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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Answers

$0\le\theta\le\dfrac\pi2$ 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

answered: Guest

no i do not : ( what is it?

answered: Guest

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

Bwill make the inequalities y < 2x + 1 and y> -x- 2 true. o a. region b o b. region c o c. r

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