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3 years ago

15

What’s the area for 16 and 8 3/4

1 answer:

Alborosie3 years ago

6 0

Answer:

Area = 140

16 x 8.75 = 140

Step-by-step explanation:

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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

3 years ago

You are watching a game of poker on ESPN with your friends. You are trying to figure out the value of each colored chip that is

klasskru [66]

9514 1404 393

Answer:

N = 5; only one rate is possible

Step-by-step explanation:

The values of the sets of chips are ...

12 +9N +8N^2 +4N^3

and

2 +N +N^3 +N^4

We want to find N such that the difference in value is zero:

N^4 -3N^3 -8N^2 -8N -10 = 0

A graphing calculator can show us the roots. There is only one positive real root to this equation: N = 5.

The exchange rate N is 5. Only one rate is possible.

3 0

3 years ago

Point B has coordinates (3,1). The x-coordinate of point A is negative 1. The distance between point A and point B is 5 unit

mina [271]

Answer:

Given in quesion:Point B (3,1) and point A is -1. Distance between A and B is 5 units.

Using distance formula for AB we obtain,

AB^2=(x2-x1)^2 + (y2-y1)^2

5^2=(3+1)^2 + (1-y)^2

25-16=(1-y)^2

9=(1-y)^2

1-y=3

y= -2

Therefore the possible co-ordinates of A are(-1,-2).This is your required answer.

3 0

3 years ago

Can someone help? Thanks a lot!!

vitfil [10]

6x+42+18x-6=180
24x+36=180
180-36=24x=144
X=6

8 0

3 years ago

Read 2 more answers

How do i solve a rubic cube?

Gemiola [76]

Answer:

Step-by-step explanation:

There are solutions on the internet. Just google it. We are not allowed to give you a link, but if you put in "solutions to rubic's cube", the first one that comes up is pretty good.

5 0

4 years ago