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2 years ago

I need help on problem 2 and 3.I want to know how to do it step by step.

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

3 0

I think u have to multiply the radius and diameter. umm if i am correct the ans is 34396.95. or i think u have to divide. if u divide, the ans is 28.31. if i am incorrect let me know pls. and sry i cant help with no.3. thats difficult.
hope my ans is right. if ans is correct pls mark as brainliest ans.

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The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the portions of the x-axis that jo

oksano4ka [1.4K]

Answer:

Required center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

Step-by-step explanation:

Given semcircles are,

$y=\sqrt{1-x^2}, y=\sqrt{16-x^2}$ whose radious are 1 and 4 respectively.

To find center of mass, $(\bar{x},\bar{y})$ , let density at any point is $\rho$ and distance from the origin is r be such that,

$\rho=\frac{k}{r}$ where k is a constant.

Mass of the lamina=m= $\int\int_{D}\rho dA$ where A is the total region and D is curves.

then,

$m=\int\int_{D}\rho dA=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}rdrd\theta=k\int_{}^{}(4-1)d\theta=3\pi k$

Now, x-coordinate of center of mass is $\bar{y}=\frac{M_x}{m}$ . in polar coordinate $y=r\sin\theta$

$\therefore M_x=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\sin\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\sin\thetadrd\theta$

$=3k\int_{0}^{\pi}\sin\theta d\theta$

$=3k\big[-\cos\theta\big]_{0}^{\pi}$

$=3k\big[-\cos\pi+\cos 0\big]$

$=6k$

Then, $\bar{y}=\frac{M_x}{m}=\frac{2}{\pi}$

y-coordinate of center of mass is $\bar{x}=\frac{M_y}{m}$ . in polar coordinate $x=r\cos\theta$

$\therefore M_y=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\cos\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\cos\theta drd\theta$

$=3k\int_{0}^{\pi}\cos\theta d\theta$

$=3k\big[\sin\theta\big]_{0}^{\pi}$

$=3k\big[\sin\pi-\sin 0\big]$

$=0$

Then, $\bar{x}=\frac{M_y}{m}=0$

Hence center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

3 0

2 years ago

Which exponential function is represented by the values in the table?

astraxan [27]

ANSWER

The exponential function is
$f(x) = 3( {2}^{x} )$

EXPLANATION

Let the exponential function that is represented by the values in the table be of the form,

$f(x) = a( {b}^{x} )$

The points in the table must satisfy this exponential function.

We substitute the point,

$(0,3)$

to get,

$3 = a( {b}^{0} )$

This implies that,

$3 = a( 1 )$

$3 = a$

Our function now becomes,

$f(x) = 3( {b}^{x} )$

We gain, plug in another point yo find the value of b too.

Let us substitute
$(1,6)$

This implies that,

$6= 3( {b}^{1} )$

We divide through by 3 to obtain,

$2 = b$

Therefore the function is,

$f(x) = 3( {2}^{x} )$

The correct answer is A.

3 0

2 years ago

Read 2 more answers

Choose the correct simplification of the expression c2 ⋅ c9.

sergejj [24]

3 0

2 years ago

Read 2 more answers

On a particular production line, the likelihood that a light bulb is defective is 10%. seven light bulbs are randomly selected.

amid [387]

Answer:

0.9995

Step-by-step explanation:

10% = 0.10

1 - 0.10 = 0.9

n = number of light bulbs = 7

we calculate this using binomial distribution.

p(x) = nCx × p^x(1-p)^n-x

our question says at most 4 is defective

= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)

= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026

= 0.9995

we have 0.9995 probability that at most 4 light bulbs are defective.

6 0

2 years ago

A snail travels 3 1/3 ft every hour. How far does the snail travel in 2 1/2 hours? Express your answer in simplest form. A. 6 1/

STALIN [3.7K]

Answer: 8 1/3 I believe

Step-by-step explanation:

4 0

2 years ago