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3 years ago

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.

1 answer:

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]

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,

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

8 0

3 years ago

Describe how the graph of y=|x| and how it is difficult

Ksju [112]

Y= to the absolute function of x?

4 0

3 years ago

Solve each of the quadratic equations. 3x=0.5x^2 0=5x^2-2x+6

Kipish [7]

Answer:

6x=0.10x< 2

Step-by-step explanation:

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3 years ago

How do you divide 2\3 divided by 7\8 using kcf answer

xz_007 [3.2K]

Answer: $\frac{16}{21}$

Step-by-Step Explanation:

KCFmeans: Keep, Change, Flip

Keep: the first fraction

Change: the sign from division to multiplication

Flip: the second fraction

$\frac{2}{3}$ ÷ $\frac{7}{8}$

= $\frac{2}{3} * \frac{8}{7}$ KCF is applied here!

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

= $\frac{16}{21}$

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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:

A round cake has a circular area on top.

We need to find the radius

d= 2r

8 = 2r

r=4

The area of the circle is pi r^2

A = 3.14 * 4^2

A = 3.14 *16

= 50.24

The area of the square cake is

A =s^2

A = 9^2

A = 81

The square cake is larger

The difference is Asquare - A round

81 -50.24

30.76

Which is close to 31 in ^2

7 0

2 years ago