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2 years ago

I’ll give brainliest HELO ASAP PLZ!!

Mathematics

2 answers:

Helen [10]2 years ago

5 0

Answer:

Step-by-step explanation:

Yakvenalex [24]2 years ago

5 0

Answer is definitely a

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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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3 years ago

The two polygons are similar. Find the measure of angle U. 120° 185°

mash [69]

It’s 80 for sure Ik this one

7 0

3 years ago

Assume that 33.4% of people have sleepwalked. Assume that in a random sample of 1459 adults, 526 have sleepwalked.

lutik1710 [3]

Answer:

Step-by-step explanation:

Given that 33.4% of people have sleepwalked.

Sample size n =1459

Sample favourable persons = 526

Sample proportion p = $\frac{526}{1459} \\=0.361$

Sample proportion p is normal for large samples with mean = 0.334 and

std error = $\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.334(1-0.334)}{1459} } \\=0.0123$

a) P(526 or more of the 1459 adults have sleepwalked.)

$=P(p\geq 0.361)\\=P(Z\geq \frac{0.361-0.334}{0.0123} \\=P(Z\geq 2.20)\\=0.5-0.4861\\=0.0139$

b) Yes, because hardly 1.4% is the probability

c) 33.4 is very less compared to the average. Either sample should be improved representing the population or population mean should be increased accordingly.

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3 years ago

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gizmo_the_mogwai [7]

The next number should be 297.

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A dog is leashed to a point in the center of a large yard, so the area the dog is able to explore is circular. The leash is 20 f

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Which is almost equal to 1256 feet.

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