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2 years ago

Describe the location of the given points in relation to the origin.

Mathematics

1 answer:

Butoxors [25]2 years ago

7 0

Answer:

$(2,-1,-3)\ \ \rightarrow \ \ \text{(2 forward, 1 left, 3 down)}$
$(-4,-3,2)\ \ \rightarrow \ \ \text{(4 back, 3 left, 2 up)}$

Step-by-step explanation:

The given two points are,

$(2,-1,-3)$
$(-4,-3,2)$

Relation of the point to the origin means how much far and in which direction the point is located from the origin (0, 0, 0)

From the attachment it is evident the the point $(2,-1,-3)$ is located 2 forward, 1 left, 3 down from the origin. And point $(-4,-3,2)$ is located 4 back, 3 left, 2 up.

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

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2 years ago

I need help I will give brainliest

Klio2033 [76]

Answer:

4.4 × 10 ^− 6

Step-by-step explanation:

Brainliest please :)?

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olasank [31]

Answer:

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Step-by-step explanation:

So since the rule is (4x, 4y) all you have to do is multiply. -1 x 4 = -4 and 1 x 4 = 4.

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2 years ago

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MrRissso [65]

Answer:

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Step-by-step explanation:

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2 years ago

Convert 2 1/5 to an improper fraction.

DochEvi [55]

Answer: 11/5

Step-by-step explanation:

you would do (2) times (5) to get 10.

then you'd add 1+10 to get 11.

write this new number as the numerator... 11/5.

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2 years ago

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