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aleksandrvk [35]
3 years ago
6

Explain how to use ordered pairs of points f(x) and g(x) to determine if f(x) and g(x) are inverses of each other.

Mathematics
1 answer:
sashaice [31]3 years ago
7 0
Whatever coordinates you have for f(x). Just switch the x coordinate with the y coordinate and thats the relation between f(x) and g(x) because they are inverses. 

if on f(x) you have (2,4) then on g(x) you would have (4,2). 

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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]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

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




8 0
3 years ago
Describe how the graph of y=|x| and how it is difficult
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Y= to the absolute function of x?
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Step-by-step explanation:

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xz_007 [3.2K]

Answer: \frac{16}{21}

<u>Step-by-Step Explanation:</u>

KCFmeans: Keep, Change, Flip

  • Keep: the first fraction
  • Change: the sign <em>from division to multiplication</em>
  • Flip: the second fraction

  \frac{2}{3} ÷ \frac{7}{8}

= \frac{2}{3} * \frac{8}{7}   <em>KCF is applied here!</em>

= \frac{2(8)}{3(7)}

= \frac{16}{21}



7 0
3 years ago
rachel is frosting the top of two cakes and wants to know which cake will require more frosting. one cake is round with a diamet
siniylev [52]

Answer:

The square cake is larger by 31 in^2

Step-by-step explanation:

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We need to find the radius

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8 = 2r

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A = 3.14 * 4^2

A = 3.14 *16

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The difference is Asquare - A round

81 -50.24

30.76

Which is close to 31 in ^2

7 0
2 years ago
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