^2

, which corresponds to a circle of radius 2. Similarly, if we consider values of

between 0 and 2, we end up with circles of increasing radii. Stacking these circles onto one another, we get a cone.

More specifically, the region is the part of the cone between the

plane and the plane z=2

restricted to the first octant.

(Image of region attached)
Cylindrical coordinates? hi, i am having problems with a homework question, i am asked to sketch th

Cylindrical coordinates? hi, i am having problems with a homework question, i am asked to sketch th

Answer from: Quest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

Answer from: Quest

step-by-step explanation:

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Cylindrical coordinates? hi,
i am having problems with a homework question,
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