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3 years ago

−2y−8+4yminus, 2, y, minus, 8, plus, 4, y

Mathematics

2 answers:

Dovator [93]3 years ago

8 0

Answer:

A and B on Khan Academy are correct.

Step-by-step explanation:

lora16 [44]3 years ago

3 0

Answer:

a number 12

Step-by-step explanation:

duh bro

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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

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

vampirchik [111]

The length is 10
The width is 4
4 + 6 = 10
4 x 10 = 40

6 0

3 years ago

Read 2 more answers

Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad. What percentage of the apples are b

stellarik [79]

I believe the answer is 25% because 6/24 is 1/4 and 1/4= 25%

3 0

3 years ago

Please answer according to the picture.

katen-ka-za [31]

-4 and 2 are the solutions, since that is where they intercept the x axis, and when plugged into the equation, make it true.

6 0

3 years ago

WORTH A WHOLE LOTTA POINTS!

dangina [55]

Where did you get that A and B? I could answer if you were much more precise.

8 0

4 years ago